INVESTIGATION INTO THE ENTERPRISE MISSION'S PROPOSITION THAT THE 19.5 AND 33.0 DEGREE STAR ALIGNMENTS CONSTITUTE A PATTERN
by
Mary Anne Weaver
Copyright (c) 1999 by Delphi Technologies
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Posted July 27, 2003
AUTHOR'S NOTE
THERE ARE ERRORS IN THIS STATISTICS PAPER THAT I HAVE NOT HAD THE CHANCE TO CORRECT. These errors do undermine the conclusions of this paper. The extent to which the errors in this paper undermine its conclusions is not currently known, and can only be determined by rewriting this paper with the corrections in place. As I do not currently have time for that, I am posting this addendum to keep readers informed.
On
It should be acknowledged that some experts believe that there are more errors in my paper, which is also possible, as I am not a statistics expert. I did my best in 1999, which wasn't enough to ensure my paper turned out error-free; so indeed -- there may be more errors that I am not aware of currently.
The text of my 1999 statistics paper follows.
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For a number of years now, researcher and former NASA consultant Richard C. Hoagland of the Enterprise Mission, has observed what he has identified as a "pattern" in star positions at the time of NASA launches and/or landings. He published his discovery a few years ago as an article entitled "Kennedy's Grand NASA Plan", and has since written many more articles and performed extensive research into this topic. Later on, Mike Bara, an Aerospace design engineer with many years experience in his field, also joined the research effort into this "stellar alignment phenomenon" and has assisted Richard Hoagland in investigating its attributes and the frequency of its occurrence.
Both Richard Hoagland and Michael Bara note that specific stars are found at particular elevations above the horizon, namely 19.5 and 33.0 degrees but also directly on the horizon and meridian, at the precise moment of a NASA launch or landing. Since 1996, Michael Bara and Richard Hoagland have done considerable research into the "star alignment" theory and posted a large amount of data. Also since that time and based on copious research into this topic, they have proposed a number of theories to account for this phenomenon.
The data posted by The Enterprise Mission was interesting, and the many interconnections such as symbology of patches, landing sites (at 19.5 degrees), and star alignments intrigued me. Still, just that data posted on the Enterprise Mission site was not enough to numerically deduce that there is a pattern to NASA launches. That's because, when dealing with a group of events that one thinks appear more often than random chance would allow, it's important to first define how often "random chance" can produce these alignments or events. And once that has been defined, then it's important to analyze all the events in a particular grouping, to see just how often within this grouping that the alignment events occur. Though their data is impressive, there are quite a few NASA missions, launches and so on, that Richard Hoagland and Mike Bara did not post data on. Since I needed to analyze all the events within a particular grouping, the first task in this investigation was to research all the launch times, dates and locations for a particular set of NASA programs, and look up the star positions for those launches.
I chose to analyze all the NASA programs which were, at one time or another, involved in the preparations to send men to the Moon and return them safely to Earth. I did this because of the high profile of the Apollo missions and importance of the Apollo program historically. I therefore began with an analysis of NASA launches leading up to and including Apollo. This includes the "preparatory" missions, which for the purposes of this analysis were limited to: Ranger, Surveyor, Pioneer, Lunar Orbiter, Mercury, Gemini, and of course, Apollo. This came to a total of 82 launches, spread out over the years 1958 to 1978. Why 1978, when Apollo ended in 1972? Because I treated each program that had something to do with the preparation for lunar landings, as a single unit. The Pioneer program lasted until 1978, beyond the Apollo "preparation" stage, but the Pioneer program itself was part of the effort to send men to the Moon, so all the launches in the Pioneer program are included in this set of 82.
Spacecraft launch times, dates and locations for Apollo landings were obtained from the book To a Rocky Moon (Don E. Wilhelms, University of Arizona press, 1993). All other spacecraft launch times and dates were obtained from the National Space Science Data Center (NSSDC) in Greenbelt, Maryland. Star locations for those dates and times were obtained from the program RedShift. This program was selected because it uses NASA data and observations to ascertain star positions at any given date and time, and because it generates star position data for locations on other bodies in the solar system, such as the surface of the Moon. When gathering data for analysis in this paper, the planned Apollo lunar landing sites were used to measure star positions from, not the actual sites. Since it has not been established whether the actual sites were more important than the planned ones, I chose the planned ones for simplicity's sake, and to keep the data consistent. It did seem to me that the "planned" sites may have been the more important, since the "original plan" was to send the spacecraft to those exact coordinates.
The next challenge faced by this investigation was coming up with a correct model for the probability of star alignments. After researching stellar motion (from the viewpoint of a planet or Moon's surface) with RedShift and via equations for same, I came up with a model which could approximate probabilities of finding a 19.5 or 33.0 degree alignment to a sufficient level of precision. I tested this model a number of times and in a number of ways, some of which I present in this paper. The model tested out correct.
This paper is only a mathematical exploration of the theory that specific star alignments observed by Enterprise Mission represent a pattern. If the numbers are supportive of the fact that this is a pattern, in my opinion then this subject should be investigated further to determine more about why it is occurring. It is beyond the scope of this paper to explore why the pattern is happening; only to report whether or not there is one.
DEFINITION OF A PATTERN
Where "A" is an event for which I wish to find the odds, then
outcomes favorable to event A Probability of A = ------------------------------- total # of outcomes
Finding the "probability" of "A" does not in itself prove there is a pattern. Suppose I travel to Las Vegas and play the roulette wheel. Further, suppose this roulette wheel has only 36 slots, all numbered from 1 to 36 (in real roulette, there are 38 slots total -- 36 slots are numbered 1 to 36, and there are two "zero" slots). In this case, the probability of event "A," where "A" is the number I placed my bet on, is 1 in 36. There is no pattern involved if I get the same number more than once, even if I've only played a few times -- because random chance allows for hitting a number more than once; it just doesn't happen very often.
That's why one must use due caution in calling something a "pattern." It must occur regularly or beat the odds on a regular basis. It also adds extra weight to the argument that something is a pattern, if there are a set number of events to analyze, and those events occur in a specified time frame.
For example, there are a set number of roulette spins I can make in fifteen minutes. Suppose I make 8 spins, and out of those 8 the ball lands on the same number all 8 times. In roulette, the odds of a ball landing on the same number 8 times in a row are 2.82 trillion to 1! In my short stretch of time (15 minutes), such odds are ridiculous and imply it's likely that the wheel is "rigged." However, if a ball lands on the same number 8 times in five days of a casino's operation, the odds would look quite different. And if I didn't know how many times the wheel was spun during that time, I could not discern anything about a pattern.
In order to explain how I would detect a "pattern," I will proceed to a simpler example -- a coin toss. I'll return to the roulette wheel later on.
Suppose I enter into a coin toss game with a friend, and I want to figure out the odds of winning. If the coin is perfectly balanced, then the odds should be 1 to 1 for tossing "heads" -- in other words, I have equal chances of tossing "heads" or "tails" on any given toss.
Next, suppose I want to compute the probability of tossing "heads". Probability is given by:
Probability = Outcomes Favorable/Total Outcomes
In a coin toss, there are only two outcomes -- Heads or Tails -- and I'm just interested in computing the probability that the coin I toss will come up "heads". Then,
Probability = Outcomes Favorable/Total Outcomes
or,
Probability(Heads) = 1/2 = 0.500.
But how can I be sure the model is right? That's straightforward, and in order to do that, I employ the Law of Large Numbers.
The Law of Large Numbers
It is a statistical fact that, the more observations I make of an event, the closer I can come to correctly defining the probability of that event's occurrence. Thus, the Law of Large Numbers states that I should draw closer and closer to the actual probability of an event with each observation I make.
So, to determine whether the formula for predicting odds is correct, I toss the coin as many times as I can in order to find the true probability. In this case, I did 100 sample "throws" with a coin-toss simulation program, and plotted the results. Refer to Fig. 1, below: Note how the graph closes in on the value 0.500, the actual probability that I computed using the "Outcomes Favorable/Total Outcomes" equation.
Fig. 1: Perfectly Weighted Coin
Number of Heads Tossed plotted against Total Tosses
To further illustrate the importance of the Law of Large Numbers, and how this Law works, refer to Fig. 2, below. It is the same as Fig. 1, except that I highlighted toss # 13.
Fig. 2: Highlight of Toss 13. Note its probability falls at 0.63 on the graph.
If I were to stop tossing coins at toss # 13, and I didn't know what the correct odds were supposed to be for a coin toss, I would incorrectly deduce that the probability of tossing heads is 0.63, or about 1.6 to 1, "for" tossing heads. Obviously, this isn't right! So, when calculating probabilities, it is important to 1) have the correct model for the odds, and 2) take enough samples to be able to make a correct estimate of the situation. Notice that, by the time I reach 80 or more samples, the probability has very closely approached what it should be -- 0.5, or 1 to 1 odds.
VARIABILITY OF RANDOM DATA
Even though the Law of Large Numbers does work the way I outlined above, when I am dealing with 100 samples or less, statistical deviations can have an impact on the results.
This is because random data is variable. That means that the above graphs of coin tosses could vary by a certain amount. That's because it's random data, and "random chance" always allows for deviations to occur. High "odds against random chance" merely indicate that it is very unlikely for that amount of deviation to have occurred by random chance. However, unless I know what that amount is or can be, I could make an incorrect assessment as to the "non-random" nature of the samples I take. The way to determine variability is to take as many "100 toss" sample throws as I can, within each 100 throws, see how many times I get "heads." Because I'm dealing with a random situation, there will be times I get 53 heads instead of 50, or 45 heads instead of 50, even though the chances are "50-50" of my tossing heads.
The graph below (Figure 3) illustrates the concept of variability.
Figure 3: Graph of Total Heads Tossed per 100 tosses, plotted against number of occurrences of Heads per 100 tosses.
Notice how 50 tosses per 100 shows up the most, as well as 49, 51, etc. In the case of the coin toss program I developed, I ran the program many times and asked it to list for me the total times "heads" came up, for every 100 tosses. Note how the graph, though rough, looks rather like the traditional "bell-shaped" curve. This simply illustrates the fact that it's more likely to hit "49," "50," and "51" tosses than (for example) 40!
Based on the above graph, I would estimate that a variation in the data of +-5 percent (+- 5 throws) is to be expected.
PATTERN DETECTION
How can patterns or "non-random" occurrences then be separated out from a set of data? The first thing to do is determine, as I did for the "coin" above, what the "random" situation looks like. Then I can test the new situation to see if it fits the "random model."
Suppose I enter a coin-tossing game with a dishonest person who has "weighted" the coin, causing it to come up "heads" 2 times out of 3, giving 2 to 1 odds "for" tossing heads instead of 1 to 1. The odds are expressed as 2 to 1 because odds are expressed as the "number of successes to the number of failures". Probability is expressed differently; i.e. the ratio of the "number of successes"/"total events".
In order to test my theory, I have to take a few samples and see for myself, what the odds turn out to be. I already know what the true random situation is supposed to look like. In order to really test this coin and to be sure it's weighted, I should take a large number of samples. Recall how, in the "balanced coin" example, if I had only progressed to "toss 13" I would have made an incorrect assumption about the probability. I still could have estimated the trend by taking the "average" of the points, but it's far more accurate to use a large number of sample "tosses" in order to truly establish that the coin is weighted.
Again, using a coin-toss simulation program, I weighted the "coin" as described above and plotted the results in Fig. 4.
Fig. 4: Plot of Weighted Coin, weighted to produce 2 to 1 occurrence of heads
Notice how the graph closes in on the correct value for this "weighted" coin, which is 2/3 or 0.67. (Recall: Heads occur two times out of three in this example.) Note also that the data points all cluster in on a line, and that the line does not waver very far from the 0.67 value. It does not drop down to the 0.500 value, for example, but instead holds its position at 0.67. This will be important to remember later.
What can I deduce from this? First of all, that the coin is weighted, and that it's not behaving like a perfectly balanced coin would. It is very unlikely, given the behavior of this graph, that the coin would not be weighted. How do I know this?
Well, for one thing I know that the variation in the data is only likely to be about +-5 throws; +-10 is unlikely but possible. Also, I know the odds against a coin that is NOT weighted, displaying a curve like that one that conforms to 0.67 random value instead of a 0.5 random value, would be 2,182 to 1. Therefore, I know that it's likely the coin is weighted and that I probably cannot use the random model for a coin toss. There was something I was not taking into account; i.e. in this case, that the coin wasn't balanced correctly.
Before I summarize this section, I will outline here how I calculated the odds against a coin displaying the "weighted" coin's behavior. Recall that
Probability = # Favorable Outcomes / Total Outcomes
In probability theory, there is an equation which describes the number of combinations as how many possible ways "r" objects can be selected from a set of "n" objects. In this case, I have 66 occurrences of "heads," out of 100. The total number of "favorable" outcomes in this case is the number of ways I could have "tossed" heads, over the total number of possible combinations. The below equation shall hereafter be called the binomial coefficient equation.
n! 100! Total ways to toss 66 heads = ------------ = ---------- (n - r)!r! 34! 66!
Where n! expresses "n factorial," n! = n * (n-1) * (n-2) * ... *2*1.
Therefore, the probability of this event is expressed as:
Total Combinations = 2 to the 100th power
Therefore,
Probability = Total ways to toss 66 heads / Total combinations = 0.000458 = 2,182 to 1 odds against random chance.
In the above example, the pattern which was generated by the addition of the "weight" to the coin, was detected by three criteria:
Criteria 1: The probability model was confirmed by two things: the equation, which predicted 1/2 = 0.5 for that situation, and my own observations of a perfectly balanced and weighted coin made over a substantial number of observations.
Criteria 2: Variability of the data should have been within +- 5 to +-10 tosses, to have accounted for random deviations in the data. Therefore, I can discount this factor.
Criteria 3: High odds against the occurrence of the graph closing on 0.67 instead of 0.5, plus the fact that the graph does not show a downward trend but rather focuses strongly on 0.67, demonstrate that it's unlikely that the events follow the correct random model.
If there is a pattern to NASA launches, then I would expect the graph to display similar behavior as the "weighted" coin, mentioned above. Such a large deviation as the "weighted coin" exhibited would imply that a pattern exists.The two criteria mentioned above need to be kept in mind in future sections. Next, I will describe the mathematical model I use to accurately predict the probability of these "ritual" star alignments, as set forth by Richard Hoagland and Michael Bara.
THE CONCEPT OF DEVIATION and "ODDS AGAINST CHANCE"
Deviation from a predicted random probability value, such as the deviation from the expected value of 0.5 in the case of the coin toss (above), happens frequently in nature. However, it's very unusual, as witnessed by the "odds against" in the previous example, for the data to converge on a value of 0.67 for 100 sample "throws".
Suppose that, instead of the data converging on 0.66, it converged on 0.34 in a graph that represents the probability of "tossing heads"? Then, in that case, heads only appear approximately 1 out of 3 times, which is too few. The graph (Figure 5) would look something like this (I inverted the previous graph for the "weighted" coin):
Fig. 5: Graph of weighted coin, this time weighted to produce too few heads (more tails).
In this case, the probability of tossing heads would be expressed in the following manner.
As we do for 66 heads, I have:
n! 100! Total ways to toss 34 heads = ------------ = ---------- (n - r)!r! 34! 66!
If I were to compute the odds, using the formula
Total ways to toss 34 heads/Total outcomes
Then, I would get the same probability value, i.e. 0.000458 and odds of 2,182 to 1 against tossing only 34 heads. But, in so doing, I've merely found the probability of tossing only 34 heads. Granted, tossing 34 heads (too few) is just as unlikely as tossing 66 heads (too many). But, I'm only interested in the likelihood of tossing at least 34 heads, not specifically 34 heads. If I'm interested in finding the probability of tossing at least 34 heads, though, then I need to write the equation a different way:
P(at least 34 heads) = P (total outcomes) - P(only 34 heads)
Or,
Total ways to toss 34 heads P(34 heads) = 1.000 - ----------------------------- = 0.999452 2**100
Or, expressed as "odds," this would come to odds of 2,182 to 1 FOR tossing 34 heads.
Therefore, for the purposes of this analysis, deviations which exceed the expected random value for alignments will be treated as "odds against chance," meaning odds against this many alignments occurring by chance. Deviations below the expected random value for alignments will be considered "odds FOR chance," meaning odds for alignments occurring by chance.
DEFINING THE ODDS FOR STAR ALIGNMENTS
In determining the odds for star alignments, one can set them up just like the "roulette wheel" example, mentioned previously. In fact, the two are quite analogous. But before demonstrating that such a model is appropriate to use, I will explain the situation in more detail.
The Earth and the Moon are, even this moment, hurtling through space in a fast orbit around the Sun. They also spin on their axes, the Earth at a rate of 24 hours per complete rotation, and the Moon at 27.322 days per rotation. In this case, one rotation is the time it takes for one star to "appear" to make a complete 360 degree rotation around a planet, and return to its starting point.
Celestial mechanics, especially the equations describing orbits precisely and rate of precession, are quite involved and non-trivial to calculate. Fortunately, there are software products which do this to a high degree of precision, one being RedShift, a highly accurate program which utilizes NASA ephemerides for star positions.
I made use of RedShift to calculate the rate of movement of a star through an angle of interest for any given location on the Earth or the Moon. Once I had these rates of motion, I could calculate how long the stars took in each angle (see Figure 6, below).
Figure 6: Illustration of the concept of apparent stellar motion.
Note how similar this looks to a roulette wheel. Expand this out to three dimensions, and imagine it spinning constantly. This approximates the condition of a planet spinning on its axis. In the course of one planetary (or lunar) day, the star appears to "move" through various angles at a specified rate, spending so much time in each degree. The time spent at each elevation increases or decreases according to the 1/(cosine of the latitude).
Though planets do move around the Sun, their "poles" generally stay fixed for longer periods of time, on one star or another. That's why the "northern star," Polaris, appears to stay in the same place all year long, every year. This is one reason why a planet's spin on its axis can be modelled after a roulette wheel, if we're dealing with short periods of time. For example, Earth and at its current rate of precession (one degree per 72 years), can change a star's position relative to the spin axis of the Earth, but over the course of twenty years (the span of time of this analysis), that star will only have moved 0.28 degrees. This does not affect its apparent rate of motion across the sky by an appreciable amount.
For more details on how certain considerations such as planetary motion and precession can be approximated using this model, click here.
This is why I modelled the star alignments after the "roulette wheel" analogy, and why I think this is feasible. My tests of this hypothesis have so far proven that this roulette wheel model provides a valid and close approximation to the real situation (see the following sections).
LIMITATIONS AND REQUIREMENTS OF THIS MODEL
Definitions: The Hoagland Star Alignment Model
The Hoagland "star alignment model" angle selections are based on tetrahedral geometry; specifically, a tetrahedron inscribed inside of a sphere. The circumscribed tetrahedron is descriptive of a kind of "hyperdimensional physics," which is simply a physics that takes higher (thus unseen!) spatial dimensions into account. I will not get into detail about the theory here, but rather summarize it briefly so that the reader will understand the basis of the related Hoagland/Bara star alignment work.
Hoagland's original "hyperdimensional physics" theory states that "rotation," such as that of a planet on its own axis, creates higher-dimensional dynamic forces inside a planet, which ultimately conform to a specific 3-D geometry; as a result, phenomena appear on the planets' surfaces in accordance with the geometric contact points of that geometry -- two interlaced 3-D tetrahedra inscribed inside a sphere. The lowest order touch points of these circumscribed tetrahedra (beside the poles of rotation) are at approximately 19.5 degrees, North and South latitude. Refer to Figure 7, below.
Figure 7: Two tetrahedra inscribed inside a sphere. Copyright (c) 1998 by The Enterprise Mission. Used with permission.
The actual "touch points" of these tetrahedra are at 19.47 degrees N or S latitude on any particular planetary body, rounded to "19.5 degrees." This is the source of the number 19.5. Next, when one takes the Sine of the tetrahedral angle, the following number results:
Sine (19.4712) = 0.33333...
This turns out to be the vertical "height" of the 19.5 angle within a unit sphere.
Richard Hoagland and Mike Bara utilize the "shortened" version of this, which is the angle 33. However, note how many "3's" there are in the above. Since the source of the Hoagland/Bara "angle 33" and angle "3 deg 30 min" is this "repeating 3's" in the Sine of the tetrahedral angle, that will be a key thing to look for in the data.
The source of the "horizon" and "meridian" alignment emphasis is Egyptian ritual practice; specifically, Egyptian star lore. Stars, to the ancient Egyptians and Sumerians, were quite important and their position in the skies were an integral part of temple layout and design and well as ceremonial applications (sources: Star Names: Their Lore and Meaning by Richard Hinckley Allen, Astrological Origins by Cyril Fagan, and historical texts on ancient Egypt and Sumer). The horizon and meridian had important symbolic values. Stars that rose were considered to be "born," stars at the meridian had reached their "peak," and stars that were setting were considered to be "dying," or about to go into the underworld. This is common knowledge to scholars of these ancient belief systems. The horizon and meridian are, of course, the basic dividing lines for the celestial sphere as well as for terrestrial geography.
Additionally, according to Egyptian belief and mythology, the stars were actually the "abode of the gods," and in many cases, were identified with the gods themselves. The constellation of Orion and Osiris were actually identified with one another, such that the constellation was considered to be Osiris. Also, Sirius was identified with "Isis."
The Hoagland/Bara hypothesis is, then, that these star alignments are symbolic of ancient star lore and hyperdimensional physics geometry. Why such an unlikely combination? No one knows for sure at this point, but if the reader wishes to embark on further explorations of these possible connections (that have been discovered and published by Richard Hoagland, as well as others), I direct them to read the other articles on the Enterprise Mission website.
A RESTRICTED VERSION OF THE HOAGLAND/BARA STAR ALIGNMENT MODEL
Now that I have ascertained the source of the angles in question, I will define a restricted version of the above Hoagland/Bara model, which I will be using in my analysis. This model is not complete because I do not use all the "temple" locations that Richard Hoagland and Mike Bara have used in their work, nor do I use all the celestial objects they do. The Hoagland/Bara temples which I do not use consist of the Mars temples -- the Viking I and II sites, and Cydonia -- as well as the Earth "temple" locations, Phoenix, JPL (Pasadena, California) and Houston. I do use Houston at one point when I am analyzing the Apollo mission events data, but not as a general rule in this analysis.
There are a total of ten "temple" sites. However, it was necessary to simplify this model for ease of numeric analysis, and to get a feel for the situation, so I only used four in this analysis. Because this is a restricted model, I do not "catch" all the alignments (nor would I expect to) that Hoagland and Bara do; nevertheless, I did expect that this "limited" approach would at least determine whether or not the "Egyptologically-important" stars I chose to examine (in the constellations of Canis Major, Orion, and Leo -- Sirius, Mintaka, Alnilam, Alnitak, and Regulus) do appear more times than random chance would allow.
In order for a "ritual" star alignment to occur in my restricted version of the Hoagland/Bara model, the limited criteria listed below must be met.
Celestial Object must be at these Angles:
Zero degrees (either horizon)
19.5 degrees (above or below either horizon)
33.0 degrees (above or below either horizon)
Meridian (highest or lowest point a star can reach in the sky)
Other angles (such as 3 deg 30 min) which are symbolic of the numbers "33" or "19.5"
The Enterprise Mission lists many celestial bodies and stars that are used in its model, but for the purposes of this analysis, and to keep it simple, I restricted myself to specific celestial objects; i.e. in this case the stars of most importance to the ancient Egyptians.
Stars used in this simplified model:
Sirius (brightest star in Canis Major)
Alnitak (Orion belt star)
Alnilam (Orion belt star)
Mintaka (Orion belt star)
Regulus (brightest star in Leo)
Temple Locations from which stars are observed:
Earth:
Giza, Egypt
Moon:
Planned Apollo 11 landing site
Planned Apollo 12 landing site
Planned Apollo 13/14 landing site
Though it is not a "temple", Cape Canaveral, Florida, USA, is also a location from which stars are observed in this analysis; but only for the launch data. This is because, in the Hoagland/Bara model, valid star observation sites consist of "temple" locations and the site at which the event takes place. In the case of launches, Cape Canaveral is used because it is the site where the actual launch event takes place.
As previously noted, the above locations represent only four (not all ten) of the Hoagland/Bara "temple" sites, from which these alignments are observed.
Below are some examples (Figures 8 - 12) of what these configurations look like in the sky over the Earth or Moon. All of these pictures were obtained from the program RedShift, and represent the sky at the particular "temple" of interest, at the date and time I specify.
Figure 8: The sky over the Apollo 11 planned landing site during the lauch of the Mercury Program's Atlas 7. This is a good example of a 19.5 alignment, and the constellation of Orion. Note, altitude is measured for the belt star Mintaka, not for the constellation as a whole.
Figure 9: The above picture depicts the sky over Giza, Egypt, during the launch of Pioneer 5. Of course, this is an example of the Orion constellation, with the Orion belt star Alnitak at 33 degrees altitude.
Figure 10: The above depicts the sky over the planned Apollo 12 landing site on the Moon, at the time of the launch of Apollo 15. This is an example of the constellation Canis Major, and the star Sirius, which here appears 33 degrees below the lunar horizon.
Figure 11: The sky over Giza during the lauch of SA-6, an unmanned Apollo test launch in 1964. This is a good example of a horizon or zero degrees altitude alignment.
Figure 12: The sky over the Apollo 12 planned landing site during the lauch of the Mercury Program's Atlas 7. This is a good example of a meridian alignment. Note how Sirius and the meridian line intersect, indicating Sirius has precisely reached its highest elevation.
Limitations
One thing that must be kept in mind is, if I'm at the Moon's poles or near them, or the Earth's poles for that matter, certain stars of interest to the Hoagland/Bara "ritual star alignments" model won't even rise to 33 degrees elevation in the course of one planetary "day". Fortunately, the sites that are claimed by the Enterprise Mission as "ritual sites" where many of these alignments occur, are all near the same latitudes on each body, and it is the latitude which determines the length of time a star stays at a particular elevation. In the Moon's case, the sites are near the equator; on the Earth, both sites (Cape Canaveral and Giza, Egypt) are both near 30 degrees North latitude. The first portion of this analysis will just concern itself with the Earth and Moon.
Also, since location on a planet's surface does make a difference in star transit times, one must be careful not to assume the odds will be the same at every location. Sensitivity to locale is a limitation of this restricted model. Again, fortunately the locations used in this analysis are close enough to the equator and to each other, latitudinally, that the odds can be closely approximated and do not vary by much at each site.
MATHEMATICAL DEFINITION OF THE "ROULETTE WHEEL" PLANETARY ODDS MODEL
Before I get into how to calculate the odds for a number of locations, I'll start with how to calculate the odds for one location. You're an observer, standing at location X. For location X, on any given planetary day, you want to calculate the probability of event "A" -- in this case, the likelihood of a star alignment at the "ritual" degrees of horizon, 19.5, 33.0, and meridian.
Recall our basic probability equation,
outcomes favorable to event A Probability of A = ------------------------------- total # of outcomes
It is straightforward to calculate "Outcomes Favorable":
Outcomes Favorable = (Time Sirius spends at 0 deg. East) + (Time Sirius spends at +19.5 deg. East) + (Time Sirius spends at -19.5 deg. East) + (Time Sirius spends at +33.0 deg. East) + (Time Sirius spends at -33.0 deg. East) + (Time Sirius spends at Nadir) + (Time Sirius spends at 0 deg. West) + (Time Sirius spends at +19.5 deg. West) + (Time Sirius spends at -19.5 deg. West) + (Time Sirius spends at +33.0 deg. West) + (Time Sirius spends at -33.0 deg. West) + (Time Sirius spends at Meridian) + (Time Mintaka spends at 0 deg. East) + (Time Mintaka spends at +19.5 deg. East) + (Time Mintaka spends at -19.5 deg. East) + (Time Mintaka spends at +33.0 deg. East) + (Time Mintaka spends at -33.0 deg. East) + (Time Mintaka spends at Nadir) + (Time Mintaka spends at 0 deg. West) + (Time Mintaka spends at +19.5 deg. West) + (Time Mintaka spends at -19.5 deg. West) + (Time Mintaka spends at +33.0 deg. West) + (Time Mintaka spends at -33.0 deg. West) + (Time Mintaka spends at Meridian) + (Time Alnilam spends at 0 deg. East) + (Time Alnilam spends at +19.5 deg. East) + (Time Alnilam spends at -19.5 deg. East) + (Time Alnilam spends at +33.0 deg. East) + (Time Alnilam spends at -33.0 deg. East) + (Time Alnilam spends at Nadir) + (Time Alnilam spends at 0 deg. West) + (Time Alnilam spends at +19.5 deg. West) + (Time Alnilam spends at -19.5 deg. West) + (Time Alnilam spends at +33.0 deg. West) + (Time Alnilam spends at -33.0 deg. West) + (Time Alnilam spends at Meridian) + (Time Alnitak spends at 0 deg. East) + (Time Alnitak spends at +19.5 deg. East) + (Time Alnitak spends at -19.5 deg. East) + (Time Alnitak spends at +33.0 deg. East) + (Time Alnitak spends at -33.0 deg. East) + (Time Alnitak spends at Nadir) + (Time Alnitak spends at 0 deg. West) + (Time Alnitak spends at +19.5 deg. West) + (Time Alnitak spends at -19.5 deg. West) + (Time Alnitak spends at +33.0 deg. West) + (Time Alnitak spends at -33.0 deg. West) + (Time Alnitak spends at Meridian) + (Time Regulus spends at 0 deg. East) + (Time Regulus spends at +19.5 deg. East) + (Time Regulus spends at -19.5 deg. East) + (Time Regulus spends at +33.0 deg. East) + (Time Regulus spends at -33.0 deg. East) + (Time Regulus spends at Nadir) + (Time Regulus spends at 0 deg. West) + (Time Regulus spends at +19.5 deg. West) + (Time Regulus spends at -19.5 deg. West) + (Time Regulus spends at +33.0 deg. West) + (Time Regulus spends at -33.0 deg. West) + (Time Regulus spends at Meridian)
Then,
Sum of: all times that all stars of interest spend at all angles of interest Probability = ------------------------------------------------------- Total planetary rotation period (one "day")
This equation adequately expresses the chances that when, on any given "day" of the planet you're standing on, you'll look up into the sky and see one of the specified stars at the angle of interest.
But, the Hoagland/Bara star alignment theory requires more than one location be used at any one time (on the Earth and Moon), not just one. This "roulette wheel" model can allow for that. It does this by assigning each angle in this restricted Hoagland/Bara star ritual model, a slot. The slot is made "bigger" or "smaller" by the amount of error I'm willing to accept; i.e. +-0.25 degrees per angle. The width of the Moon is 0.5 degrees, therefore, historically, there is a precedent for choosing a window of 0.5 degrees (+-0.25 degrees).
If I'm standing on the Moon, and I want to find the odds of an alignment not just where I'm standing, but also at another location on the Moon, then I would do the following:
Let:
P_total = Total Probability (two locations, same planet) Sum1 = Sum of all star times for location 1 Sum2 = Sum of all star times for location 2
Then, for two locations on the same planet:
Sum1 Sum2 P_total = ----------------------- + ----------------------- Total Rotation time Total Rotation Time
Note, I am adding these together because I am interested in finding the probability of an event at either location.
Imagine a totally smooth wheel, that I am going to make into a roulette wheel. It has no slots on it yet, it's just flat, so a ball would roll off of it because there is nothing to catch the ball. Suppose next, I carve so many slots into it, but leave large spaces of it totally smooth. That means that a ball could land on a smooth space and roll off (no alignment event) or that a ball could land on a slot (an alignment).
Now imagine that those spokes I've created are for location 1, and location 1 only. At location 1, there are just so many Hoagland/Bara star ritual angles at which a star can appear, the rest of the space is not counted as a "hit." But, if I am to add another location on the same body, and then want to figure the odds of the ball (star) landing on either one, then I need to add more slots. This is so because at location 2, I could have an alignment happening while there is nothing happening at location 1. So, I add slots for location 2's angles. Thus, the two probabilities are additive.
Or,
P_total = Probability (location 1) + Probability (location 2).
If you want to find the probability for three locations on one planet, the same applies. However, it's possible that at some locations you could have two alignments happen at the same time. It would be like having overlapping slots on the roulette wheel I'm designing. For example, at location 1 Sirius could be at the horizon, and location 2 it could be at 33.0 degrees. So, I only need one slot for this, not two, because the star will "hit" an alignment angle in both locations at the same time. To account for this, I have to anticipate and subtract out alignments that occur in two places, in order not to count them twice.
The two pictures below indicate an example of such a "recurring" alignment configuration. (I dubbed these occurrences of more than one alignment occurring on the same planet or at the same location "recurring" alignments because a Hoagland/Bara alignment "recurs" or occurs more than once at the same location). You will note that there are two alignments here that occur at the same date and time, on the same "planet", in this case, the Moon. One alignment occurs at the planned Apollo 11 landing site, and one at the planned Apollo 12 landing site.
These pictures are the same as the Atlas 7 examples shown earlier, placed here again for ease of viewing (Figures 13 and 14, below).
Figure 13: The sky above the planned Apollo 11 site on the Moon, at the time of launch of Atlas 7.
Figure 14: The sky above the planned Apollo 12 site on the Moon, also at the time of launch of Atlas 7.
Thus, we have, for two locations on the same planet:
P_total = Probability (1) + Probability (2) - P[recurring alignment(s)]
How about locations on another planet?
Think of the Earth and Moon as two separate roulette wheels. When talking about one wheel, I can count different "slots" on each one and add the odds together. For example, on one roulette wheel, if I want to find the odds for two more numbers in addition to the one I originally selected, I add the odds together -- and get:
Probability (3 roulette numbers) = 1/36 + 1/36 + 1/36 = 3/36 = 1/12
So, the odds are 12 to 1 that the ball will land in one of my three numbers. But, suppose I'm dealing with two roulette wheels -- and I want to find out what the odds are of a ball landing in selected numbers on each wheel?
There are two locations on the Earth in my restricted example of the Hoagland/Bara ritual star alignments model -- the launch site, in the case of NASA mission launches, and the Giza pyramid complex. Though Houston played a role in the actual launching of the manned Apollo missions, I did not include it in this analysis of the launch data because I wished to stay consistent. I could not, for example, use Houston for the Apollo missions and not for all the others.
In my restricted model, there are three locations on the Moon of interest: the planned Moon landing locations of Apollo 11, Apollo 12, and Apollo 13/14. These are all considered "valid" Hoagland/Bara ritual star alignment "temple" sites.
Now, to get down to defining probabilities for the above:
P(Earth) = total probability of an event on Earth, given two locations of interest
And,
P(Moon) = total probability of an event on the Moon, given three locations of interest
Of course, then we have:
P (Earth) = Prob. (at Launch site) + Prob. (at Giza) - (recurring alignments)
P (Moon) = Prob. (at Apollo 11) + Prob. (Apollo 12) + Prob. (Apollo 13/14) - (recurring alignments)
Then, we have:
P (Earth+Moon) = P(Earth) + P(Moon) - ( P(Earth) * P(Moon) )
Probabilities of two separate "wheels" add, but I'm only interested (for the time being) in correctly modelling the probability of one event. Because of that, I subtract out the times when both roulette wheels have a "hit" on the number of interest. Otherwise, as with the recurring alignments in the case of multiple alignments on one planet, I will have counted the odds twice.
A TEST OF THE "ROULETTE WHEEL" MODEL
In order to test my model of the odds, I constructed a random number generator to generate random days out of a year, and random times during the day. Because of the importance of the year 1969 to the Apollo mission, I chose it as my test year.
Also, because certain lunar alignments do not "recur" on different years (I tested this out with RedShift), I must calculate the odds for each year depending upon whether or not I can subtract these recurring alignments. However, note: even if I did not subtract these items out, or subtracted two too many, it makes very little difference in the odds. That's because these "recurring" or "double" configurations don't make up a sizeable "chunk" of the odds calculations.
I did not wish to use one Moon cycle (27.322 days) or one Earth cycle (1 day), as I felt neither would yield an accurate test for how well my model approximates the actual times that stars spend at the degrees of interest, over an extended periods of time. My model needs to approximate the motion of the Earth and Moon well enough over the course of one Earth year and more, in order to be workable.
After I had my 100 randomly generated samples of dates and times, I again utilized the program RedShift measure every star of interest at every angle and location of interest (this came to about 2500 measurements total, just to get 100 samples of every star at every location). The locations I used were Cape Canaveral and Giza on the Earth, and Apollo 11, Apollo 12, and Apollo 13/14 planned sites, on the Moon.
For my initial test of the odds, I started with a simple situation and set my tolerances to +-0.25 degrees for the angles 0, 19.5, 33.0, and the meridian.
For lack of space, I did not include all my data which I used to derive the odds with, such as star motions for all stars at all locations, and so on.
Plugging the star motion numbers into the below equation,
P (Earth+Moon) = P(Earth) + P(Moon) - ( P(Earth) * P(Moon) )
P (Earth+Moon) = 0.36587
My equation predicts, then, that out of a sample of 100, I should get:
Number "hits" = P (Earth+Moon) * 100 = 37 hits.
Out of my sample of 100 times in the year 1969, I did indeed obtain 37 "hits" on 0, 19.5, 33, and the meridian!
The graph below (Figure 15) plots my one hundred sample data points against the odds:
Author's note: Probability axis = Hits/Samples.
As the number of samples increases, the "hits/samples" approaches the true probability of an alignment event, which recall, was expressed as:
Probability = Outcomes Favorable/Total Outcomes.
Figure 15: Plot of Random Star Alignment Observations for the year 1969
Note that the graph zeroes in on the value 0.37. This is due to the "Law of Large Numbers." This law states that the more repetitions of a random event that you measure, the closer a value you will obtain for the actual "real life" probability of an event. The more samples I obtain, the straighter that line becomes to a number which represents the exact probability.
The beauty of the "Law of Large Numbers" is, once a certain number of samples is reached (in this case, 100), a large deviation from the value being "closed in" on is unlikely. For example in this case, it's unlikely that the next 100 samples would produce probability values that vary much over or under 0.37.
For additional tests of my model, refer to subsequent sections where I analyze NASA launch data. There are two other instances where I use my probability equations to come up with a value beforehand, then test that value with plotted graphs of random data (in the NASA analysis, the random samples were over a period of decades, i.e. 1958 through 1978).
The graphs in all cases -- the one for 1969 (above) and the subsequent graphs in the NASA analyses -- indicate that this sample model does model the odds sufficiently well, if not precisely.
Therefore, the data indicates that this model is an acceptable model, that it closely approximates the real situation, and that it can be used to model the odds in the remainder of this paper. I do encourage the reader to verify this for themselves by taking their own measurements.
Note that the formulas I use express the odds as follows: What are the odds that, on any given day of a given year, an observer at any of the 5 locations (2 on Earth, 3 on the Moon), will notice an alignment of an important star at or near the angles 0, 19.5, 33.0, and the meridian?
IS THERE A PATTERN TO NASA LAUNCHES?
Before analyzing the Apollo Missions, it is important to determine that there is a pattern. In the next section, an analysis of 82 NASA launches attempts to do just that.
The Law of Large Numbers states that the more samples taken of an event, the closer I draw to the actual probability. If the NASA launches really aren't following a pattern, then I would expect the star positions at the launch dates and times to "close in" on a random value.
In order to assure the most accurate odds calculations as possible, I decided to plot up 100 samples taken at random from the years 1958 through 1978. Years, dates and times were selected at random to generate this set of data, then measurements were made with RedShift at all 5 locations of interest to this analysis (launch site, Giza, and the "planned" Apollo 11, 12 and 13/14 landing sites on the Moon).
ANALYSIS OF NASA LAUNCH DATA: CHOOSING TOLERANCES FOR ANALYSIS
In the previous section where I test my "roulette wheel" model, I arbitrarily assigned equal "tolerances" to all the angles; i.e. +-0.25 for each angle. However, it is more useful and appropriate in the case of actual data, to use the margins of error which actually occur in the data.
For example, suppose I am a hypothetical conspirator who wishes to perform NASA events at the same time as specific stars are at alignment positions. Because of real world considerations, such as crew safety, device limitations, physical obstacles or unexpected delays, I can't always hit an alignment dead on. Therefore, there will be a margin of error around each angle. In order to find this hypothetical "margin" of error, I decided to analyze the data for each angle, to see what the values near 0, 19.5, 33, and the meridian would "center" around. I did not really expect to see any kind of "centering" trends if the data was truly random, anyway; if the data is random, then data could center around 32.7 just as easily as 33.0, for example -- and in that case, the arbitrary margins of +-0.25 degrees or +-0.5 degrees would be suitable to analyze the data. However, if I did see "centering," I could proceed from there on the supposition that someone was "trying" to hit these angles dead on, perhaps accepting certain limits or criteria for each angle.
Why select error margins based on real data, instead of arbitrary fixed ones like +-0.5 and +-0.25? Because the probability of an alignment event occurring within an actual observed error margin (not a "made up" fixed one) is expressed as
Time for star to traverse error margin P(alignment within error margin) = ------------------------------------------ Total rotation time
This gives the true probability of the event. If I were to assign an arbitrary +-0.25 margin to this data, it would not accurately describe the probabilities involved. This is because, as the reader will see in the below sections, not all the data falls evenly within +-0.25 degrees, so this error margin does not accurately express the probability of an actual alignment events that occur.
Analysis of Actual NASA Launch Data
I now direct your attention to an analysis of data obtained from 82 NASA launches. I'll start with the horizon, or zero degrees. The graph for zero degree alignment events is displayed in Figure 16, below.
Figure 16: Number of occurrences of star alignment values between zero and one degrees.
These launch data values do center close to zero. There are less and less hits as I proceed away from zero (and more as I approach zero). In fact, the launch data values range from 0 deg 0 min to 0 deg 19 min, with all of the values but two ranging from 0 deg 0 min to 0 deg 12 min! Which means, I can catch most all the "zero degree" alignment events by focusing on the zero to 12 arc minute range!
Notice the graph of 19.5 degrees, shown in Figure 17, below.
Figure 17: Number of occurrences of star alignment values between 19 and 20 degrees.
Note that the range of launch data values here is between 19 deg. 23 min and 19 deg. 37 min., plus there is an additional spike in the range of 19 deg 50 min to 19 deg 53 min. I will get into the significance of this later ... for now, just note that 19 deg 50 min is also symbolic of the number 19.5.
However, for now I simply settled on the widest tolerance that would "catch" this concentration of values near 19.5, and that was +-7 min. This would mean a range of 19 deg 23 min to 19 deg 37 min.
Notice the graph of 33 degrees, shown in Figure 18, below.
Figure 18: Number of occurrences of star alignment values between 32 and 34 degrees.
This graph does have noticeable spikes, just as the others do, though these launch data values also seems to be spread out, also. These spikes are in the ranges 33 deg. 0 min through 33 deg. 19 min, with most of the values below the 15 arc minute range, and also between 33 deg 30 min and 33 deg 39 min. Note again, that 33 deg 30 min is also symbolic of the number "33," or more specifically, "3" repeated as many times as possible.
However, for now I will ignore the "33 deg 30 min" range of values and focus on the one spike, that indicates a larger concentration of "33" angle values cluster from 33 deg 0 min to 33 deg 19 min, with most of them below 15 arc min. I therefore chose an error margin here of 15 min.
Notice the graph of the meridian, shown in Figure 19, below.
Figure 19: Number of occurrences of star alignment values between 179 and 181 degrees azimuth (180 = meridian).
Once again, these launch data values cluster closely around the actual value of 180 degrees (azimuth), just as the did for degrees altitude in the previous cases. The range in this case is 179 deg 48 min to 180 deg 7 min. So, I surmised that since adding 12 min. to 179 deg 48 min would give precisely 180, that an error margin of +- 12 min. would be appropriate for the meridian.
Finally, please note that all the graphs above contained spikes or data points which centered closely around the actual angles 0, 19.5, 33, and the meridian. This in itself indicated to me that the data was favoring the Hoagland/Bara model, and that it warranted further investigation.
TOLERANCES RESULTING FROM ABOVE ANALYSIS
0 degrees +- 12 arc min. 19.5 degrees +- 7 arc min. 33 degrees +- 15 arc min. meridian +- 12 arc min.
Therefore, the above tolerances were used for the initial analysis of the NASA launch data. But, before the launch data was analyzed, I tried these tolerances out on a set of random star observation data, where the observations were made at Cape Canaveral, Giza, and the planned Apollo 11, 12, and 13/14 lunar landing sites (as before). The following graph resulted:
Notice how the graph zeroes in on 0.28, the expected random value for these tolerances (Figure 20, below).
Figure 20: Plot of random star observations taken between the years 1958 through 1978.
Once again, according to my 100 random observations, my equations have successfully predicted the random value for the tolerances I selected. Now that I've discovered what happens in the random case, which is displayed above, I can move on to real NASA launch data and see how it performs.
Analysis of Actual NASA Launch Data
Using the above error tolerances on the NASA launch data yields the following graph (for observation locations of Cape Canaveral, Giza, and the planned Apollo 11, 12, and 13/14 lunar landing sites). See Figure 21, below:
Figure 21: Plot of actual NASA launch data
Notice how the data does not converge on the expected random value, but rather stays above the expected random value. This yields odds of 1,255 to 1 against random chance. The high odds indicate how unlikely it is to have this much deviation from the random value. Think back to the "weighted coin" example, where the odds were over 2000 to 1 against random chance. These "odds against" for NASA launches are high, indicating that it's likely that these alignments that happen during the 82 launches do not occur by chance.
While it's always possible that variation in the data could produce such a curve, the odds indicate that it's very unlikely. Additionally, the two sets of random data that I did obtain, showed no such large deviations from the expected random values. While it would be best to obtain at least ten or more sets of 100 random values (the more the better) to get a true measure of variability, what I have obtained so far (as well as my experience with RedShift and with taking these hundreds of these measurements), leads me to the conclude that this is not due to variability. It is just too unlikely, and no such great degree of variability was observed in my random samples. The data does tend to favor the Hoagland/Bara star ritual theory, and deserves further investigation. And, as the reader will see, there are continued deviations in other sets of NASA data, which make the "variability" idea more and more unlikely.
Additionally, there are many other aspects to this data that have not yet been dealt been dealt with; such as, those spikes at 19 deg 50 min and 33 deg 30 min. I will get into this analysis next.
The Hoagland/Bara model stresses the importance of the actual numbers 19.5 and 33, not just those particular angles. Therefore, I took another look at the data with this in mind. I saw that there were quite a few instances of numbers in the launch data such as "3 deg 30 min" and "19 deg 50 min," and "0 deg 33 min," and the like. Therefore, it occurred to me that since there were other ways of expressing the numbers 19.5 and 33, looking for occurrences of these might be in order. The above odds also indicated to me that there was a tendency to favor the Hoagland/Bara model, so these additional tests of the launch data were initiated to see if there was more to this picture.
TOLERANCES AS SLOTS ON THE PLANETARY ROULETTE WHEEL
Adding windows or "tolerances" for such things as "3 deg 30 min" and "19 deg 50 min" is like adding extra slots on the roulette wheel.
Suppose again I have a totally smooth disk, and I wish to make a roulette wheel out of it. I can create indentations, each of specific widths, in which to "catch" a ball. The more slots I place on the wheel, the more likely I am to catch a ball, therefore the odds against a ball landing in any slot go down the more slots there are.
Therefore, as I add slots, the chances of a star hitting any particular slot go up. However, if there are far more "hits" than there should be, then the odds should reflect this. So, keep in mind -- the more I allow for different occurrences of the numbers 19.5 and 33, the more likely I am to find them. This just reflects common sense. Still, if I find way too many than random chance would allow, this will show up in high odds "against random chance." This is allowed for in the following sections.
SETTING TOLERANCES FOR OTHER OCCURRENCES OF 19.5 AND 33
The combination of degrees and arc minutes expressed by "19 deg 50 min" is most meaningful when it ranges from "19 deg 50 min" to "19 deg 59 min," because it preserves the "19 deg 5__" combination, or in other words, it's yet one more way of expressing the number 19.5. The same applies to "3 deg 30 min," i.e. it should range from "3 deg 30 min" to "3 deg 39 min," to preserve the connection with the number "33." However, because of real world factors such as crew safety, weather conditions, and the unexpected events that come up when planning a space mission, I did allow a +-2 min error margin around 3 deg 30 min, allowing it to dip down into 3 deg 28 min. as well as go up to 3 deg 39 min. Keep in mind that this ONLY drives up the probability and lowers the odds; it means nothing and will do nothing if there is nothing there to "catch." It's like designing a fish net for a particular size fish -- if that fish isn't in the lake, it won't get caught. The same is true for this "net" that I'm designing.
In a similar fashion as above, I let the data drive these tolerances, i.e. if the data ranges between "19 deg 50 min" and "19 deg 53 min" (as was indeed the case with this launch data), this was the range I chose. Please see the above sections for a detailed explanation of my rationale for doing this; I will state it briefly again here, however: if I do not select an appropriate error range for the actual error ranges found in the data, then I will not accurately express the probabilities of these occurrences. Therefore, this must be data driven.
When dealing with the value "0 deg 33 min," I simply chose a +-2 min. tolerance value. This is because, again, I'm dealing with a "real world" where scheduling and other factors come into play. A star moves through one arc minute very quickly, therefore it's possible, even when planning the timing of an event, to miss the "33 min" mark by an arc minute -- or two. Therefore, in this case, I allowed +- 2 min.
With that in mind, the following set of tolerances were used for the angles in question:
Tolerance Set # 1
33.0 degrees +- 15 min. 33 deg. 33 min. Ranges from 33 deg 30 min to 33 deg 39 min. 19.5 degrees +- 7 min. 19 deg. 50 min. + 3 min. (19 deg 50 min to 19 deg 53 min) 3 deg. 33 min. Ranges from 3 deg 28 min to 3 deg 36 min. 0.0 degrees +- 12 min. 0 deg 33 min +- 2 min. Meridian +- 12 min.
The below graph is a plot of random data as a test of my model, to be certain I am working with the correct odds for the 82 NASA launches that I will be analyzing. My model predicts that I will get 38 "hits" out of 100, or Probability (alignment) = 0.38. Once again (as before), this graph represents random observation data taken from Cape Canaveral, Giza, and the planned Apollo 11, 12, and 13/14 lunar landing sites (Figure 22, below):
Figure 22: Plot of random star observations taken between the years 1958 and 1978.
Note how the above graph takes a longer time than the others to converge on a value, and in fact "hovers" near 0.38 finally. This is because not all random data is the same. Sometimes it takes awhile to reach an accurate value for the odds. Because the value the graph ends up on is actually 0.39, I am going to use 0.385 to calculate probabilities for this next section. Though this could just be normal "variability" in the data, I wanted to err on the conservative side.
Methodology of counting "hits"
In the above model, double hits were counted as one hit (if they both fell in the specified tolerances). "Double hits" are alignments that occur on the Earth and Moon simultaneously. If there is one hit at Cape Canaveral and one hit at Giza simultaneously, these are not considered "double" hits because it is simply the geometry of the Earth that is causing the stars in question to both hit alignment angles at the same time.
For a listing of star alignments, launch times and dates, etc., I direct the reader to my raw data page. This gives a complete listing of launch times, alignment positions, etc. used in this analysis.
Next, I plotted the NASA launch data (again, see raw data for the actual launch data itself), for the following space missions: Pioneer, Mercury, Ranger, Gemini, Surveyor, Lunar Orbiter, and Apollo, in that order, for the same five observation sites I used for the random data (Cape Canaveral, Giza, and the Apollo 11, 12, and 13/14 lunar landing sites). This comes to a total of 82 launches. Here is what happened (Fig. 23, below):
Figure 23: Actual NASA Launch data
Note how the graph does NOT close in on the expected random value. Also, note how it behaves very much like the "weighted coin" example above! This was the result of 47 hits out of 82 launches. In order to assess how unlikely this wide a divergence from random would be, I have to calculate the odds for the above graph.
The odds were computed using the bionomial coefficient equation. Where "**" means "to the power of," I have:
82! Probability = ------------ x [P(align)]**47 x [1 - P(align)]**35 47! 35!
Where P(align) = 0.385, I come up with odds of 4,193 to 1!
This is significant, as it essentially tells me that NASA launches probably do not fit random chance, but some other model must therefore be used, as with the "weighted coin" example. Though the variability of the data could use more testing, with the data I have so far, this kind of deviation is just too far off to be random. Since this test was aimed at discovering if NASA launches are "weighted" in favor of the pattern described by Hoagland and Bara, I must conclude that is probably the case here.
A core hypothesis of the Hoagland/Bara model is that there are specific "temples" at which these events occur. Cape Canaveral is not a temple, but was included so far in this analysis due to it being the location of launch. However, I noted that most alignments seemed to occur over Giza and the planned Apollo landing sites, Apollo 11, 12 and 13/14. Therefore, I narrowed the locations down to just these to find out what would happen. If the odds went up, I felt this would further corroborate the tendency of the data to favor the Hoagland/Bara model.
Test # 2: NASA launch data, Cape Canaveral excluded
Limiting the locations is like eliminating "roulette wheel" slots. I.e. if I eliminate 18 of the 36 slots on a roulette wheel, I reduce the probability of a ball landing on a slot, by a factor of 2. By eliminating Cape Canaveral, I only reduce the probability to 0.32. Why not more? Because now, I only have one location on Earth, and cannot discount alignments that occur in more than one Earthly location. Therefore, the probability only goes down by a small amount.
The below graph is another plot of random data as a test of my model, to be certain that my predicted value of 32 out of 100 hits was correct. The following data resulted (Figure 24, below):
Figure 24: Plot of random star observations taken between the years 1958 and 1978
Note that the above graph converges precisely on 0.32, or "32 out of 100," just as my model predicted. Therefore, I will use P(align) = 0.32.
The below graph is a plot of the NASA launches and the predicted random value (=0.32), with the above tolerances used. As expected, the number of hits went down -- but not by much. See Figure 25, below.
Figure 25: Actual NASA Launch data.
In the above graph, I ended up with 44 hits out of 82. As before, I wanted to find the improbability of this many hits occuring in 82 launches. To do that, I used the same equation as before:
82! Probability = ------------ x [P(align)]**44 x [1 - P(align)]**38 44! 38!
This time, I obtained odds of 40,192 to 1 against random chance! This is not a misprint. The high odds against random chance are due to the fact that the number of hits are still very high (44 this time as opposed to 47 last time), and the probability is lower than in the previous example. This is far too improbable to be considered the result of random processes.
Yes, statistical data does often show deviations ... but, the odds calculation I performed above shows how unlikely this much deviation is. Therefore, it cannot be random. Additionally, though launching NASA rockets is far from a random process, the scheduling of NASA launches should not correspond to a "star pattern" even so -- unless one wants to accept the validity of Astrology, where correspondences of weather and so on are tied to stars and planets. Otherwise, considerations of weather and launch windows should not be tied to the position of stars in the sky in any way.
How can I tell that these results follow the pattern outlined by Richard Hoagland and Mike Bara? Because of the numbers and analysis method I selected. My analysis approach only emphasizes the frequency of star positions at specific locations. This serves as a "filter," because of the fact that NASA launches are tied to the position of planets, weather, and lighting conditions (the position of the Sun), NOT "star positions." The method of analysis that I chose emphasizes star positions and nothing else; not weather, lighting, planets, or other factors. Unless one accepts the validity of Astrology, where the positions of stars do have an effect on weather conditions or so on, there is no reason to tie star positions in with launch conditions.
The probabilities involved here clearly require that, if the NASA launches really were taking place in a random fashion, then these "samples" I've taken of NASA "events" (i.e. launches in this case) should close in on a random value. Furthermore, the deviation from a random value should not be this high on a consistent basis, which is indicated by the very high odds against this much deviation. This sample set of NASA launch data does not close in on a random value, therefore these NASA launches follow a predictable pattern. Because this analysis was geared to test whether or not the launches occur according to the Hoagland/Bara model, the numbers indicate that the pattern NASA follows is the one predicted by Hoagland and Bara.
Two of the three criteria for determining if something is a "pattern" have been clearly been met ... high improbability, and a "trend" that is above random chance by a noticeable amount. Recall, there is another criteria to be satisfied ... variability.
How do I account for variability? Well, I can't do that very accurately with just data samples in this case, because I've not taken enough measurements -- I only have two sets of 100 samples. However, I can say that in the two sets of 100 random time samples that I've analyzed (resulting in over 5,000 actual measurements), I have not seen much variability; perhaps at the most, +-2 alignment hits away from the predicted random value. Also, the lower the probability, the less likely the deviation is to be +-5 or +-10 percent of 100 (+-5 to +-10 alignments); it is most likely to be lower for probability values less than 0.5 (that's why the "odds against" this much deviation are so high).
Now that the numbers show that there is most likely a non-random pattern, it is worthwhile to investigate the Apollo missions in more detail.
ANALYSIS OF THE APOLLO PROGRAM
So, it has now been demonstrated beyond reasonable doubt that there is a pattern to the 82 launches (including Apollo) analyzed above. As I mentioned previously, I chose those programs for their "pre-Apollo" significance (Surveyor, Lunar Orbiter, etc.), since those programs were designed to survey potential landing sites and test procedures later used to safely land men on the Moon.
My findings do not imply that every other NASA program has this pattern. That would require further analysis. I do state however that this analysis proves to my satisfaction, that the pre-Apollo and Apollo program itself follows this pattern. That much is obvious because attempting to model the NASA launches with a random process demonstrably failed!
DO THE APOLLO MISSIONS FOLLOW THE 19.5 AND 33.0 PATTERN?
Before doing an analysis on Apollo, I thought it wise to determine whether or not the program as a whole conforms to the "star ritual" theory. To analyze the data for the 82 launches, I (of course) had to lump Apollo in with all the rest. But how would Apollo perform all by itself? In order to connect it with the bigger pattern, I wanted to make sure first that it conformed to the "ritual star" pattern and was not behaving "randomly."The total number of launches, counting unmanned missions now also, for Apollo was 16. (Author's note: actually, there are a total of 18 launches, because AS-201 and AS-202, two unmanned Apollo test launches, were overlooked prior to publication of this paper. For an explanation in detail of how these two missing Apollo launches actually reinforce the conclusions reached in this paper when added to the 82 launches, see my addendum.) Using my tolerance set that generated 4,193 to 1 odds against random chance for the 82 NASA launches, I found a total of 11 out of 16 launches had "hits." The odds against this many alignment occurrences, computed with the binomial coefficient equation, come to 93 to 1 against random chance.
DETAILED ANALYSIS OF THE APOLLO PROGRAM
The pattern of which Apollo is a part was "preparation" for the Apollo missions themselves. Apollo 11 was the "capstone" on the pyramid that was built by previous missions such as Surveyor, that tested lunar landing equipment, and Lunar Orbiter, that shot the photos of the landing sites, not to mention all the other manned missions such as Mercury and Gemini. If Apollo was the "crowning achievement" of all this effort, then its missions would be "celebrated" with even more "star rituals" than other missions, because of its importance. The next step is to see whether or not this holds true. If so, it will be yet another confirmation of the Hoagland/Bara star alignment theory. The odds against data being consistent down to a level of minute by minute mission planning -- engine firing, manuevering, docking, landing, splashdown and so on -- would indeed be "astronomical."
As an additional check of the Hoagland/Bara theory, I decided to examine the manned lunar landing Apollo missions on that level of detail. The most appropriate Apollo mission with which to begin this examination is Apollo 11, for the reasons cited above.
DETERMINING ODDS FOR DETAILED APOLLO ANALYSIS
Prior to analyzing the Apollo missions in detail, I had to determine whether or not my former model of the odds would work sufficiently well.
First of all, there is mission duration to consider. When just considering launches, where a launch could happen anytime in a twenty year span, there is no need to factor in the rotation of the Moon. But, because Apollo missions vary in length (the ones to the Moon, at any rate) between 195 hours and 302 hours, this does not allow for the full range of lunar alignments to take place. Does this affect the odds?
I say no, and for the following reason. In Figure 26 below, notice that the pie-shaped piece of the "Moon," representing the arc distance through which it rotates in 195 hours, contains so many alignments depending on which part of the cycle it is in when the astronauts land. The stars of interest here form about a 66 degree-wide pie slice (measured in ecliptic longitude, for simplicity's sake), which could be anywhere and fall on any of the alignment positions. In the case of Apollo 11, this 66 degree pie slice will move a total of 107 degrees, because 195 hours (mission duration, Apollo 11) is about 0.297 lunar rotation cycles. This means then, that "hits" can be made on almost half of the alignment values possible, or a total span of 107 + 66 degrees = 173 degrees.
Figure 26: Illustration of arc-distance covered by stars of interest to this analysis, during a 195 hour rotation of the Moon.
However, 66 degrees is a close approximation in this case, to the actual configuration of the stars as they rise above the planned Apollo sites on the Moon. The tilt of the Moon relative to the ecliptic is only 5 degrees. Cosine(5 degrees) = 0.996, and the sites in question are close if not dead on the Moon's equator. Therefore, this approximation is acceptable.
It is true that, because of the irregular spacing of the stars, there can be more or less of a chance of stars hitting an alignment value in that 173 degree span, depending on where the 173 degree "span" begins in the Moon's rotation cycle. However, if I consider that NASA could launch or do any mission activity at any time, then this averages out. In the span of three years, during which time the lunar landings were taking place, there were around 40 lunar rotation cycles. During any of these times, that pie slice could be in any position. So at any random time, I have
Total time, possible lunar alignments in 195 hours Probability (align, Moon) = ------------------------------------- 195 hours
Now, if I consider that, at any given time, the Moon could be in any part of its cycle, and could contain more or less alignments, all I need to do is utilize the law of averages, which eventually should give me:
Total possible alignments in 195 hours = Total alignments, one rotation cycle * Fraction of lunar orbit cycle
Therefore, the probability of a lunar alignment occurring during a mission is given by
Time per alignment*Total possible alignments Probability, align = ------------------------------------------------- Length of Mission
From the law of averages, I know that:
Total alignments, mission = Total alignments, one lunar rotation * (mission duration/lunar rotation)
Therefore, I can rewrite the P(align) equation as
Total alignments * (Mission time/Lunar rotation) Probability, align = --------------------------------------------------- Mission time
The "Mission times" cancel out, leaving the familiar and same equation used for the previous section of this paper, namely:
Sum, times for alignments at locations of interest Probability, align = ------------------------------------------------------- Total rotation time
Objections could be raised, and with good reason, for doing this. Certainly, at some times during the Moon's rotation cycle, there would be a good chance of numerous alignments, and at other times, especially if the "pie" section centers on the meridian, much less of a chance, because the majority of the "hit" angles are nearer to the horizon than to the meridian. Figure 27 illustrates this concept.
Figure 27: Illustration of the "density" of alignments. Notice how more alignments are clustered near the horizon line, and that there is a relatively large "empty" space around the meridian (represented by the two red dots at the top and bottom of the circles).
Nevertheless, my aim here is not to examine just Apollo 11, but the entire Apollo series. So my point is that the law of averages works because at any time during that three year period, there will be times when there are more alignments occurring at any given time, and times when there are fewer. Because I must assume missions are being scheduled in a semi-random fashion, then any time during that three year period there could be more or less alignments during a mission. So, therefore, unless I'm only examining one mission, the same rules apply to examining the missions in detail, as they did to the 82 launches.
Considerations of Lighting
Though I indicate above that I choose the same random model I use for the 82 launches, to estimate the odds for the Apollo minute-by-minute mission events, there are other considerations which would "up" the odds against random chance considerably. That is, that specific conditions of lighting would need to be present during lunar landings, so that the astronauts could see to land the spacecraft.
Typically, lighting from the Sun would need to be 10-12 degrees above the lunar horizon. This limits the times of the year in which lunar missions can be executed. Because of this limiting "light" factor, then, having a star alignment occur at the same time as this "light" factor would up the odds against random chance, because there are only specific "time windows" in which the Sun is at 10-12 degrees above the horizon on the Moon. Further, this means there are specific times during a year (fall, spring, etc.), which facilitate both the lighting conditions on the Moon, and ease of travelling to that particular lunar location.
I did not choose to include this factor, though it would have boosted the odds against random chance alignments. The reason I did not was to choose the most conservative approach to this analysis, and to keep it simple. Keep in mind, however, that had I included this factor, the "odds against random chance" for the Apollo series would have gone up.
ANALYSIS OF APOLLO 11
If indeed the Apollo missions are filled with this symbolism, and Apollo 11 is the very first -- therefore, very special -- mission where humanity walks on the Moon, then many of the tasks done to get to the Moon may have been "timed" also to correspond with star patterns. To find out whether or not this was true, I once again consulted the NSSDC archives to find out the timing of many of the Apollo 11 events. I then consulted RedShift to find out the positions of the stars involved.
The below table highlights what I found. Note that all "Sirius" and "Mintaka" entries are highlighted. There is a reason for this that I will get into shortly.
TABLE OF STAR POSITIONS DURING APOLLO 11 ACTIVITIES
Apollo 11: 7-16-1969 to 7-24-1969
Mission Activity Date, Time Star Angle Location ------------------------- ----------- ---------- -------- ---------- Launch 7-16 13:32 Mintaka 3 deg 29' Giza S-IVB stage ignition 7-16 16:16 Mintaka 180 deg 36 min Houston Regulus 33 deg 46 min Giza LM and CSM dock 7-16 16:56 Regulus 33 deg 0 min Houston Sirius 32 deg 43 min Giza Lunar Orbit insertion 7-19 17:22 LM and CSM separation 7-20 18:12 Mintaka 0 deg 18 min Ap. 12 site LM engine fires 7-20 19:08 Mintaka 0 deg 10 min Ap. 12 site LM descent engine fires 7-20 20:05 Alnilam 0 deg 19 min Ap. 12 site Lunar landing 7-20 20:18 Alnilam 0 deg 12 min Ap. 12 site Sirius 333 deg azm Giza Ceremony begins 7-20 20:41 Sirius 19 deg 22 min Ap. 11 site Alnilam 0 deg 01 min Ap. 12 site First "Moon walk" 7-21 2:56 Mintaka 331 deg azm Houston Moon walk ends 7-21 5:11 Sirius 0 deg. 47 min Houston LM lifts off from Moon 7-21 17:54 Sirius 0 deg. 13 min Ap. 13/14 site Sirius 195 deg. azm Houston LM docks with CSM 7-21 21:34 Mintaka 19 deg 56 min Ap. 13/14 site LM jettisoned 7-22 0:01 Sirius 3 deg 31 min Ap. 12 site Sirius 19 deg 38 min Houston Trans-Earth injection 7-22 4:55 Regulus 3 deg 32 min Ap. 11 site CM separates from SM Splashdown 7-24 16:51 Regulus 19 deg 22 min Giza
Interesting Facts About the Above Table
Notice the frequent occurrences of Sirius and Mintaka. This caught my eye, as Sirius and Mintaka have a P(Sirius+Min) = 0.49 probability of occurring in a set of alignment data; i.e., the should appear only about half the time, and in this set of data, they appear unusual, with Sirius and Mintaka appearing trend, this time with Sirius and Mintaka appearing 14 times while other stars appear only 7 times total! (Note, however, that I am counting things in this case such as "azimuth 195" and "180 deg 36 min," which I do not count as hits. I include them here as more "interesting information.")
I will compute the odds for this Sirius and Mintaka trend later, as it actually turns out that not only Sirius and Mintaka appear more often than other stars, but so does the star Alnitak. This is true for the Apollo lunar landing missions as well as the launch data. (The star Alnitak does not make an appearance in the above data, which is unusual; however, it does show up often in other Apollo lunar landing missions, along with Sirius and Mintaka). Later on, I will also select which of these Apollo 11 table entries I will count as "hits." Meanwhile, I wish to point out some other interesting facts.
Note the occurrence of "19 arc minutes". 19 minutes is the length of time Aldrin waited before coming out of the Lunar Module after Armstrong, to join him on the lunar surface. Also, note the occurrence of "47 arc minutes". It was exactly 47 minutes after landing, that the star Sirius rose above the Lunar Module's landing site to reach 19.47 degrees or 19 degrees 28 minutes precisely, over the actual Apollo 11 landing site. This occurred during the ceremony that Armstrong and Aldrin were conducting. What is special about that? Well, the exact "latitude" of an inscribed tetrahedron is 19.47 degrees, not 19.5, which translates into 19 degrees 28 minutes. Note there also are occurrences of "19 min" as well as "47 min," in this set of data.
For the rest of the impressive Apollo 11 correspondences to the Hoagland/Bara NASA ritual theory, please refer to the subsequent section "OTHER CONSIDERATIONS," which appears later in this paper. The reader will see there are many other odd and unusual correspondences to the numbers 33 and 19.5; i.e. in terms of mission duration (195 hours), and so on. For now, I wish to continue with the analysis of the star alignment data.
The repetitive appearance of these numbers suggested the proper way to analyze the "detailed" mission data for other missions may be to include the "arc minutes" portion of the data in the analysis. I will get into this, and more about the Sirius/Alnitak/Mintaka trend, in subsequent sections.
Analysis of Apollo 11 data, using same parameters as for the "82 launches"
For now, analyzing the data in the table above using the previous methodology and tolerance set, and substituting Houston for Cape Canaveral, I would get 8 hits out of 17 entries, with P(align) = 0.385. The odds against this many alignments out of 17 entries is 6 to 1 against random chance, indicating that the data tends to favor the Hoagland/Bara model. Though this isn't a strong indicator, it does point in that same direction and not in the opposite one. If I were to do data analysis on this set of data, to better determine the odds of getting "hits" in the ranges that this data has, I would expand the tolerances for 19.5 out to +- 8 min, and expand the range of 19 deg 50 min to 19 deg 56 min. This would then yield 10 hits out of 17 and P(align) = 0.39, or odds of 19 to 1 against random chance for this many Hoagland/Bara ritual alignments in this set of data.
However, since I don't use Houston in the 82 launches, I decided to remove it from this Apollo 11 analysis and focus just on Giza and the planned lunar landing sites. Using the "data analysis" parameters (expanding 19.5 and 19 deg 50 min as described in the previous paragraph), since these more accurately express the probability of these alignments occurring in this set of data, I have P(align) = 0.33.
Using P(align) = 0.33 and the same tolerances as for the 82 launches, I get 9 hits out of 17, and odds of 21 to 1 against random chance. Taken with other indicators, it suggested to me that Apollo 11 favors the Hoagland/Bara ritual star pattern.
Eventually, if a set of data is truly random, there has got to be deviation from this trend somewhere. At some point, I should see a situation where the odds are "for" instead of "against" random chance, i.e. where there are "too few" of these 19.5 and 33.0 degree star alignments instead of too many. In this case, I have my first indication here that the data is continuing in the same pattern as the 82 launches, since that is what I am testing for in this case.
Refer to Figure 28, below. Apollo 11 is a tiny subset of a much larger pattern.
Figure 28: Illustration of the concept of a "pattern within a pattern."
Figure depicting increasing levels of order in data, and the concept of a "Pattern Within a Pattern"
Note from the above figure that, first the launches are assumed to be random. In the above figure, I depict this as a series of rectangles, oriented randomly with respect to each other. As mentioned previously, these launches are a cross-section, taken from several different NASA programs geared for the most part to manned lunar exploration preparation. I discovered (see earlier sections) that these 82 launches were organized according to a pattern. Again, in the figure above, I depict this as a series of rectangles all "ordered" the same with respect to one another. Finally, suppose I want to view one of these "rectangles" close up, to see if it is organized as the "launches" are. This smaller rectangle is contained within the larger pattern, therefore, I am viewing a "pattern within a pattern." If the same pattern which organizes the larger set of data also organizes the smaller set, this becomes highly unlikely in a random scenario.
The 82 launches previously examined represent the launch data for different NASA programs spanning two decades, most of which occurred prior to the Apollo Program and were preparation for the Apollo Program. Before I can say that Apollo 11 or any other Apollo mission, or the Apollo Program as a whole, conforms to the Hoagland/Bara star ritual pattern found in this cross-section of NASA launches, I must establish that this pattern exists in the set of 82 NASA launches. This ("larger" pattern) that includes the 82 launches takes place over twenty years, and Apollo missions take place on (as mentioned earlier) a day-to-day basis, with mission events frequently happening as little as 30 minutes apart.
In order to find out the probability that a smaller pattern would be found within a larger, it's first necessary to define "outcomes favorable".
Outcomes Favorable = Consistent alignments happening in a mission which is part of the 82 launches. Probability (pattern inside pattern) = Probability(outer pattern) * Probability(inner pattern)
The Importance of Consistency
Though I have detected a "pattern within a pattern," I can't multiply probabilities together until I use the same locations for both sets of data. That's another reason why I left out Houston and Cape Canaveral in the two sets of data (the launch data and the Apollo mission events data). If I use the same locations in both sets of data, I can then multiply them together because they represent the same set of measurements and refer to the same set of locations. In statistics analysis, it's important to be consistent as possible when comparing sets of data. Otherwise, the results obtained when probabilities are multiplied together become meaningless or dubious, at best.
Therefore, before I multiplied the probabilities together as discussed above, I limited myself to Giza, and the planned Apollo 11, 12 and 13/14 lunar landing sites as observation points for alignments. As I noted above, these limitations were imposed on both sets of data -- the launch data, and the Apollo 11 mission activities data. I shall do this again in future sections.
Though the odds against random chance for Apollo 11 are not terribly significant, I am doing the following exercise to illustrate how the "pattern within a pattern" concept is expressed mathematically. Recall that the "odds against random chance" for the number of alignments that occur for the 82 launches (excluding Cape Canaveral) are 40,192 to 1 against random chance. If I expand the tolerance set as described earlier (for 19.5 and 19 deg 50 min) then, I have odds of 18,223 to 1 against random chance. Considering now the odds against random chance for Apollo 11 alignments, I get 8 hits out of 16 if I exclude the launch from the Apollo 11 data (the Apollo 11 launch is counted already in the data for the 82 launches). This yields odds of only 13 to 1 against random chance without considering the launch as a "hit" (it's already counted in the "82 launches" data set).
In combination, their probabilities multiplied together would yield odds of 248,000 to 1 against random chance.
This expresses numerically what I was saying prior to this -- that it is increasingly unlikely for other sets of data, in this case the Apollo 11 mission events, to favor the Hoagland/Bara ritual pattern in the same fashion as the 82 launches did.
However, there is much, much more to be gained from examining the entire Apollo lunar landing series, taken as a whole.
Apollo Missions 11, 12, 14, 15, 16 and 17 taken together
Because of time constraints, I only obtained data for all the successful Apollo lunar landing missions, which total six in number. I limited myself to them because they all have the same theme -- successful lunar landings -- and can therefore all be classed in the same grouping. This created a set of 106 events, not including launches!
I did not make judgments as to what constituted "mission milestones" or important mission activities. If any judgments were made, they were made by the NSSDC, which listed what I assume were the most important mission activities and/or the ones that were logged and had a time attached. It was these which I analyzed, and these which resulted in the 106 data points. Including launches, the entire Apollo mission data set came to 112 mission activities!
For this calculation, I used the same tolerance set as that used for the 82 launches, as an experiment to see if this set of data would respond to those same tolerances as the 82 launches did. Keep in mind in the previous section, how "spikes" seemed to center around specific numbers, such as 33 deg 30 min, or exactly 33 degrees, or exactly 0 degrees 0 minutes, etc. This set of data, representing 106 mission activities, should not have these "spikes" in the same location as the launch data, unless the two sets of data are consistent. If that is the case, they are not random. Randomization implies chaos, not consistency.
With the same set of tolerances used for the 82 launches, I came up with 42 "hits" out of 106 and P(align) = 0.32. This was obtained using a very narrow tolerance set. Also, Houston hits were left out of this particular data set, and because Cape Canaveral was not included, this further constricted the number of "hits." However, even 42 hits out of 106 generated 49 to 1 odds against random chance. These odds do indicate that the Apollo mission activities tend to conform to the Hoagland/Bara star ritual pattern, not counting launches.
When Houston is included in the Apollo analysis, as it should be (since it is the base of operations on Earth, which serves as the communications tie between the astronauts and Earth), then I have P(align) = 0.38 and 55 hits out of 106, or 860 to 1 against random chance.
These odds are high enough to indicate the data does favor the Hoagland/Bara model. This was an important discovery in light of the fact that the 82 launches follow this same pattern, though (seemingly) to a much larger extent than the Apollo program. I say "seemingly" because, later on when I include more tetrahedral numbers in my analysis, the Apollo mission activities and the 82 launches will both yield very high odds against random chance.
(What was most interesting to me about the Apollo mission data was the re-appearance of certain tetrahedral numbers [refer to Apollo 11 section, above]. This seemed very non-random to me, and so I decided to investigate just how non-random it is, later on in the paper.)
Now I am going to do the same thing I did earlier for Apollo 11; which is, examine the likelihood of all these mission activities reflecting the same pattern as the "larger" pattern of 82 launches, which was generated by the launches of many programs, Apollo included. Because the Apollo launches are not included in this set of 106 mission activities, I won't be counting them twice by multiplying these probabilities together.
Recall, in order to find the probability of one pattern or non-random event occurring inside another, I have to multiply the probabilities together. Recall also, that the larger picture of which Apollo is a part, and which takes place over the span of decades, is also unlikely. It is therefore even more unlikely that Apollo would reflect this adherence to the Hoagland/Bara pattern in its daily mission activities. What I am getting at here is finding the probability of the data being organized in a non-random fashion, right down to the very details.
Tying the Apollo Lunar Landing Mission Activities together with the 82 Launches
This is simply obtained by multiplying the "odds against random chance" for the 82 launches by the "odds against random chance" for Apollo mission events, minus the Cape Canaveral site and Houston (because Houston and the Cape are two separate statistical "buckets" which can't be multiplied together).
Since P(small pattern inside larger) = P(large)*P(small), I get odds of 1.99 million to 1 against random chance that the Apollo program would show a trend such as this on a day-to-day level, while being part of a larger pattern which does the same thing.
EXAMINING THE DATA IN ANOTHER WAY
Because there are shorter time spans to work with when dealing with Apollo mission activities, such as docking, landing, etc., I deemed it appropriate to include tolerances for arc minutes. If indeed a pattern was being followed, it would be impossible or very difficult, to follow it solely based on degrees only, especially in the case of the Moon, which rotates so slowly with respect to the Earth.
Before I adopted this approach however, I performed an analysis to see just how much correlation there was to acknowledged tetrahedral numbers, such as 19, 27, 33, and 47. Refer to Figure 29, below, which plots the number of hits which fall at every possible "arc minutes" value for 0 and 33 degrees altitude. Note how, in every case, there is not only a "spike" at or near 19, 27, 33, or 47, but also there is a "mound" or solid base beneath and around the spike, clustered at +-1 min away from the tetrahedral number. (In the case of 47, there is not as large a "spike," but a solid "base" or in other words, large number of "hits" near 47 arc minutes.) Thus, in this case, I chose a +-1 min range for these "arc minutes" values.
Figure 29: Number of occurrences of "arc minutes" values between zero and one degrees altitude, and between 32 and 34 degrees altitude.
Note also, the "spike" at 39 arc minutes. 39 = 19.5 x 2, which is interesting, but for the sake of simplicity I only used the "tetrahedral numbers" 19, 27, 33, and 47 for this "arc minutes" analysis approach. (Also, many of these occurrences of "39" occurred in "33 deg 39 min," which is covered in my range of 33 deg 30 min to 33 deg 39 min.)
I performed a similar analysis for the "arc minutes" portion of 19.5, shown below in Figure 30.
Figure 30: Number of occurrences of arc minutes for 19 to 20 degrees.
I included here my analysis for the "arc minutes" portion of 3 degrees, shown in Figure 31, below:
Figure 31: Number of occurrences of arc minutes for 3 degrees 15 minutes to 3 degrees 40 minutes altitude.
And finally, I display my analysis for the "arc minutes" portion of the meridian, shown in Figure 32, below:
Figure 32: Number of occurrences of arc minutes for 179 to 181 degrees azimuth, and 359 degrees to 0 degrees azimuth. The range of 359 degrees azimuth to 0 degrees azimuth is also considered "the meridian".
In the case of the meridian, there was not much to work with. However, since there were a couple more "hits" in the +-9 min. range, I went with this tolerance factor. I could have expanded it out to +-13 min, but I saw little point to it, because there isn't much going on. (There are other hits at 36 to 40 min. away from the meridian, that are beyond the range of this graph. I chose not to use these data points anyway, because I did not wish to extend tolerances past +-0.25 degrees.)
These analyses made it possible to identify the actual "error" factors in the data so that proper tolerances can be set. Thus I can accurately compute the probability values by allowing for these error factors.
Other analysis were performed on the data, just as in the launch section, to determine proper tolerances for 0, 19.5, 33.0, and the meridian, in addition to 3 deg 30 min, etc. Therefore, the following tolerances were used to analyze the Apollo mission events:
Tolerances
Tolerances for Degrees ---------------------- 0 degrees +- 13 arc minutes 3 deg 33 min. +- 5 arc minutes 3.3 deg +- 0.5 arc minutes 19 deg 30 min +- 8 arc minutes 19 deg 47 min +- 1 arc minute 19 deg 50 min Range: 19 deg 50 min to 19 deg 56 min 33 degrees +- 13 arc minutes 33 deg 33 min 33 deg 30' to 33 deg 39' Meridian +- 9 minutes Arc Minutes portion of Zero degrees: ------------------------------------- 0 deg. 19 min. +- 1 arc minute 0 deg. 27 min. +- 1 arc minute 0 deg. 33 min. +- 1 arc minute 0 deg. 47 min. +- 1 arc minute Arc Minutes portion of 33 degrees: ------------------------------------- 33 deg. 19 min. +- 1 arc minute 33 deg. 27 min. +- 1 arc minute 33 deg. 47 min. +- 1 arc minute Also, "32 deg. 27 min" to "32 deg. 47 min." were considered valid, and had the same tolerances as for 33 degrees, above. Of course, I already had a tolerance value built in for "33 deg 33 min" (see above). I did not include any special "arc minutes" tolerances for the meridian, as there were few.
Of course, when extra tolerances are added, probability of hitting an alignment goes up. The above tolerances created a P(align) = 0.49 as opposed to P(align) = 0.38, because of the extra allowances made here.
For a complete listing of all mission activities dates and times used in this portion of the analysis, plus star alignments observed at these dates and times, please refer to my raw data.
INCLUDING HOUSTON AS A "TEMPLE" SITE
Houston is considered one of the "temple" sites in the Hoagland/Bara model, whereas Cape Canaveral is only included when there is a launch. In this new approach to the data, I decided to follow different ground rules for "locations." But before I describe them, I want to address the need for consistency and rules when doing probability analysis.
Ground Rules for Statistics Analysis
As mentioned previously, when doing probability and statistics analysis, it's important to be consistent as possible when comparing sets of data, so that the results are meaningful. Therefore, in the following instances and for all sets of data, I keep the rules and procedures the same. That way, the probabilities will all express the same thing when multiplied together, and the results will be meaningful.
New "location" ground rules for Analyzing Apollo lunar landing missions:
1. Cape Canaveral is left out of the Apollo launches, and substituted with Houston. 2. Houston is used as a temple site for all mission activities, along with Giza, Egypt and the planned Apollo 11, 12, and 13/14 landing sites. 3. For the sake of consistency, I did not include alignments which occurred at the actual lunar landing sites of any of the Apollos, though this practice would be allowable in the Hoagland/Bara hypothesis. With the rest of the data, I had limited myself to the planned sites; therefore, I continued in that vein. 4. Again, for simplicity's sake and to keep the data consistent, I did not consider alignments that occurred at the actual splashdown location, when an Apollo mission splashed down. I looked at the above locations only.
Using the above ground rules for the Apollo mission analysis, the above tolerances for arc minutes values and degrees, I obtained P(align) = 0.49. Next, I again tested my model by plotting this set of tolerances for my set of random data from the 50's through the 70's, as an additional test to make sure my model was still predicting probabilities correctly. This is what I obtained (Figure 33, below):
Figure 33: Plot of random star observations taken between the years 1958 through 1978.
Note how the graph centers on 0.49 for a time, but dips below it at 0.47. This is probably due to 1) my expanded tolerances creating new "recurring alignments" which I did not allow for (and counted too many times), or 2) normal variation in random data. For now, I'll do as I did before and use a value in between the random data's prediction and my model's, and settle on the value P(align) = 0.48. I would use 0.47, but the trend this data takes indicates it is probably higher than that. However, ideally, it would settle things once and for all if I had (for example), a thousand random data points instead of 100.
Next, I plotted the Apollo "mission activities" data using the above tolerances, on the graph below (Figure 34). There were a total of 76 hits out of 112 . Of course, this graph contains all Apollo lunar landing mission activities including launches; recall that Cape Canaveral data points are left out and Houston has been substituted.
Figure 34: Plot of actual star alignments taking place during Apollo Mission events
Using the standard probability equation for this graph yields odds of 100,010 to 1 against random chance. Clearly, this indicates even more organization in the data than the 82 launches analyzed in the first NASA section!
There is great significance to this because of the fact that the 82 launches reveal the same trends. Because it is so unlikely for two sets of data to share the same deviations to this great an extent, I consider this evidence that a non-random tendency definitely exists in the Apollo mission activities data from the NSSDC. Recall, two criteria for a pattern have been met -- high odds and lack of convergence. Even more to the point though, is that this data conforms to the Hoagland/Bara pattern as closely or more as the launch data does.
Leaving out Houston and only focusing on Giza and the Apollo "planned" landing sites on the Moon, yields P(align) = 0.39 and 59 "hits" out of 106. This yields odds of 5,152 to 1 against random chance. Obviously, Houston plays a big role in creating those large odds, given above. However, because I'm not including Houston now, I can apply these same standards and conditions to the 82 launches I analyzed previously.
So, applying the same tolerances to the 82 launches analyzed in the previous section, and (as I did with the previous data set) only considering Giza and the Apollo 11, 12, and 13/14 lunar landing sites, I have:
P(align, 82 launches only) = 0.39 and 46 "hits" out of 82, giving odds of 1,489 to 1 against random chance for the 82 launches, using this tolerance set.
Note how both sets of data respond well to the new "arc minutes" analysis approach. This means the approach emphasizing tetrahedral numbers can work well for catching this non-random behavior.
In a similar fashion as above, I multiplied the two probabilities together, because both sets of data reflect the same locations and the same procedures used in analyzing them. The odds against the Apollo program being consistent, on a mission by mission basis with the launch data analyzed above is 7.68 million to one against random chance.
The Sirius, Alnitak and Mintaka Trend
I also note here for the reader that, in the 82 launches analyzed above (leaving out Cape Canaveral), there is a Sirius, Alnitak and Mintaka trend. Sirius, Alnitak and Mintaka appear a total of 49 times out of 61 total alignments, which is more than they should appear in the data by random chance. The number 61 is obtained from using the arc minutes tolerances given previously, plus is the total number of alignments including doubles.
I already know that
Sum of: all times that all stars of interest spend at all angles of interest Probability = ------------------------------------------------------- Total planetary rotation periodAnd, of course, the basic probability equation is:
outcomes favorable to event A Probability of A = ------------------------------- total # of outcomes
"Total number of Outcomes" in this case is, P(align, all 5 stars)*(Total Measurements), which gives me the expected total number of alignments that will occur for the 5 stars used in this analysis, per set of measurements I make.
"Outcomes favorable" is in this case, P(align, 3 stars)*(Total Measurements), which gives me once more, the expected total number of alignments that will occur, in this case for the 3 stars of interest to me, per set of measurements I make.
Recalling that the above probability is the ratio of (Outcomes Favorable) / (Total Outcomes), the probability of 3 stars of interest occurring as often as they do in my set of 5 stars is
P(Stars 1,2,3) = P(align, 3 stars) / P(align, all 5 stars)
Notice that "Total Measurements" cancels out in each case, and all I have here is the ration of two probabilities. Therefore, if the probability of the occurrence of these three stars is P(Sirius+Alnitak+Mintaka) = 0.25, and P(align, all 5) = 0.39 (see previous section), then the probability of Sirius, Mintaka and Alnitak appearing as often as they do within a set of data is:
P(Stars Sirius, Alnitak, Mintaka occurring in alignment data) = 0.64
As I mentioned before, the stars Sirius, Alnitak and Mintaka all appear 49 times out of the 61 alignment "hits" obtained from the launch data (Cape Canaveral excluded).
For 49 hits out of 61, the odds are 380 to 1 against random chance that Sirius, Alnitak and Mintaka would appear as often as they do. Refer to the graph in Figure 35 below, which illustrates this:
Figure 35: Number of occurrences in the actual NASA launch data of the five stars of interest (Sirius, Mintaka, Alnilam, Alnitak, and Regulus) shown against the predicted random values for each of those stars.
Note that all the launch data alignment "hits" are marked in red, and organized by star. The predicted random values, marked in white, all fall below the "red" marks in the case of Sirius, Mintaka, and Alnitak. (Though in the case of Mintaka, the number of times it occurs in the data does not go over the expected value, it still occurs more than the other stars and more than it should given the fact that Alnitak and Sirius occur so frequently.)
What is notable about this is that this same trend shows up in the Apollo mission events data! The Sirius, Alnitak and Mintaka trend in the Apollo mission data shows up a total of 48 times out of 68 total alignments, which gives odds of 17 to 1 against random chance. This does indicate the data favors Sirius, Alnitak and Mintaka, though not as much as the launch data does. However, "impressive odds" aren't the point here. Random variations in data could produce odds of 17 to 1 against random chance. But, the point is that there is a tendency to favor Sirius, Alnitak and Mintaka in both sets of data. Because the data is not behaving in a random fashion, this strengthens the conclusion that these alignments do not take place by chance. This also serves to tie the data togeter in yet one more way, pointing out yet more consistencies carried over from one set of data to the next. Consistency is the opposite of randomness; it implies organization and planning.
Please refer to the graph below, which organizes the number of alignment hits in the Apollo mission events data by star, as in the previous graph of the Sirius, Alnitak and Mintaka trend in the launch data.
Figure 36: Number of occurrences in the actual Apollo mission events of the five stars of interest (Sirius, Mintaka, Alnilam, Alnitak, and Regulus) shown against the predicted random values for each of those stars.
Note that, although Sirius and Mintaka are above the predicted random values, Alnitak is slightly below. However, Alnitak still occurs more often than Regulus or Alnilam in this Apollo mission event data.
Variability and the "Sirius/Alnitak/Mintaka" Trend
Would variability in the data account for this trend? Yes, it could. I still think the odds are useful and interesting, because the trend continues throughout both sets of data and serves as an additional "tie-in" and indicator of consistency. If all I had to go on was this Sirius/Alnitak/Mintaka trend, I would only note it and move on. But because this is yet one more thread in a tapestry, it takes on additional meaning. If there were only this thread and no tapestry, then simply noting this as a possible but normal deviation from the expected random values would be all that's necessary.
The equation I use to express the probability of 1) a pattern and trend existing in 82 launches, 2) a pattern and trend existing in individual missions (Apollo, in this case), is:
P (trend+pattern) = P(Apollo pattern)*P(82 launch pattern)*P(Apollo trend) *P(82 launch trend)
The odds against this data having a trend, both on the macro level of launches throughout other NASA programs, and the "micro" level of daily mission activities, plus have adherence to the Hoagland/Bara pattern, are 53.5 billion to 1 against random chance!
Why does the Sirius, Alnitak and Mintaka trend exist?
I can only speculate, but I will mention some possible connections here. There is a connection between Cape Canaveral and Egypt that goes beyond Cape Canaveral's translated "Spanish" name, which means "cape of reeds" (corresponding, perhaps, to the Egyptian "field of reeds" or the afterlife). When Mintaka is 33 degrees below the horizon at Cape Canaveral, Sirius is 33 degrees above the horizon in Giza, Egypt. Also, when Mintaka is within a degree of the meridian at Cape Canaveral, it is also at 19 degrees in Giza (depending on whether the Nadir or "Midheaven" meridian is utilized). When Alnitak is 33 degrees below the horizon at Giza, Sirius is at 19 deg 50 min below the horizon at the Cape. And so on.
I have not performed a study to be certain that Mintaka, Alnitak and Sirius have the most such alignments. So, I can only note that this is interesting. However, in light of the fact that Cape Canaveral has been and is the launch site of NASA space missions, and the fact that so many other things in this picture tie together, I would not be suprised if the Sirius and Mintaka alignment geometry between Cape Canaveral and Giza stood out over other possible configurations.
Another interesting fact is, the Arabs called the zodiac -- that band of sky through which the Sun and planets travel -- "Al Mintaka al Buruj," the "girdle of the Signs". (Source: Richard Hinckley Allen, "Star Names: Their Lore and Meaning," page 3.) "Mintaka" itself means "belt," and it is a star in Orion's belt. I do not know if this has significance, but I find it interesting that Mintaka is the one star in Orion's belt whose name actually means "belt," and that the entire zodiac was also named "Mintaka."
Can the Sirius/Alnitak/Mintaka trend be dismissed based on the recurring alignments at Cape Canaveral and Giza, Egypt? No, because the trend existed even after Cape Canaveral was excluded from the data, and the only remaining location