THE LUNAR RENDEZVOUS

This web page deals about the lunar rendezvous as it is described in the Apollo lunar surface journal.

 When the LEM takes off, if first must get out of the lunar attraction, and it starts vertical. As the CSM has a horizontal velocity relatively to the moon, which is its orbital speed, the LM must gain this speed to dock to the LCM; that is why the LM starts turning to a horizontal position to gain this speed; but it must do it very gradually because, if it was doing it too abruptly, it would no more counter the lunar attraction with its engine, and would start falling toward the moon. As the LM is gaining horizontal velocity, the centrifugal force increases and contributes to counter the lunar attraction, which means that the LM has less to counter the lunar attraction with its engine; it can give a greater part of the engine's thrust to increasing the horizontal velocity by adopting a more horizontal attitude. So, all along the parabolic trajectory, the LM gradually turns from a vertical attitude, it has when it takes off, to a horizontal attitude, it has when it reaches the orbit of the CSM. The moment of the takeoff must be well timed, so that, when the LM reaches the orbit of the CSM, it is a little ahead of the latter; a bad timing could result in the LM arriving behind the CSM, which would cause a problem for the docking. As the CSM is going faster horizontally than the LM on most of its travel, that means that the LM must take off before the CSM is above it.

 When the LM is on the orbit of the CSM, it doesn't have the good position to dock to the CSM, for it is its nose it must present to the CSM and not its back. So the LM must do a flip over maneuver to rotate half a turn before docking to the CSM; during this flip over maneuver the CSM stays behind the LM; when this maneuver is over, the CSM can get nearer to the LM to dock to it. In order to dock, either the LM has to slighly decrease its speed, like I show it on this animation, or the CSM has to slightly increase its own; in fact, in the Apollo documentation, it's the second option which has been chosen; it's justified by the fact that the pilot of the CSM sees better the LM than the astronauts of the LM see the CSM; this may be true, but the radar of the LM perfectly sees the CSM, and it would be possible for the astronauts of the LM to monitor this maneuver with the indication of the radar.

 Before the flip over, the astronauts of the LM can't see the CSM, it is not in their field of view. And after the flip over, the astronauts of the LM can't see the CSM either. So, the astronauts of the LM should not be able to take photos of the CSM getting closer to the LM, for it is only during the flip over maneuver that they can have a view of the CSM, and during this maneuver, the CSM must not come closer to the LM, but only after this maneuver has been completed.

 This animation shows the various views that the astronaut of the LM can have of the CSM during the flip over; here I have made the LM turn clockwise, but, it is turns anti-clockwise instead, the views will be the same, but in reverse order. Yet, in Apollo 14, we can see photos of the CSM rotating, but always keeping the same position on the photo (the bottom), whereas this position should change with the orientation like I showed on the examples I gave.

 The demonstration of the LM returning to the CSM I showed is monoplanar, it supposes that the trajectory of the LM is in the orbital plane of the CSM (which should normally be the case). In fact, the moon is in a three-dimensional system, and there are many ways for a satellite to orbit the moon. Here I show two CSM orbiting in two orbital planes which are perpendicular to each other.

 Ideally, the LM should descend in the orbital plane of the CSM; It originally has the same orientation as the CSM, and it can track the CSM with the radar, so it should not be a problem. If the LM descends in the orbital plane of the CSM, then the landing site will be in the orbital plane of the CSM, and the CSM will pass over the landing site at each revolution. And when the LM returns to the CSM, it just has to ascend along the orbital plane of the CSM, and it will be aligned with the CSM when it reaches its orbit.

 Now it can take the fantasy to the LM not to descend along the orbital plane of the CSM, but along an orbital plane which makes an angle with the CSM's orbital plane. In that case the landing site will not be in the orbital plane of the CSM, and the CSM will not pass over it at each revolution. And when the LM returns to the CSM, it can't follow a trajectory in the orbital plane of the CSM, but it can manage to maneuver so that its trajectory cuts the orbital trajectory of the CSM; when it does, the LM must change its orientation to get aligned with the CSM.

 What I have described till now is a quick rendezvous technique; but this technique requires precision. It must be precisely timed so that the LM arrives just a little ahead of the CSM. It seems that the NASA engineers were not too much trusting their system; in the documentation, they suggest that the fact that the radar and guidance systems perform perfectly are "mere fantasy in the eyes of any engineer!" Furthermore, they also consider the fact that the system could fail and that the astronauts could have to perform the maneuver manually. That's why, over the quick rendezvous technique, they prefer a more progressive approach, leaving more time to do the maneuver. This technique could involve several revolutions of the moon; on the first missions, there were two revolutions, but they say that, on the last missions, they managed to reduce it to one single revolution. So, you are going to think that, as the distance which is covered by the LM in this progressive approach is much greater than in the quick rendezvous technique, the LM is going to consume more fuel to do it? In fact not at all, there is not much difference of consumption of fuel with the fast rendezvous technique in spite of the greater distance covered; so, how is that possible? In this alternate technique, the LM starts like in the fast rendezvous technique: It starts vertical, and slowly rotates to horizontal to gain horizontal speed; the difference is that, instead of acquiring the orbital speed when the LM reaches the CSM's orbit, the LM acquires it sooner, as it is on a lower orbit; it even goes a little faster than this orbital speed, and then shuts off its engine; then, with the engine off, the LM lets the centrifugal force which is excess over the lunar attraction slowly drag the LM away from the moon closer to the CSM's orbit. As the LM gets away from the moon, the lunar attraction slightly decreases, but so does the centrifugal force; indeed, if the horizontal velocity remains constant, such is not the case of the angular velocity which decreases as the distance of the LM to the moon increases, and it is the angular velocity which creates the centrifugal force, and not the horizontal velocity. At a given moment, the centrifugal force is not going to be in excess over the lunar attraction any more, which means that the LM cannot move away from the moon any more; at that moment the LM momentarily fires its engine to increase it horizontal velocity and recreate an excess of centrifugal force over the lunar attraction; then the LM shuts off its engine, and lets the centrifugal force continue to drag it away from the moon, and closer to the CSM's orbit. Some, who don't like the concept of centrifugal force (why this hatred?), explain it differently: they explain the trajectory of the LM as a series of connected arcs of ellipse, and a local increase of speed at the junction of two arcs allows to proceed from one arc to the next larger one. Whatever the explanation, this technique, known as Hohmann transfer, allows to go from one orbit to a larger one with a minimal consumption of fuel.

 If ever the LM is not in the same orbital plane as the one of the CSM, then it must change its direction when if crosses the orbital plane of the CSM to get aligned with the latter.

 On the shown figures, the orbits are consistently farther away from the moon than they are in reality. But it may be comprehensible for a reason of convenience, otherwise there would not be room enough to place the text. What is less comprehensible is that the orientation of the LM's flight is clockwise. Yet the LM and the CSM should follow the rotation of the moon which is (like for the earth) counter-clockwise. Indeed, if the CM follows the moon's rotation, its speed relatively to the moon is equal to its orbiting speed minus the moon's rotation speed, and, if the CM orbits in the converse direction, its speed relatively to the moon is equal to its orbiting speed plus the moon's rotation speed; and it is the interest of the LM to have an as small horizontal speed as possible relatively to the moon, for it will make less horizontal speed to nullify when landing on the moon.

 So, what made me tick when I read the documentation of the lunar rendezvous? A series of points I am going to expose in what follows.

 They say "Working together, the radar and the computer were able to calculate the exact location of the CSM and its relative position to the LM". The formulation is incorrect: The radar computes nothing, it just gives indications to the computer it can exploit, and it is the computer which makes the calculations; in fact what the radar gives is the relative position of the CSM to the LM, and it's up to the computer to deduce from it the location of the CSM by the knowledge of the location of the LM and the relative position of the CSM to the LM.

 They say "By using a collection of specialized charts and tables, the LM crew could plot their position and calculate the required burns by hand (remember this was before the days of even hand held calculators!)" I thought they were using an abacus! Seriously, I thought the Apollo's computer was a super-computer!

 The principle of a radar is that it sweeps space and continuously emits a signal; when the signal finds an object, the signal is echoed back to the radar; the radar then knows the signal has met an object, which thus gives the direction of the object, and, by measuring the time between the emitted and received signals, the radar may also know at what distance the object is.

 In case that the radar would show a failure, they had devised something very "efficient"! There is another technique than the radar which also allows to measure the distance between two spaceships, provided that these spaceships are active vehicles (that is equipped with a transponder); this technique is called "VHF ranging". The first spaceship inserts a ranging bip into the transmission it sends to the second vehicle; the second vehicle receives this transmission, extracts the ranging bip, and inserts it into the transmission it sends back to the first vehicle; the first vehicle receives this transmission, and measures the time between the emitted bip and the received bip (which has traveled the double of the distance between the two vehicles); knowing that the transmission travels at the speed of light, this time allows to calculate the distance between the two spaceships. They say: "Onboard the CSM, the Command Module Pilot was also taking distance and relative position marks of his own. Distance information to the LM was obtained from a VHF ranging system, where the LM broadcast a signal in the VHF frequency band that was received by the CSM's transponder." But, this is perfectly absurd, because the signal has been emitted from the LM and not the CSM, so the CSM's transponder only knows when it receives the signal, and not when it has been transmitted, and, without this information, it cannot deduce the distance of the LM; it may always retransmit the VHF signal, but that won't help it, because it will receive no echo for this retransmission.

 And for the orientation, they have imagined to use a sextant. The principle of a sextant is that if allows to measure the angle of a spatial object relatively to a reference which is the horizon line. The problem is that, in order for the sextant to be usable, the horizon line must remain perfectly stable. If the moon's horizon line moves because the attitude of the CSM varies, then the CM's operator will be unable to use the sextant. There also is a maximal angle to use the sextant, and if the LM is beyond this angle, its orientation cannot be measured by the sextant either. And even if the conditions to use the sextant are met, measuring with a sextant is not a fast operation; it will take at least several seconds to the astronaut, even if he is well trained. If moreover he has to do manual operations to exploit the measured angle, it is obvious that computing the position of the LM will be far from being a quick operation; when the spacecrafts are still far from each other, it may not be critical, but it will be when they come close to each other.

 They say that the alignment of the guidance platform was done using the Moon's gravity as a vertical reference, and a star as its other reference. A star? I thought stars were not visible from the moon, so said the astronauts! An Apollo fan told me that the astronauts could see through the optics the stars they could not see with the naked eye! Let's assume so. The guidance platform measures in a three dimensional system, so it needs three references for a correct alignment. One might think that the moon gravity gives a double reference, because it gives the plane which is perpendicular to it, but this plane only has a local meaning; if you take two different points on the moon, the plane which is perpendicular to the moon gravity is different; so, in an absolute system, the moon gravity only gives one reference point (the direction of the moon's center). So, moreover the moon gravity (the direction of the moon's center), two other reference points are still needed, and these two other points will be two different stars. So, it is not one star that Armstrong needs to take as a reference, but two stars, and two stars easily identifiable, like in the constellation of the big bear (and as it must be two stars not too close to each other, it should be stars from different constellations). So, where is the second star? And what is the star Armstrong took as a reference?

 They say that the crew provides values for the insertion velocity parameters and verifies stored attitude parameters. On what basis does the crew provide these values? Couldn't these values be known in advance? And if these values were communicated from Houston, couldn't these values be directly given to the computer without the intervention of the crew, which would have been safer?

 They also say that, as the LM is ascending, it suddenly pitches in an important way. They say that this may be disconcerting to people who are used to see rockets rotate gradually and not make a brutal pitch, but this is because, in earth's atmosphere, rockets must "keep the pointy end into the wind"! This is of course a completely ridiculous explanation (and intended to be!). The LM must certainy not do a sudden pitch, because if it was doing it, it would not counter the lunar attraction with its engine, and, as the centrifugal force is not still strong enough to counter it, the LM would stop its ascension and start falling down. The rotation of the LM must absolutely be slow and regular. This explanation makes me think of what Apollo fans told me when I gave them the example of an obus of which its orientation was following its trajectory. To my great surprise, they told me that it was because of "deflection of air". The poor guys have apparently never heard about the torque effect.

 They say "The spacecraft's center of gravity must be over the thrust line of the ascent engine within a small margin, otherwise the RCS system will have to work especially hard to keep the vehicle on course". If the center of gravity is on the thrust line, it can be anywhere on this line. The problem is not if the center of gravity is over the thrust's line, but if it is laterally shifted relatively to this line, because in that case, it will create a lever effect which will make the LM rotate (rotation which should then be contradicted with the lateral engines of the RCS, which would effectively give them a hard work).

 They say "The LM's crew checks to see if there are any out-of-plane corrections that need to be made to match the the LM and CSM's orbital planes". Normally it should be up to the guidance system to do it at the appropriate moment that is at the intersection of the CSM's and LM's orbital planes. If the guidance system can't take the good decisions, what is it good for?

 They say "To aid the CSM's tracking of the LM, the CMP runs Program P76, LM Target Delta V. As input, the CMP gives P76 the key parameters of the LM's burn, the time of ignition and the expected velocity components in all three axes". This is completely ridiculous: These LM's parameters are supposed to make it follow a trajectory, so the CSM just has to follow this trajectory. And if the LM fails to follow this trajectory, the trajectory computed by the CMP will not correspond with the LM's actual trajectory, but with the expected trajectory instead.

 They say "Such information (for the attitude of the CSM) is necessary if the computer is to maintain attitude where the transponder is pointed at the LM's rendez-vous radar Antenna and so that the sextant can be driven to where the LM should appear in the field of view". This is perfectly ridiculous: The transponder does not have to be pointed toward the LM's radar, it is the LM's antenna which has to be oriented toward the CSM, the transponder will retransmit the signal emitted by the LM's radar whatever its orientation relatively to the LM's rendez-vous radar Antenna, provided that the latter is correctly oriented toward the CSM. And what's for the sextant, it will be unusable if the attitude of the CSM is not perfectly stable, because the horizon's line of the moon will move, which will prevent the CMP from taking it as a reference. The CSM doesn't have to modify its attitude for such stupidities. Its attitude only depends on its normal maneuvers.

 They say "As the LM is now approaching the point where the two orbital planes intersect, the crew must decide whether the out-of-plane component is sufficiently large to justify a special burn, or if the error can be corrected during subsequent maneuvering". And how do they decide it? With dices? If there is an out-of-plane correction to make, it has best be immediately corrected at the intersection of the orbital planes.

 They say "Near the time for the plane change burn, the LM emerges from behind the dark side of the moon, and is still below and behind the CSM. Once in the sunlight, the tracking beacon is turned off, as the light would be washed against the lunar surface below. Q: Can the CSM see the LM now?" Because the CSM could not see the LM before in the darkness with its beacon on? It's a common fact that a car can be better be localized in the night with its lights on than in full day with its lights off.

They say "The LM PGNS is generally more accurate than the AGS, and any source is better than the backup charts".
I really wonder why the astronauts bother to use their charts; I doubt they are very useful to them.

They say "If a set of solutions for the next maneuver do not settle into a narrow range of values, or disagree significantly with the solutions from other sources, they are disregarded".
And what if the most reliable source disagrees from the other less reliable sources which agree with each other?
It may be a dilemma to know which solution to use!
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 They say "An entry "410+10000" on the DEDA starts CDH computations on the AGS. Can't the AGS start these computations on its own when it's time to do them? What if the astronaut doesn't remember what to type to start these computations, or mistypes what he has to type?

 They say "The invocation of one program automatically terminates the currently running one". What they say is that, when a program X is currently running and a request is made for Program Y, Program X is immediately terminated, whatever the point it is currently at, and Program Y is immediately executed. It may be a big problem if Program X has something important to do which must be entirely done to be operational. This is not the way it should work: If a request is made for Program Y, it should be queued and wait for Program X to normally terminate, which will automatically begin the processing of Program Y. Or there should be a way for Program X to indicate when it can be interrupted.

 They say "However, while P20 is active, it will remain running in the background when the various targeting programs (such as P33 here) are started". This is fantasy, because the AGC has no capabilities of multitasking. The AGC has no stack and no real-time kernel (and a real-time kernel needs a stack), and thence cannot execute two tasks simultaneously.

 They say "But the CSM's orbit is usually a bit elliptical due to the effects of mascons perturbing the orbit and the fact that the moon, like the earth, is not perfectly spherical". They say this like it only had an effect on the CSM and not the LM; it acts exactly the same on the LM.

 They say "During the last phase of rendezvous, the CMP has selected P79 to align the CSM with the LM ascent stage for docking". It seems that the AGC has to be systematically told what it has to do, and is totally unable to take initiatives from its own. Yet, it is supposed to track the CSM and it should know when it is time to make this alignment.

 They say "Several minutes of "station keeping" or orbital information flying are performed to allow the crews to photograph each others spacecraft". The problem is that the astronauts of the LM don't have the CM in their field of view during these minutes; they can always photograph the moon instead!

 They say "As crews stayed longer on the surface, the Moon's slow rotation moved the landing site away from the CSM's orbital plane, and beyond the capabilities of the LM to change orbital planes". The fact that the moon is rotating on itself should not be a problem is the CSM orbits the moon in the orbital plane of the moon's rotation (and this is besides what it has better do). The landing site will not move away from the CSM's orbital plane for it will remain in the CSM's orbital plane. But, even if the CSM does not exactly orbit in the orbital plane of the moon's rotation, it has all the time to make continuous corrections during the stay of the LM on the moon so that the LM does not have to do an important change of orbital plane to join the one of the CSM!

 They say "If the orbital parameters were significantly off, or if there was a failure of the LM's guidance and navigation's systems, a "bail-out" maneuver might be recommended. A bail-out burn would place the LM into an orbit higher than that of the CSM. The CSM now in the lower faster orbit is now on position to become the active vehicle in the rendezvous". It may seem a good idea, but it is not a so good one, in fact. Why? Because, if the LM is failing, it does not control things properly, and it may arrive on the higher orbit anywhere, behind the CSM, for instance; the CSM will then have to do a full rotation of the moon to catch up with the LM. If the LM remains in an orbit lower than the one of the CSM and is behind the CSM, the CSM waits for the LM to overpass it, then goes to an orbit lower than the one of the LM, then maneuvers up again to the orbit of the LM to catch up with it; that way it won't have to do a full revolution of the moon.

 They say "During the prelanding checks on Apollo 14, an errant solder ball in the Abort pushbutton was intermittingly triggering the abort discrete in the computer". Isn't it incredible that, in an as big project as the Apollo one, they can be so careless as to let a solder ball create problems in an as important button as the Abort button is? If this had happened in the "real" mission, it could have had dramatic consequences! (But there was no real mission).

 They say "Aborts can also be initiated through directly entering the abort program number through the DSKY (Program 71 for aborts using the DPS, Program 72 for APS aborts), but given the likely time pressures of the situation, simply hitting the abort button is generally the easiest way of recovering from a bad situation". The problem is that, according to the technical documentation, the AGC has no way to directly command the abort, it has no output on the communication channels to do it. Another problem is that the astronaut can press either of the two abort buttons in whichever situation. If the LM is close to the moon, it is too late to do an abort with keeping the descent stage, the descent stage should be dropped; that means that, at this moment, only the "ABORT STAGE" button should be operational, and the Abort button (whick keeps the descent stage) should not be accepted; if, in this situation, the Abort button is accepted, it could have dramatic consequences, because the LM could be unable to return to the CSM with its descent stage attached. Now, if we consider that confirming the abort adds too much delay to the acceptance of the Abort maneuver, a solution could be to have an unique Abort button which would take the good decision of aborting with or without the descent stage according to the fact that the LM is at the beginning or the end of the descent; this abort button would be completely separated from the other controls, to be sure it can't be pressed by mistake.

 They say "By simply flipping the guidance control switch, control of the LM is taken away from the PNGS, and places the AGS in control". The problem is that it is not an as simple maneuver as it seems; the change of control should only be made when there is no doubt that the AGC has become inoperational; if the control is changed as the AGC is still operational, it will introduce a perturbation in the guidance of the LM. That is why this change of control should be made in a more secure way than the flip of a simple switch.

 They say (about the AGS) "Far less capable than the PGNS, with specifications so meager that at the at first glance they seem to be a typographical error, the AGS nonetheless was capable of placing the LM into orbit, and calculate all the necessary maneuvers for rendezvous, plus maintain control of the spacecraft attitude. All with only 4096 words (!not kilobytes, nor megabytes and certainly not gigabytes - just 4,096 15-bits words) of memory, and a processor that was several times slower than a 1970's era Apple II computer." What a marvel! They forgot to say that it could also do coffee! So the AGS was doing even better than the more powerful AGC with corrections from the astronauts! If you don't see they are mocking at us, you seriously lack common sense!

 They say "Because, during descent, the LM is slowing down and the CSM is moving ahead, any abort and subsequent rendezvous is complicated by the fact that the two spacecrafts are now significantly out of position for a either of the rendezvous solutions described above. Because the CSM is so far ahead, the best solution is to let it continue around and catch from behind. To do this, the traditional roles are reversed, and the LM boots itself into a higher, 115-45 nautical mile orbit. With the LM in the slower orbit, the CSM "catches up" from below after two revolutions. Once proper phasing angles are restored, the LM lowers its orbit to circular, 45 nautical mile orbit. Hence the beauty and simple elegance of the rendezvous design becomes apparent. Even after a very bad day, with an abort resulting with the two spacecraft in very different orbits, we have recovered to the point where we can use the standard coelliptic rendez vous technique". Why is this absurd? Because, if the CSM orbits from below to catch up with the LM, it can play the role of the active vehicle, directly arrive on the orbit of the LM and dock to it. It is then useless for the LM to do the rendezvous maneuver itself since the CM can logically do it when it catches up with the LM. Unless the LM is a prima donna which can't stand the CM making the rendezvous maneuver and absolutely wants to do the rendezvous maneuver itself!

 They say "The external Delta V series of programs use data relayed from the ground and includes the velocity to be gained, the time and duration of the burn, and the attitude of the spacecraft". The ground provides the LM with more parameters than it needs: It doesn't have to specify the duration of the burn, for this can be determined by an internal loop of the AGC which will stop the engine when the desired velocity is attained. ...Unless this information is provided in case the computer would fail; that shows a lack of trust in the onboard computer.

 They say "Program 40 is for burns with the descent propulsion system, Program 41 uses the RCS plus X thrusters, and Program 42 is for burns with the ascent engine". Why does it make no sense to have separate programs for the propulsion engines? The lateral thrusters allow to control the attitude of the LM; this attitude is important for it allows to distribute the thrust of the main engine (whether it is the descent or ascent engine) on the horizontal and vertical axes; the control of the main thrust and the thrust of the lateral engines of the RCS can't be separated, they constitute a whole which must be simultaneously controlled. This is why it is absurd to have separate programs to control them, they should be controlled by a unique program. This is especially true since the AGC is not able to make multi processing... ..but is only able of processing the tasks sequentially!