## E3 - - - Spherical Coordinates - - - 10/03/2004

The position of a star (or other celestial object) on the surface of the celestial sphere may be located in several ways. In each case two great circles are taken as standards of reference, and the position of the star is determined by means of two quantities called spherical coordinates.

The declination-right ascension system. (used by astronomers)
If we consider as great circles of reference the celestial equator and the hour circle (meridian) through the vernal equinox, the coordinates of the star are its declination and right ascension.

The vernal equinox (first point of Aries) is the intersection of the equator with the annual path of the sun in March as the declination of the sun changes from South to North. (The autumnal equinox is in September).

The declination is the angular distance north or south from the celestial equator measured along a great circle passing through the celestial poles.

The right ascension of a star is the angle between the meridian of the vernal equinox and the meridian of the star measured eastward from from the vernal equinox 0 to 360 degrees, or in hours from 0 to 24 hours.

The declination-Sidereal Hour Angle system. (used by navigators)
If we consider as great circles of reference the celestial equator and the hour circle (meridian) through the vernal equinox (as above), the alternate coordinates of the star are its declination and Sidereal Hour Angle (S.H.A.).

This is similar to the declination-right-ascension system (see above) but the S.H.A. is measured westward from the vernal equinox to the meridian of the star (0 to 360 degrees).

The declination-Greenwich hour angle system
If we consider as great circles of reference the celestial equator and the hour circle (meridian) through Greenwich , the coordinates of the star are its declination and Greenwich Hour Angle (G.H.A.)

The G.H.A. of a star is the angle between the meridian of Greenwich and the meridian of the star measured westward from from the Greenwich meridian 0 to 360 degrees. The G.H.A. of the sun, moon, planets, and Aries (vernal equinox) may be found for any hour of the year in the nautical almanac.

The declination-hour angle system.
If we consider as great circles of reference the celestial equator and the meridian of the observer, the coordinates of the star are its declination and Local hour angle ( L.H.A. or t ).

The Local hour angle is the angle between the celestial meridian of an observer and the hour circle of a celestial object.

The altitude-azimuth system.
If we consider as great circles of reference the horizontal plane at the position of the observer, and his celestial meridian, the coordinates of the star are its altitude and azimuth. If we know these we can locate the star.