Zenith telescope is used in case of obtaining high precision in measurement of star positions. It involves simplification of telescope construction. The actual purpose of designing it involves in management of zenith.

The area of spherical triangle can be given by
A = ?R²E / 180. On substitution, we get
A = ?*43²*186.54 / 180
A = 6019.85 sq. m.

The formula for green witch mean time can be given as
G.M.T = L.M.T ± longitude of place. The sign plus or minus depends upon direction of longitude, towards east plus and towards west minus.

Celestial sphere is an assumption in which it is assumed that stars lie on it. The radius of sphere can be of any value that means it is varying. Because of fact that stars are far from us, we assume centre of earth as centre of celestial sphere.

The corrected azimuth can be determined by summation of azimuth with correction applied.
Correction = b*tan ? = 23*tan 29?42?31?? = 13?7?24.8??. On summation,
Corrected azimuth = 54?32?15?? + 13?7?24.8??
Corrected azimuth = 67?39?39.78??.

Relation between co-ordinates must be established in such a way that y might form a relation. In case of altitude and latitude, y must be equal so that y can satisfy required relation in case of solving problem.

The G.M.T calculation can be done by using formula,
G.M.T = L.M.T + longitude. On substitution, we get
G.M.T = 9^h 24^m 17^s + 10^h 23^m 32^s
G.M.T = 19^h 47^m 49^s.

Though zenith telescope is capable of providing required information, it is an old age method. In modern technique, radio astronomical quasar is adopted which can acquire information within minutes.

The difference can be calculated by
B ? A = 160?- 30? = 130?. In case of change in direction, angle must be subtracted or multiplied with 180. This will help in change in its direction.

The dependent co-ordinate system contains two co-ordinates off which first co-ordinate is depended on observer?s position and second is independent of it. Here, first co-ordinate represents hour angle and second one represents declination.