Question

A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Calculate the radius of such an orbit.

1. Based on T=2(pi)SQRT(r^3/GM)

2. Based on the data for the moon: average orbital radius 3.85x10^5 km, orbital period 27.3 days.

Answer 1

As orbital period is given as,

T = 2*π*√(r³/G*M)

where T is orbital period, r is radius of orbit, G is gravitational constant, M is the mass of the central body.

given :- T = 1 day

as Mass of the earth ea not given instead of which we have provided the data for moon so, first we find the mass of earth using that information.

27.3² = 4*π²*(3.85*10^8)³/(M*G)

M*G = 3.30 * 10^-25

using this value for that geosynchronous satellite,

1 = 4*π²*r³/(3.3 * 10^-25)

r = 9.42 * 10^7 m

thus radius of that orbit is 9.42 * 10⁴ Km.