Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates.
these are called geosynchronous orbits. the altitude of a geosynchronous orbit is 3.58×107m(≈22,000miles).

part a
what is the period of a satellite in a geosynchronous orbit?

part b
find the value of g at this altitude.

part c
what is the weight of a 2000 kg satellite in a geosynchronous orbit?

a) 24 Hs. b) 0.224 m/s² c) 448 N

Explanation:

a) As satellites in a geosynchronous orbits, stay directly over a point fixed on the Equator while the Earth rotates, the only way that this can be possible, if the period of the satellite (time to complete a full orbit) is equal to the time that the Earth uses to complete a spin itself, which is exactly one day.

b)

The value of g, is just the acceleration due to the gravitational attraction between the satellite and the Earth.

According the Universal Law of Gravitation, this force can be written in this way:

Fg = ms . a = G me. ms / (re+rs)² ⇒a=g= G me / (re + rs)²

Replacing by the values of G, me, re, and rs, we get:

g = 6.67. 10⁻¹¹ . 5.97.10²⁴ / (6.37 10⁶ + 3.58.10⁷)² m/s²

g= 0.224 m/s²

c) If we call "weight" to the magnitude of the gravitational force on the satellite (as we do with masses on Earth), we can find this value, just solving the equation for Fg, as follows:

Fg = G me . ms / (re + rs)²

Replacing by the values, we find:

Fg = 448 N