A geosynchronous satellite is one that stays above the same point on the equator of the Earth.

Question

Such satellites are used for such purposes as cable TV transmission, weather forecasting, and as communication relays. Determine (a) the height above the Earth’s surface such a satellite must orbit and (b) such a satellite’s speed.

(kepler's laws)

Answer 1

Kepler's 3rd Law says that kR³ = T² or, if we are solving for period where k is a constant based solely on the central body's mass:

(T₂/T₁) = (R₂/R₁)^3/2

You can look up the T in days and R of orbit of the moon and solve tor the R of the satellite with a period of 1 day.

The velocity = 2πR/T (remember to convert units as needed)

Good luck!