I'm really struggling trying to understand what formulas to use for the following:

Question

A satellite orbits the earth with a radius of 7000 km. (a) what is the acceleration of gravity at this distance? (b) what is the velocity of the satellite? (c) how long does it take the satellite to make one orbit.
Can someone help please?

Answer 1

the radius of the Earth is ... 6371 km

g (at the surface) is ... 9.81 m/s²

(a) using the inverse-square relation
... a / g = (7000/6371)²

(b) the velocity of the satellite is
... v² / r = a ... v = √(a²/r)
... keep the units consistent by converting a to km OR r to m

(c) use the velocity from (b)
... t = d / v
... the distance is the length of the orbit ... 2 * π * 7000 km
... once again, keep the units consistent

Answer 2

Thank you