What is a satellites distance from the surface of earth?

Question

A satellite orbiting earth has a orbital period of 3.2h.

Answer 1

Student,

 

I will explain the steps, but YOU do the calculations.  Start by converting the period T to seconds, so you can work in the MKS system of units.  Assuming a circular orbit,

 

r = radius of orbit = distance from center of earth (we will get height h from r later)

M = mass of earth (look it up in kg)

G = constant of universal gravitation (look it up in Nm²/kg²)

R = radius of earth (look it up in meters)

v = speed in circular orbit = 2πr/T

 

v²/r = GM/r² (centripetal acceleration under gravitational force)

 

(2πr/T)²/r = GM/r²

 

4π²r²/(rT²) = GM/r²

 

Solve for r and get

 

r = [GMT²/(4π²)]^1/3

 

Finally,

 

h = r - R = [GMT²/(4π²)]^1/3 - R

 

Now just plug in the numbers and get h in meters.