Question

Deriveting for orbital speed of a satellite

Answer 1

Multiply both sides by GMr  − − −  √  

GMr

:

T×GMr  − − −  √ =2πr  

T×GMr=2πr

Square both sides:

T 2 ×GMr =(2πr) 2  

T2×GMr=(2πr)2

Divide both sides by GMr  

GMr

:

T 2 =(2πr) 2 GMr    

T2=(2πr)2GMr

Clean it up:

T 2 =(2πr) 2 ×rGM  

T2=(2πr)2×rGM

Take out r  

r

to get the final answer:

T 2 =(2π) 2 GM r 3  

T2=(2π)2GMr3

If you take out the constant you get Kepler's law (as Ross Millikan said):

T 2 ∝r 3  

T2∝r3