Question

derivation of time period of satelite​

Answer 1

I've worked it out again, this is my working:

I put Newton's law of gravitation and the centripetal force equation equal to each other:

GMmr2=mv2r

Multiply both sides by r:

GMmr=mv2

Sub in v=2πrT for v:

GMmr=m(2πrT)2

Divide both sides by m:

GMr=(2πrT)2

Root both sides:

GMr−−−√=2πrT

Flip both sides and divide by 2πr:

T=2πrGMr√