Question

derive an expression for orbital velocity of satellite in the orbit reduce if to an orbit close to the Earth surface​

Answer 1

Answer:

combining three equations from my physics text book:

Newton's law of gravitation: F=−GMmr2

The centripetal force equation: F=mv2r

The equation for the speed of an object traveling in a circle: v=2πrT

I wanted to create an equation to find the Time period, T and ended up with: T=2πr2GM Which is wrong...

EDIT

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√

EDIT 2 Which I can simplify:

Multiply both sides by GMr−−−√:

T×GMr−−−√=2πr

Square both sides:

T2×GMr=(2πr)2

Divide both sides by GMr:

T2=(2πr)2GMr

Clean it up:

T2=(2πr)2×rGM

Take out r to get the final answer:

T2=(2π)2GMr3

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

T2∝r3

Answer 2

Answer:

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