Question

Derive expressions for a planet revolving around sun in circular motion irrespective of its time of revolution?

Answer 1

Answer:

See here's your answer

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Answer 2

Answer:

According to LAW STATED BY KEPLER

T

2

∝R

3

It is known as Law of periods.

Let us consider a planet P of mass m moving with a velocity v around the sun of mas M in a circular orbit of radius r.

The gravitational force of attraction of the sun on the planet is,

F=GMm/r

2

The centripetal force is, F=mv

2

/r,

euqating the two forces,

mv

2

/r=GMm/r

2

.

v

2

=GM/r−−−−−−−−−−(i)

If T be the period of revolution of the planet around the sun, then

v=2π/T−−−−−−−(ii)

Substituting (ii) in (i)

4π

2

r

2

/T

2

=GM/r

r

3

/T

2

=GM/4π

2

M=4π

2

r

3

/GT