Question

If a planet is revolving around the sun in a circular orbit in uniform circular motion, then the centripetal force acting on the planet towards the sun must be mv^2/r where, m is the mass of the planet, v is it's speed and r is it's distance from the sun​

Answer 1

Explanation:

Correct option is A)

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

2r 2 /T 2=GM/r

r

3

/T

2

=GM/4π

2

M=4π

2

r

3

/GT