Question

Driver Kepler's 3rd law from the assumption that the earth moves in a circular orbit about the sun of radius r = 1.50 ×10^13 cm.use this information to calculate the mass of Sun.

Answer 1

YOUR ANSWER GOES IN THE WAY OF LAW STATED BY KEPLER.

3rd LAW OF KEPLER:

T² ∝R³

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 mass M in a circular orbit of radius r.

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

F=GMm/r².

The centripetal force is,F = mv²/r.

equating the two forces,

mv²/r=GMm/r².

v²=GM/r -----›(i)

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

v=2πr/T-------›(ii)

Substituting (ii) in (i)

4π²r²/T²=GM/r

r³/T²=GM/4π²

GM is a constant for any planet.

•°• T²∝R³.

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