T² = (4π²r² / GMe) r³, how do you do this for earth revolving around the sun?
Answers
Explanation:
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.
Answer:
Explanation: The forces that work upon the body are the Gravitational force and centripetal force both radially inwards...Now see, it is the gravity which creates the centripetal force..therefore Fg =Fc