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A planet P revolves around the Sun in a circular orbit, with the Sun at the center, which is coplanar with and concentric to the circular orbit of Earth E around the Sun. P and E revolve in the same direction. The times required for the revolution of P and E around the Sun are T P and T E . Let T s be the time required for P to make one revolution around the Sun relative to E: show that l/T s = 1/T E - 1/T p , Assume T p ; > T E .

A planet P revolves around the Sun in a circular orbit, with the Sun at the center, which is coplanar with and concentric to the circular orbit of Earth E around the Sun. P and E revolve in the same direction. The times required for the revolution of P and E around the Sun are TP and TE. Let Ts be the time required for P to make one revolution around the Sun relative to E: show that l/Ts = 1/TE - 1/Tp, Assume Tp; > TE.

Grade:10

2 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
235-2171_1.PNG
shifa
17 Points
2 years ago
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.
THANK YOU!!☺️
ALL THE BEST.
 

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