let the period of revolution of a planet at a distance R from a star be T. Prove that if it was a diatance of 2R from the star, it's revolution will be √8T
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Qᴜᴇsᴛɪᴏɴ:- let the period of revolution of a planet at a distance R from a star be T. Prove that if it was a diatance of 2R from the star, it's revolution will be √8T
Aɴsᴡᴇʀ:- According to Kepler's third law, The square of orbital period of revolution T of a planet around a star is directly proportional to the cube of the mean distance R of the planet from the star. Thus, for a planet, at a distance of 2R from the star, its period of revolution will be √8 T.
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According to Kepler’s third law
T
2
∝a
3
T is time period of planet and a is semi major axis of its orbit.
So, according to question
T
2
=kR
3
..........(1)
When distance is 2R then
T
′
2
=k(2R)
3
T
′
2
=8R
3
k...........(2)
Taking ratios of (1) and (2)
T
′
2
T
2
=
8R
3
k
kR
3
T
′
2
T
2
=
8
1
T
′
2
=8T
2
T
′
=
8
T
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