Question

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​

Answer 1

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.

Answer 2

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