+1 vote
39 views

4. Let the period of revolution of a planet at a distance R from a star be T. Prove that if it was at a distance of 2R from the star, its period of revolution will be \(\sqrt8\) T.

in Chapter 1: Gravitation by (5.4k points)
reopened by | 39 views

1 Answer

+1 vote
Best answer

Thus, when the period of revolution of the planet at a distance R from a star is T, then from kepler's  third law of planetry motion, we have

\(T^2\propto R^3 \space\space\space\space.........(1)\)

now , when the distance of the planet from the star is 2R, then its period of revolution becomes

\(T_1^2\propto(2R)^3\)

\(T_1^2\propto8R^3 \)    ........(2)

Dividing equation 2 by 1

\(\tfrac{T_1^2}{T^2}=\tfrac{8R^3}{R^3}\)

\(T_1^2= 8 T^2\)

\(\therefore T_1=\sqrt8T\)

 

Video solution 

by (5.4k points)
500 questions
477 answers
8 comments
12 users