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 sqrt(8)T.

Let the period of revolution of a planet at a distance R from a star b

1.	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 sqrt(8)T.
Answer» Solution :Given: DISTANCE from sun `=R` TIME to ROTATION `=T` New distance `=2R` To find: New time `T_(N)=?` FORMULA: `(T^(2))/(R^(3))=k` Solution: Case (i) `(T^(2))/(R^(3))=k`…..i Case (ii) `(T_(N)^(2))=k` or `(T_(N)^(2))/(8R^(3))=k`............ii From i and ii `(T_(N)^(2))=(T^(2))/(R^(3))` `T_(N)^(2)=8T^(2)` `T_(N)=sqrt(8T^(2))` `T_(N)=sqrt(8)T`