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`.

Explanation

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`