A planet is revolving around the sun. its distance from the sun at apogee is `r_(A)` and that at perigee is `r_(p)`. The masses of planet and sun are 'm' and `M` respectively, `V_(A)` is the velocity of planet at apogee and `V_(P)` is at perigee respectively and `T` is the time period of revolution of planet around the sun, then identify the wrong answer.

Options

A. `T^(2)=(pi^(2))/(Gm)(r_(A)+r_(P))^(3)`
B. `T^(2)=(pi^(2))/(2GM)(r_(A)+r_(p))^(3)`
C. `v_(A)r_(A)=v_(P)r_(P)`
D. `v_(A)ltv_(P), r_(A)gtr_(p)`

Answer

A

Explanation

`T^(2)=(4pi^(2))/(GM)[(r_(A)+r_(P))/2]^(3) ( :' r=(r_(A)+r_(p))/2)`
By the law of conservation of angular momentum `v_(A)r_(A)=v_(P)r_(P)`