A planet orbits the sun in an elliptical path as shown in the figure. Let `v_(p) " and " v_(A)` be spped of the planet when at perohelion and aphelion respectively. Which of the following relations is correct ?

Options

A. `(r_(p))/(r_(A))=(v_(A))/(v_(p))`
B. `(r_(p))/(r_(A))=(v_(p))/(v_(A))`
C. `(r_(p))/(r_(A))=sqrt((v_(p))/(v_(A)))`
D. `(r_(p))/(r_(A))=sqrt((v_(A))/(v_(p)))`

Answer

A

Explanation

(a) Angular momentum of planet at P, `L_(P)=m_(P)v_(P)r_(P)`
According to the law of conservation of angular momentum
`L_(P)=L_(A), m_(P)v_(P)r_(P)=m_(P)v_(A)r_(A)`
`or (r_(P))/(r_(A))=(v_(A))/(v_(P))`