Let the speed of the planet at the perihelion `P` in figure be `v_(P)` and the Sun planet distance `SP` be `r_(P)`. Relater `r_(P), v_(P)` to the corresponding quantities at the aphelion `(r_(A),v_(A))`. Will the planet take equal times to transverse `BAC` and `CPB`?

Options

A. `r_p/r_a = v_p/v_a`
B. `(r_p^2)/(r_a^2) = (v_a)/(v_p)`
C. `v_p/v_a = r_a/r_p`
D. `(v_p^2)/(v_a^2) = r_a/r_p`

Answer

C

Explanation

At the perihelion `r_p` and `v_p` are mutually perpendicular. So `r_a` is normal to `v_a` . The angular momentum is conserved,
`therefore m v_a r_a = mv_p r_p rArr v_p/v_a = r_a/r_p`