The kinetic energies of a planet in an elliptical orbit about the Sun, at positions `A,B` and `C` are `K_(A),K_(B)` and `K_(C)` respectively. AC is the major axis and `SB` is perpendicular to `AC` at the position of the sun as shown in the figure. Then

Options

A. `K_(B) gt K_(A) gt K_(C)`
B. `K_(A) lt K_(B) lt K_(C)`
C. `K_(B) lt K_(A) lt K_(C)`
D. `K_(A) gt K_(B) gt K_(C)`

Answer

D

Explanation

When a planet orbit about the sum, the angular momentum of the planet about the sun remains conserved.
`mvr` =constant or `v.r`=constant
it means `v prop1/r`
At position `A`, the distance of the planet from the sun is least and at position `C`, it is largest
Hence speed of the planet is greatest at `A` and least at `C` hence `K_(A)gtK_(B)gtK_(C)`