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

Answer

B

Explanation

When planet revolves in elliptical orbit around the Sun, then gravitational force of the Sun on planet always acts towards the centre of the Sun, hence it doesn.t produce any torque about this point and thus angular momentum of planet about the centre of the Sun remains constant.
So, mvr = constant `rArr` vr = constant
As shown in figure `r_(A) lt r_(B) lt r_(C ), v_(A) gt v_(B) gt v_(C )`
Kinetic energy of planet is directly proportional to the square of velocity.
So, `K_(A) gt K_(B) gt K_(C )`.
Hence option (b) is correct.