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NEET PHYSICSEasy

The kinetic energies of a planet in an elliptical orbit around the Sun, at positions A, B and C are KAK_A, KBK_B and KCK_C respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S, as shown in the figure. Then:

A

KA>KB>KCK_A > K_B > K_C

B

KB>KA>KCK_B > K_A > K_C

C

KA<KB<KCK_A < K_B < K_C

D

KB<KA<KCK_B < K_A < K_C

Step-by-Step Solution

According to Kepler's Second Law (Law of Areas) and the conservation of angular momentum, a planet moves faster when it is closer to the Sun and slower when it is farther away.

  1. Point A (Perihelion): This is the point closest to the Sun on the major axis. Here, the distance rAr_A is minimum, so the speed vAv_A is maximum. Consequently, the kinetic energy KAK_A is maximum.
  2. Point C (Aphelion): This is the point farthest from the Sun on the major axis. Here, the distance rCr_C is maximum, so the speed vCv_C is minimum. Consequently, the kinetic energy KCK_C is minimum.
  3. Point B: This point lies at the end of the semi-latus rectum (perpendicular to the major axis at the focus). Its distance rBr_B is intermediate between rAr_A and rCr_C (rA<rB<rCr_A < r_B < r_C). Therefore, the speed and kinetic energy are also intermediate.

Thus, the order of kinetic energies is KA>KB>KCK_A > K_B > K_C.

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