The kinetic energies of a planet in an elliptical orbit around the Sun, at positions A, B and C are $K_A$, $K_

Question

The kinetic energies of a planet in an elliptical orbit around 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 S, as shown in the figure. Then:

Accepted Answer

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.

Point A (Perihelion): This is the point closest to the Sun on the major axis. Here, the distance $r_A$ is minimum, so the speed $v_A$ is maximum. Consequently, the kinetic energy $K_A$ is maximum.
Point C (Aphelion): This is the point farthest from the Sun on the major axis. Here, the distance $r_C$ is maximum, so the speed $v_C$ is minimum. Consequently, the kinetic energy $K_C$ is minimum.
Point B: This point lies at the end of the semi-latus rectum (perpendicular to the major axis at the focus). Its distance $r_B$ is intermediate between $r_A$ and $r_C$ ( $r_A < r_B < r_C$ ). Therefore, the speed and kinetic energy are also intermediate.

Thus, the order of kinetic energies is $K_A > K_B > K_C$ .

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