The kinetic energies of a planet in an ellipt | vedclass

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(B) According to Kepler's second law of planetary motion,the areal velocity of a planet is constant. This implies that the planet moves faster when it

Vedclass · Accepted Answer

$K_A > K_B > K_C$

Vedclass · Answer

(B) According to Kepler's second law of planetary motion,the areal velocity of a planet is constant. This implies that the planet moves faster when it is closer to the Sun and slower when it is farther away.Point $A$ is the perihelion (closest to the Sun),and point $C$ is the aphelion (farthest from the Sun). Point $B$ is at an intermediate distance.Therefore,the orbital speeds at these positions follow the relation: $v_A > v_B > v_C$.Since the kinetic energy $K$ is given by $K = \frac{1}{2}mv^2$,it is directly proportional to the square of the speed $(K \propto v^2)$.Thus,the kinetic energies at these positions follow the relation: $K_A > K_B > K_C$.

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 $S$ as shown in the figure. Then

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