Question

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

• A. K_B > K_A > K_C
• B. K_A < K_B < K_C
• C. K_B < K_A < K_C
• D. K_A > K_B > K_C

Hint:

According to Kepler’s 2nd Law of planetary motion, a line segment joining the sun and planet sweeps out equal areas during equal intervals of time.

Answer 1

The Correct Option is D

As per, Kepler's Law - \(dA \over dt\) = constant

As dA/dt is constant, point A is perihelion and C is aphelion. 

So, K_A > K_B > K_C

Read More: Gravitation

Answer 2

Planets move around the sun in orbits without leaving the trajectory due to gravitational force.

According to Kepler’s third law, the square of the time period of the satellite is directly proportional to the third power of the radius of the orbit.

T² ∝ r³

From Kepler’s second law, the areal velocity of the satellite remains constant. 

The planet moves in an elliptical orbit and its velocity will be maximum when its distance from the sun is minimum. 

as mvr = constant = angular momentum.

Since no external force acts on the system, angular momentum is constant. Thus, v_A > v_B > v_C and kinetic energy is directly proportional to velocity.

So, Option D)  K_A > K_B > K_C is correct.

Note: The angular momentum of the planet when it moves around the sun remains constant.

Answer 3

The correct option is K_A > K_B > K_C.

Magnitude of angular momentum of the planet, L = mvr

As a planet has constant angular momentum, its orbital velocity will be inversely proportional to the distance of the planet from the sun.

∴ v ∝ 1/r

Therefore, the minimum velocity of the planet will be at the farthest point and vice versa.

Point A is perihelion and C is aphelion.

∴ vA > vB > vC

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. Then K_A > K_B > K_C.