Question

Kepler's second law is a consequence of
A. Conservation of kinetic energy
B. Conservation of linear momentum
C. Conservation of angular momentum
D. Conservation of speed.

Answer 1

Kepler gave three laws and they were important in the field of astronomy. Working on such laws only Newton was able to come up with the Famous law of gravitation. According to Kepler's second law all planets move around the sun in elliptical orbits. We know unlike circular orbits which have only one centre, elliptical orbits have two foci.

Complete answer:
The second law states that the sun remains at one of the two foci of the elliptical orbits always. So, when the planet is moving around the sun in such elliptical orbit, when it comes near to the sun its velocity increases and when it goes far off from the sun its velocity decreases.

Thus, the areal velocity remains constant and we know that the law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur. As external torque acting is zero, the angular momentum remains conserved.

Hence option C is the correct answer.

Note: Angular momentum of a rotating body is a parameter which is product of its mass counterpart in linear motion that is moment of inertia and angular velocity. Just as in linear motion of bodies, external Force equals rate of change of linear momentum, its rotational counterpart is external torque which equals rate of change of Angular momentum.