Question

state the law of conservation of angular momentum and illustrate it with the planetary motion?

Answer 1

Conservation of Angular Momentum and
Kepler’s Second Law
Conservation laws are very important laws for
celestial objects in the universe. Without
conservation laws, all these celestial objects will
not obey predictable motions as they do in this
universe. I am going to talk about conservation
of angular momentum in this post.
Any objects orbiting or rotating have angular
momentum. To change angular momentum of
the object, we need to apply a “twisting force”,
or torque. Conservation of momentum holds that
the total angular momentum in a closed system
is always conserved. With no external torque, an
object can only change its angular momentum by
transferring angular momentum to or from other
objects in the system.
Most celestial objects have both orbital angular
momentum and rotational angular. The
conservation of orbital momentum actually
explains Kepler’s second law of planetary
motion. According Kepler’s second law of
planetary motion, as a planet moves around its
orbit, it sweeps out equal areas in equal time.
The formula for orbital angular momentum is:
angular momentum = m*v*r
Where m is the mass of the object, v is the orbit
speed of the object, and r is the radius of the
orbit.
When applied to celestial objects, let’s imagine
Earth orbiting the Sun. Because the angular
momentum is conserved, and mass of Earth is
unchanged, when Earth is closer to the Sun, i.e.
the radius is smaller, the orbit speed must be
greater, and vice versa. As a result, it sweeps
out equal areas in equal time.