Question

Conversation of linear momentum is a necessary condition for which Kepler's laws?

Answer 1

The conservation of linear momentum is a necessary condition for Kepler's Second Law, also known as the Law of Equal Areas.
Kepler's Second Law states that the line segment connecting a planet to the Sun sweeps out equal areas in equal time intervals. This means that as a planet orbits around the Sun, it covers equal areas in its orbital path over equal time intervals.
The conservation of linear momentum is necessary to understand this law because the angular momentum of a planet remains constant as it moves in its elliptical orbit around the Sun. Angular momentum is related to linear momentum, and when linear momentum is conserved, angular momentum is also conserved.
In the absence of external forces, conservation of linear momentum implies that the planet's velocity will change as it moves along its elliptical orbit. As the planet approaches the Sun, it speeds up, and as it moves away from the Sun, it slows down. This change in velocity ensures that the area swept by the line segment connecting the planet to the Sun remains constant over equal time intervals, fulfilling Kepler's Second Law.
Therefore, the conservation of linear momentum is a necessary condition for Kepler's Second Law, which describes the equal areas law.