Kepler's+Second+Law+(1609)




 * An imaginary line joining a planet and the sun sweeps out an equal area of space in equal amounts of time.**

"A [|line] joining a planet and the sun sweeps out equal areas during equal intervals of time."[|[1]] Symbolically: where is the "areal velocity".

The line joining the Sun and planet sweeps out equal areas in equal times, so the planet moves faster when it is nearer the Sun. Thus, a planet executes elliptical motion with constantly changing angular speed as it moves about its orbit. The point of nearest approach of the planet to the Sun is termed //perihelion//; the point of greatest separation is termed //aphelion//. Hence, by Kepler's second law, the planet moves fastest when it is near perihelion and slowest when it is near aphelion.

This is also known as the law of equal areas. To understand this let us suppose a planet takes one day to travel from [|point] //A// to point //B//. The lines from the Sun to points //A// and //B//, together with the planet orbit, will define an (roughly [|triangular]) area. This same area will be covered every day regardless of where in its orbit the planet is. Now as the first law states that the planet follows an ellipse, the planet is at different distances from the Sun at different parts in its orbit. This leads to the conclusion that the planet has to move faster when it is closer to the sun so that it sweeps an equal area.

Kepler's second law is an additional observation on top of his first law. It is equivalent to the fact that the net tangential force involved in an elliptical orbit, as per his first law, is zero. The "areal velocity" is proportional to angular momentum, and so for the same reasons, Kepler's second law is also a statement of the conservation of [|angular momentum].