Second Law
- "A line joining a planet and the Sun sweeps out equal areas during equal intervals of time."
In a small time the planet sweeps out a small triangle having base line and height .
The area of this triangle is given by
and so the constant areal velocity 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. So the planet has to move faster when it is closer to the Sun so that it sweeps equal areas in equal times.
The total area enclosed by the elliptical orbit is
- .
Therefore the period
satisfies
or
where
is the angular velocity, (using Newton notation for differentiation), and
is the mean motion of the planet around the Sun.
Read more about this topic: Kepler's Laws Of Planetary Motion
Famous quotes containing the word law:
“There are no fixtures in nature. The universe is fluid and volatile. Permanence is but a word of degrees. Our globe seen by God is a transparent law, not a mass of facts. The law dissolves the fact and holds it fluid.”
—Ralph Waldo Emerson (1803–1882)
“We ourselves are Jews by birth and not Gentile sinners; yet we know that a person is justified not by the works of the law but through faith in Jesus Christ. And we have come to believe in Christ Jesus, so that we might be justified by faith in Christ, and not by doing the works of the law, because no one will be justified by the works of the law.”
—Bible: New Testament, Galatians 2:15-16.