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:
“Our law very often reminds one of those outskirts of cities where you cannot for a long time tell how the streets come to wind about in so capricious and serpent-like a manner. At last it strikes you that they grew up, house by house, on the devious tracks of the old green lanes; and if you follow on to the existing fields, you may often find the change half complete.”
—Walter Bagehot (1826–1877)
“These, having not the law, are a law unto themselves.”
—Bible: New Testament St. Paul, in Romans, 2:14.