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:
“Villain, thou know’st nor law of God nor man;
No beast so fierce but knows some touch of pity.”
—William Shakespeare (1564–1616)
“Nobody dast blame this man.... For a salesman, there is no rock bottom to the life. He don’t put a bolt to a nut, he don’t tell you the law or give you medicine. He’s a man way out there in the blue, riding on a smile and a shoeshine. And when they start not smiling back—that’s an earthquake. And then you get yourself a couple of spots on your hat, and you’re finished. Nobody dast blame this man. A salesman is got to dream, boy. It comes with the territory.”
—Arthur Miller (b. 1915)