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:
“The only law was that enforced by the Creek Lighthorsemen and the U.S. deputy marshals who paid rare and brief visits; or the “two volumes of common law” that every man carried strapped to his thighs.”
—State of Oklahoma, U.S. relief program (1935-1943)
“The very existence of government at all, infers inequality. The citizen who is preferred to office becomes the superior to those who are not, so long as he is the repository of power, and the child inherits the wealth of the parent as a controlling law of society.”
—James Fenimore Cooper (1789–1851)