kepler laws notes

First Law – Law of the Ellipses

Second Law – Law of Equal Areas

Third Law – Law of Harmonics

Kepler's First Law - The Law of Ellipses

1) An ellipse is a closed, curved shape that is defined by two foci

2) While the Earth makes a big circuit each year, the Sun also makes, a very small one, around the Sun-Earth center of gravity.

3) The long one is called the major axis, and the short one is called the minor axis

4) The shape of an ellipse is measured by its eccentricity – Whether it is like a circle or oval

5) Eccentricity can be from 0 ( a circle) to .95 (almost a line)

Kepler's Second Law - The Equal Areas Law

1) The motion this law describes also tells us that the average distance from a planet to the Sun is equal to the length of the semi-major axis

2) The line connecting the Sun to a planet sweeps equal areas in equal times.

3) Although the orbit is symmetric, the motion is not. A planet speeds up as it approaches the Sun, gets its greatest velocity when passing closest, then slows down again.

What would happen if the Earth’s orbit was a Circle?

Kepler's Third Law: The Harmonic Law1) There is a relation between the time of a planet's orbit and its distance from the Sun:

2) The revolution of the planet squared is equal to the semi-major axis cubed

P2=a3

Where P is the orbital period in Earth years and a is the length of the semi-major axis (average distance from the Sun) in Astronomical Units.