Kepler's laws describe the motion of planets: 1) Planets orbit the sun in ellipses with the sun at one focus. 2) A line connecting a planet to the sun sweeps out equal areas in equal times. 3) The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit.

2. First Law –
Law of the Ellipses
Second Law –
Law of Equal Areas
Third Law –
Law of Harmonics

3. 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.

4. 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)

5. 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.

6. 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?

7. Kepler's Third Law: The Harmonic Law
1) 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
P
2
=a
3

8. 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.