Kepler's Laws

What
Kepler's laws describe plantary motionlanet orbits

Kepler's First Law
A planet orbits the Sun in an ellipse, with the sun at one focus of the ellipse

Kepler's Second Law
A line connecting a planet to the Sun sweeps out equal areas in equal time intervals

$$v^2 = G(m_1 + m_2)(\frac {2}{r} - \frac {1}{a})$$

where $$r$$ is the distance from the principal focus

Kepler's Third Law
This law is also known as the harmonic law, relates the period of orbit to the average distance of the planet from the sun

$$P^2 \propto a^3$$

Using Newton's form of the equation, we get that

$$P^2 = \frac {4 \pi^2}{G(m_1 + m_2)} a^3$$

Note that the units of $$P$$ are in years and the units of $$a$$ are in AU