# Kepler's Laws of Planetary Motion

## Kepler's first law

The orbit of every planet is an ellipse with the sun at one of the two foci.

## Kepler's first law

A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

## Kepler's third law

The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

### Kepler's third law formula

\(P^2 = a^2 \)

Where:

\(P\) = planet's distance from the sum

\(a\) = semi-major axis of the planet's orbit

\(G\) = universal gravitational constant

\(t\) = satellite orbit period (time)

\(r\) = satellite mean orbital radius

\(m\) = planet's mass

Solve for:

\(t = \sqrt { \frac {4 \pi^2 r^3} {Gm} }\)

\(r = \sqrt { \frac {t^2 G m} {4 \pi^2} }\)

\(m = \frac {4 \pi^2 r^3} {Gt^2} \)

Tags: Equations for Motion