Kepler's Laws of Planetary Motion

Written by Jerry Ratzlaff. Posted in Properties

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:

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

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

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