# Kepler and Gravitation

## Contents

#### Terms

Period  -  The period of an orbit, usually denoted $T$, is the total time taken for an object to complete one full revolution on its orbit.
Kepler's First Law  -  The planets orbit the sun in ellipses, with the sun at one focus.
Kepler's Second Law  -  The radius of a planet sweeps out a constant area per unit time.
Kepler's Third Law  -  $$T^2 = \frac{4\pi^2a^3}{GM}$$ where $T$ is the period, $G$ is the gravitational constant, and $M$ is the mass of the sun.
Eccentricity  -  The eccentricity is a measure of the elongation of an ellipse. It is defined as: $$\epsilon = \sqrt{1 - \frac{b^2}{a^2}}$$ where $a$ and $b$ are the semimajor and semiminor axis lengths respectively.
Aphelion  -  The point of a planet's furthest distance from the sun on its orbit.
Perihelion  -  Is the point of a planet's closest approach to the sun.
Apogee  -  For an earth orbit, the furthest distance from the earth.
Perigee  -  For an earth orbit, the closest distance to the earth.