Kepler and Gravitation
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
-
\begin{equation} T^2 = \frac{4\pi^2a^3}{GM} \end{equation}
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:
\begin{equation} \epsilon = \sqrt{1 - \frac{b^2}{a^2}} \end{equation}
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.
