Planetary motion, gravity, orbits
Mostly Kepler's laws with some graphics too!
Kepler's 1st Law
The orbit of every planet is an ellipse with the Sun at one of the two foci.
The orbit size and shape can described by $a$ and $b$, $a$ and $e$, or $b$ and $e$
Kepler's 2nd Law
A line joining a planet and the Sun sweeps out equal areas, $A$, during equal intervals of time $\Delta t$.
(not to scale)
Kepler's 3rd Law
"The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."
Where $T$ is the period, $a$ semi-major axis of the orbit, $M$ is the larger mass, and $G$ is the gravitational constant
By definition $T^2$/$a^3$ = 1 yr2 / 1 A.U.3 where A.U. is an astronomical unit = 1.5x1011m = 9.2x107miles.
Kepler's Laws in action!
Sweeping out equal areas means that the orbiting planet moves faster when it is nearer the star.
To put eccentricity into perspective:
- Objects with e equal to 0 have circular trajectories
- Objects with e equal to 1 have parabolic trajectories
- Objects with e greater than 1 have hyperbolic trajectories
- Earth currently has e = 0.0167 (nearly circular)
- Mercury has the highest eccentricity (e = 0.2056) of all of the planets in the Solar System
- Pluto has a higher eccentricity (e = 0.248) but it is no longer considered a planet :(