Vis Viva: orbital energy conservation equation; for any Kepler orbit (elliptic, parabolic, hyperbolic, or radial), the vis viva equation is
, where v is the relative speed of the two bodies, r is the distance between them, and a is the semimajor axis (a>0 for ellipses, a=∞ for parabolas, and a<0 for hyperbolas).Redshift:
Surface Gravity: the luminosity of a star L* goes as logg*.
Hill sphere: the region around a body where it dominates the attraction of satellites
![r \approx a (1-e) \sqrt[3]{\frac{m}{3 M}}](http://upload.wikimedia.org/math/5/0/f/50fc57604cad722d8fae9e49a0544d13.png)
Lies between L1 and L2, although the true region of stable satellite orbit is inside 1/2 or 1/3 of this and dependent on other forces (radiation pressure, Yarkovsky effect). Note that retrograde orbits at a wider orbit are more stable than prograde orbits. Also, in any very loworbit, a spherical body must be extremely dense in order to fit inside its own Hill sphere and be capable of supporting an orbit.
Yarkovsky effect: for small bodies (d<10km) a force caused by anisotopic thermal emmision (photons with momentum)
Roche limit: the radius at which an (only) gravitationally-bound satellite disintegrates by tidal forces.
If held together by their tensile strength (Jupiter's Metis and Saturn's Pan) satellites can orbit within their Roche limits. Almost all planetary rings are located within their Roche limit, with Saturn's E Ring and Phoebe ring being notable exceptions.
Roche lobe: the region around a star which orbiting material is gravitationally bound to the star.
If the star expands past its Roche lobe, material can escape. In a binary system escaped material will fall in through the inner Lagrangian point (mass transfer).
Just some things we should understand. :P
