http://en.wikipedia.org/wiki/Lagrangian_point
Lagrangian point
The Lagrangian points (also Lagrange points, L-points, or libration points) are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects (such as a satellite with respect to the Earth and Moon). The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to rotate with them. They are analogous to geostationary orbits in that they allow an object to be in a "fixed" position in space rather than an orbit in which its relative position changes continuously.
Lagrangian points are the stationary solutions of the circular restricted three-body problem. For example, given two massive bodies in circular orbits around their common center of mass, there are five positions in space where a third body, of comparatively negligible mass, could be placed which would then maintain its position relative to the two massive bodies. As seen in a rotating reference frame with the same period as the two co-orbiting bodies, the gravitational fields of two massive bodies combined with the satellite's circular motion are in balance at the Lagrangian points, allowing the third body to be stationary with respect to the first two bodies.
The three collinear Lagrange points were first discovered by Leonhard Euler around 1750.
In 1772, the Italian-French mathematician Joseph Louis Lagrange was working on the famous three-body problem when he discovered an interesting quirk in the results. Originally, he had set out to discover a way to easily calculate the gravitational interaction between arbitrary numbers of bodies in a system, because Newtonian mechanics concludes that such a system results in the bodies orbiting chaotically until there is a collision, or a body is thrown out of the system so that equilibrium can be achieved.
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http://en.wikipedia.org/wiki/Lunar_phase
Lunar phase
A lunar phase or phase of the moon is the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. The lunar phases vary cyclically as the Moon orbits the Earth, according to the changing relative positions of the Earth, Moon and Sun. One half of the lunar surface is always illuminated by the Sun (except during lunar eclipses), and hence is bright, but the portion of the illuminated hemisphere that is visible to an observer can vary from 100% (full moon) to 0% (new moon).