http://cr4.globalspec.com/blogentry/2073/Two-Martian-Moons-Newsletter-Challenge-05-29-07

Two Martian Moons: Newsletter Challenge (05/29/07)
Posted May 27, 2007 5:01 PM
Pathfinder Tags: challenge questions
The question as it appears in the 05/29 edition of Specs & Techs from GlobalSpec:
Mars has two moons, Deimos and Phobos; both orbit in the same direction. Standing near the equator on the Martian surface one night, you watch them both. To your astonishment, Deimos appears to be slowly moving from east to west relative to you, while Phobos is slowly moving from west to east. How can this be? Supporting calculations will score extra points!
Thanks to Jorrie who submitted the original question (which we revised a bit).

(Update: June 5, 8:35 AM EST) And the Answer is...
The closer a satellite (natural or artificial) is to the planet it orbits, the faster it travels around that planet. Both Martian moons travel around Mars from west to east. Deimos, however, is sufficiently far from Mars (like the Earth's moon is from Earth) that it travels around the planet slower than Mars rotates on its axis. Thus, to an observer on the surface of Mars, Deimos appears to be "left behind in the sky" and appears to move from east to west. Phobos, on the other hand, is much closer and actually orbits around Mars faster than Mars rotates.