How many satellites orbit their planet faster than the planet rotates? Phobos is so close to Mars that it orbits Mars much faster than Mars rotates. This means that it rises in the west and sets in the east, even though its orbit is prograde.
Are there any other known natural satellites that orbit their planet faster than the planet rotates, or is Phobos unique in this regard?
Uranus rotates once every 0.718 days. 11 of its satellites have a shorter orbital period. These are inner satellites of Uranus which are roughly in the equatorial plane of Uranus. I don't quite understand what direction they orbit in compared to the direction in which Uranus spins.
Neptune rotates once every 0.671 days. 5 of its satellites have a shorter orbital period and orbit prograde.
Jupiter rotates once every 10 hours. 2 of its satellites have a shorter orbital period and orbit prograde.
Saturn rotates once every 0.4 days and none of its satellites orbit faster than that.
So Phobos is not alone in its case. Around Mars, Jupiter and Neptune (and maybe Uranus), there are moons that orbit so fast that they rise in the west and set in the east.