Mars rotates toward the east and takes about 24 1/2 hours for one rotation. Phobos, the inner satellite of Mars, revolves around Mars toward the east and requires about 7 1/2 hours to circle the planet once. Viewed from the surface of Mars, how long does it take Phobos to traverse the 180° across the sky from rising to setting (in hours)?
A)17
B)8 1/2
C)7 1/2
D)5 1/2

Question

Quizplus · Accepted Answer

Phobos orbits Mars faster than Mars rotates, taking 7 1/2 hours to complete an orbit. Since Mars takes about 24 1/2 hours to rotate once, Phobos appears to move quickly across the sky. To find the time it takes for Phobos to go from rising to setting (180°), we need to consider the relative motion between Phobos' orbit and Mars' rotation. The effective motion is the difference between Phobos' orbital period and the time it takes Mars to rotate the equivalent angular distance. Since Phobos completes an orbit in less than a third of a Martian day, it moves across the sky much faster than the Sun as seen from Mars. The correct calculation involves understanding the relative speeds and results in Phobos taking approximately 5 1/2 hours to traverse 180° from rising to setting.

Mars Rotates Toward the East and Takes About 24 1/2