How long Phobos stays up

Adapted from IOAA 2011 (Katowice), theory problem 4. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.

Assume that Phobos moves round Mars on a circular orbit in Mars's equatorial plane. For how long is Phobos above the horizon for an observer on Mars's equator? Mars has radius $R_{\text{M}}=3393$ km, rotation period $T_{\text{M}}=24.623$ h and mass $M_{\text{M}}=6.421\times {10}^{23}$ kg, and Phobos orbits at $R_{\text{P}}=9380$ km from Mars's centre.

AnswerPhobos stays above the horizon for about 4.25 hours, and rises again about 11.1 hours after it last rose.