# Two months

Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies?

Result

t = 13877:06

#### Solution:

$7 h \ 39 min = 459 \ min \ \\ 30 h \ 14\ min = 1814 \ min \ \\ 459 = 3 \cdot 3 \cdot 3 \cdot 17 \ \\ 1814 = 2 \cdot 907 \ \\ \ \\ \text{LCM}(459, 1814) = 832626 \ \\ t = \ min = 578 d \ 5 h \ 6 min \ \\ r = 13877:06 \ \\$

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