For The Mathematically Inclined

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Problems from M-02/25/21

Problem 1:

Earth takes 365 days to orbit around the Sun and Mars takes 687 earth days to orbit around Sun. If Sun, Earth, and Mars are in a straight line of Feb 25, 2021 when will they be co-linear next time? Assume circular orbits for Earth and Mars.

Problem 2:

Let's add Venus to the mix. If say, Venus, Earth, Mars, and Sun were aligned today (February 25, 2021), when will they align again? Venus takes 225 days to orbit around the Sun. Assume circular orbit for Venus too.