3. (100 points) The planet Mars has a mass M = 6:4 1023 kg. It has two moons, Deimos (mD = 1:5 1015kg) and Phobos (mP = 1:1 1016 kg). At a particular instant, Mars is located at ~rM =< 0; 0; 0 > m, Phobos islocated at ~rP =< 6 106; 0; 0 > m, and Deimos is located at ~rD =< 0; 2:3 107; 0 > m and is moving with avelocity of ~vD =< ??1200;??500; 0 > m/s. Determine the position of Deimos one hour later. You can assume onehour is a small enough time to do your calculations in a single timestep.
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