You are working on a project with NASA to launch a rocket toMars, with the rocke

Question

You are working on a project with NASA to launch a rocket toMars, with the rocket blasting off from earth when earth and Marsare just aligned along a straight line from the sun. As a firststep in doing the calculation, assume circular orbits for bothplanets. If Mars is now 64.1 degrees ahead of the earth in itsorbit around the sun, when should you launch the rocket?

Give your answer in days to the nearest whole number (i.e. 45.6= 46)

Note: For this problem you need to know the fact that all theplanets orbit the sun in the same direction, and the year on Marsis 1.90 earth years.

Explanation / Answer

      Here mars is 64.1degreesahead of earth. So for the earth and mars to allign in a straightline, earth should have the angular displacement 64.1degrees morethen the angular displacement of mars.       ThereforeE = M + 64.1o       or Et =Mt + 64.1o       or t =64.1o/(E - M)       But angular speed of earthis E = 360o/1yr             angular speed of mars is M =360o/1.9yr       Then (E -M) = (360o/1yr) -(360o/1.9yr)                                = (360o)(1.9yr - 1yr)/(1.9yr2)                                 =170.5o/yr       Then t =64.1o/(170.5o/yr)                 = 0.37595yr                 = (0.37595yr)(365d/yr)                  =137days.       or t =64.1o/(E - M)       But angular speed of earthis E = 360o/1yr             angular speed of mars is M =360o/1.9yr       Then (E -M) = (360o/1yr) -(360o/1.9yr)                                = (360o)(1.9yr - 1yr)/(1.9yr2)                                 =170.5o/yr       Then t =64.1o/(170.5o/yr)                 = 0.37595yr                 = (0.37595yr)(365d/yr)                  =137days.

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