midterm_W08

# midterm_W08 - MAE146 Astronautics Midterm Exam Important...

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MAE146: Astronautics – Midterm Exam Important Notes: Please justify all of your answer with equations and sentences in order to receive full grade. 10 pts will be given to presentation; any clean, readable copies will receveive these points. Exams must be worked out individually. No communications with outside sources allowed. This is an open book, closed notes examination. Only the textbooks are allowed. The midterm is to be completed in 50 minutes. Problem 1 (30 pts) Binary asteroids We consider two asteroids, α and β orbiting uniformly in circular orbits about their center of mass, O (i.e. the center of mass of each asteroid, O 1 and O 2 respectively, lies on a circular orbit centered at the center of mass of the system) with a period or motion T = 4 h . α is located at a distance R 1 from O , while β is at a distance R 2 . α has mass M 1 , and β has mass M 2 . α and β do not have a regular shape, but are both contained within spheres of radii D 1 and D 2 centered at their respective center of mass. We assume that an

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