midterm_W07 - MAE146 Astronautics Midterm Test Important...

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MAE146: Astronautics – Midterm Test Important Notes: Please justify all of your answer with equations and sentences in order to get full grade. 10% of the grade will be given to presentation. Exams must be worked out individually. No communications with outside sources allowed. This is an open book and notes, but only the course textbook, lecture notes and homeworks are allowed. No results from other sources allowed. The midterm is to be completed in 50 minutes. Problem 1 (45pts) Local Measurement Transformations We consider two observatories, O 1 and O 2 , on the Earth. The observatories are located at longitudes, latitudes and altitude of θ 1 , φ 1 , h 1 and θ 2 , φ 2 , h 2 , respectively. The altitudes h 1 and h 2 are measured relative to the mean spherical Earth whose radius is denoted R e . The local frame associated with an observatory is Fxed with respect to the surface of the Earth and with origin at the location of the observatory. The x -axis chosen to point Eastward, tangentially to the ground. The
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