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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