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1 of 2 Orbital Mechanics Academic Year 2017-2018 Lecturer: Camilla Colombo Exam 24 January 2018 Duration: 3 h All solution sheets have to be written in clear form in pen. On top of each sheet, please report in capital letters your surname, name and student number. In the solution of the exercise all the analytical and numerical procedure has to be reported. Please report the number of the answers from the text of the exercise. EXERCISE A spacecraft is launched from the surface of the Moon with a two-stage sequential launcher. The initial mass of the rocket is 750 kg and the specific impulse is 2 80 s for both stages . The structural ratios of 1 st and 2nd stages are respectively 0.14 and 0.18. The first stage detaches 80 s after launch. During thi s first phase, the motion of the rocket is purely vertical and 450 kg of propellant are burned. After the 2nd stage burn out, the velocity of the spacecraft is 3.9 km/s. Assume that gravity losses affect the dynamics of the launcher only during the 1st stage phase. Find: 1. The burn out velocity of 1st stage 2. The burn out velocity of 2nd stage if the launcher was optimized 3. The mass launched to orbit after 2nd stage burn out The spacecraft escapes from the attraction of the Moon and is inserted into an Earth-centered orbit, co-planar with Moon’s geocentric orbit . At escape the spacecraft has a geocentric flight path angle of 12 degrees. The period of the orbit is 1.2 T M, where TM is the period of the Moon’s geocentric orbit . Assume Moon’s geocentric orbit to be circular and its plane identified by 𝑖𝑀 = 19.4 𝑑𝑒𝑔 ; ΩM = 9.4 𝑑𝑒𝑔 Find: 4. The velocity at infinity on the escape hyperbola 5. The angular momentum of the spacecraft geocentric orbit 6. The time elapsed from escape before the spacecraft encounters the Moon again…