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1 of 2 Orbital Mechanics Academic Year 2016-2017 Lecturer: Camilla Colombo Exam 01 September 2017 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 Earth using a three-stage sequential launcher (1st stage + 2nd stage + upper stage). At the 1st stage burn out, the launcher is at an altitude of 115 km, with a true anomaly of 173 deg on its osculating orbit whose eccentricity is 0.87. At the 2nd stage burn out, the rocket is left on a circular LEO (Low Earth Orbit) at 450 km altitude. The specific impulse is equal to 350 s for all stages. The initial mass of the rocket is 32 tons and the structural ratio of the 1 st stage is 0.12. The overall effect of gravity and drag losses is qu antified into, respectively, 1.1 km/s and 0.3 km/s. Assume that gravity and drag losses affect the dynamics of the launcher only during the 1st stage phase. Find: 1. The burn out velocities of 1st and 2nd stage 2. The mass ratios of 1st and 2nd stage 3. The mass of propellant consumed during 1st and 2nd stage phases The upper stage provides a single impulsive maneuver , which is used to put the spacecraft on a lunar transfer orbit, starting from the circular LEO. The orbital plane of the circular LEO is identified by 𝑖𝐿𝐸𝑂 = 5.1 𝑑𝑒𝑔 ; ΩLEO = 0 𝑑𝑒𝑔 The lunar transfer orbit has its perigee at the maneuvering point on the LEO. The spacecraft will encounter the Moon when its true anomaly on the transfer orbit is 168 deg. Assume Moon’s orbit to be circular. The lunar transfer orbit…