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1 of 2 Orbital Mechanics Academic Year 2016-2017 Lecturer: Camilla Colombo Exam 17 February 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 The return module of a martian probe is launched from the surface of Mars with a two-stage sequential rocket. The multi -stage launcher is optimized and it is capable of inserting 45 kg on a trajectory that escapes the gravitational attraction of Mars. The burn out of the second stage occurs at 7700 km altitude from Mars’ surface. The specific impulse is equal to 240 s for all stages. The overall effect of gravity and drag losses is quantified into 0.47 km/s. Assume that gravity and drag losses affect the dynamics of the launcher only during 1 st stage phase. The burn out velocity of the first stage is 2.7 km/s and the structural ratios of 1 st and 2nd stage are respectively 0.15 and 0.19. Find: 1. The mass ratios of the 1st and 2nd stage 2. The total specific energy provided by the launcher 3. The total fuel mass consumed After leaving Mars, the spacecraft perform s a flyby of the Earth after an interplanetary cruise. The velocity at infinity on the hyperbola is 2.7 km/s and the distance between the incoming asymptote and the Earth is 28500 km. A scientific package is released at the pericenter of the hyperbola, which is located above the south pole of the Earth. The flyby occurs when the Earth is at its autumn equinox, on a plane normal to the Earth-Sun position vector. The spacecraft approaches the Earth trailing. Assume Earth’s…