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1 of 2 Orbital Mechanics Academic Year 2016-2017 Lecturer: Camilla Colombo Exam 03 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 A spacecraft is launched from Earth using a three-stage sequential launcher (1st stage + 2nd stage + upper stage). After the 2 nd stage burn out, the rocket is on a circular orbit around the Earth, at 500 km altitude. The specific impulse is equal to 340 s for all stages. The initial mass of the rocket is 42 tons and the mass ratio of the 1st stage is 4.5, while the structural ratios of 1st and 2nd stage are, respectively, 0.12 and 0.14. The overall effect of gravity and drag losses is quantified into, respectively, 1.7 km/s and 0.4 km/s. Assume that gravity and drag losses affect the dynamics of the launcher only during 1st and 2nd stage phases. Find: 1. The burn out velocity of the 2nd stage 2. The mass ratio of the 2nd stage 3. The total mass left on the orbit after the 2nd stage burn out After the upper stage burn out, the spacecraft is inserted into a trajectory that escapes the Earth. After leaving the Earth, that the spacecraft is required to have a heliocentric velocity with ||𝑣+|| = 32.49 𝑘𝑚/𝑠 Also, 𝑣+ is required to be parallel with respect to Earth’s heliocentric orbital velocity. Follow a linked conics approach to design the escape trajectory and assume Earth’s heliocentric orbit to be circular. Find: 4. The cost of the maneuver to be provided by the upper stage (assume that the upper stage provides a single impulsive…