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1 of 2 Orbital Mechanics Academic Year 2016-2017 Lecturer: Camilla Colombo Exam 30 June 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 multi-stage launcher (core stage, two boosters and upper stage). At time zero the core stage is ignited simultaneously with two boosters. Once the boosters are fired out, they are detached from the rocket. The initial total mass of the rocket (at launch) is 251 tons. Data about the core stage and boosters are provided as follows 1 booster (tot: 2) Core stage Fuel mass [tons] 52 105 Structural mass [tons] 4.8 9 Specific Impulse [s] 240 275 Burning time [s] 145 278 Assume pure vertical motion and no drag losses from time zero until burn out of the core stage. Consider gravity losses. Assume constant thrust for each stage. Find: 1. The velocity of the rocket after the burn out of the boosters 2. The velocity of the rocket after the burn out of the core stage After the burn out of the boosters, core and upper stages, the spacecraft is released at an altitude of 1245 km at the pericentre of an equatorial orbit whose eccentricity vector (expressed in the geocentric equatorial frame) is 𝑒 = [0.1; 0.15; 0] Find: 3. The right ascension and declination of the release point 4. The celestial latitude and longitude (with respect to the ecliptic plane) of the release point 2 of 2 The spacecraft is required to perform a single impulsive maneuver to align its pericentre direction with the direction of the gamma…