02 07 18

Pagina 1

1 of 2 Orbital Mechanics Academic Year 2017-2018 Lecturer: Camilla Colombo Exam 2 July 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 An interplanetary probe is launched from Earth using a multi-stage launcher (core stage, third stage, upper stage and four boosters ). At time zero the core stage and the boosters are ignited. The third and upper stages are sequential after burn out of the core stage . The launcher has a cost function of 54.1 and the following data is provided 1 booster (tot: 4) Core stage Fuel mass [tons] 46 94 Structural mass [tons] 3.9 8.8 Specific Impulse [s] 262 290 Burning time [s] 113 278 The summed overall gross mass of third and upper stages is 27.3 tons. Assume pure vertical motion from time zero until the burn out of the core stage. Consider gravity losses affecting the dynamics of the rocket only in this phase. The loss due to drag is quantified into 0.42 km/s and shall be considered only until the burn out of the boosters. Assume constant thrust for each stage. Find: 1. The mass of the probe 2. The velocity of the rocket after the burn out of boosters (boosters are detached just after burn out and the detach operation is instantaneous) 3. The velocity of the rocket after the burn out of core stage (the core stage is detached just after burn out and the detach operation is instantaneous) The interplanetary probe is released on a geocentric orbit with eccentricity of 0. 67, semi-major axis of 27040 km and inclination of 5.2 deg. The spacecraft…