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Orbital Mechanics Academic Year 2016-2017 Lecturer: Camilla Colombo Exam 14 July 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 launcher (1 ​ st ​ + 2 ​ nd ​ + upper stage). The initial mass of the rocket is 35 tons and the specific impulse of both stages equals 320 s. The structural ratio of the 1 ​ st stage is 0.15, while the nominal mass ratio of the 2 ​ nd stage is 4.3. The burn out of the 1 ​ st stage is reached after 93 s from launch, with the rocket reaching a velocity of 3.48 km/s. At this time, a failure in the separation mechanism prevents the structure of the 1 ​ st ​ stage to detach from the rocket. Assume no losses due to drag for all stages. Assume pure vertical motion during 1 ​ st stage burning. Consider gravity losses only from time zero to burn out of the 1 ​ st ​ stage. Find: 1. The burn out velocity of the 2 ​ nd stage in the nominal design condition (with detachment of the first stage) 2. The mass ratio of the 2 ​ nd ​ stage in the non-detached condition 3. The burn out velocity of the 2 ​ nd ​ stage in the non-detached condition After the upper stage burn out, the spacecraft (named “A”) is released on a circular equatorial orbit about the Earth at an altitude of 2500 km. A second spacecraft (named “B”) is orbiting the Earth on the same circular orbit. On this orbit, spacecraft “B” is following spacecraft “A” with a time delay of 27 min and 15 s. Spacecraft “B” is required to perform a phasing…