23 07 18

Page 1

1 of 2 Orbital Mechanics Academic Year 2017-2018 Lecturer: Camilla Colombo Exam 23 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 A 320 kg spacecraft is launched from Earth using a multi -stage sequential launcher (first, second and upper stage). The mass and structural ratios of first stage are, respectively, 3.6 and 0.14. The mass ratio of the second stage is 3.1 and the structural ratio of the second stage is equal to that of upper stage. The mass of the rocket after detachment of first and second stage are, respectively, 3970 kg and 790 kg. Consider gravity and drag losses only during first stage burn. The overall effect of losses due to gravity and drag is quantified into 1.1 km/s. Each stage has specific impulse of 285 s. Find: 1. The mass of propellant and structure for all stages 2. The velocity of the rocket after the burn out of first, second and upper stages The spacecraft is released in an elliptic equatorial orbit with a flight path angle of -12 deg, and the release point has the following coordinates in the Earth-centered equatorial inertial frame 𝑟⃗𝑅𝑃 = [ 9700 2300 0 ] 𝑘𝑚 At its first opportunity, the spacecraft performs a single maneuver to align its pericenter direction with the 𝛾- point direction. The shape and plane of the orbit are not changed by the maneuver. Find: 3. The geometry (a, e) of spacecraft’s release orbit and the true anomaly of the release point 4. The cost of the maneuver 5. The time between release and the maneuver 2 of 2 While…