Exam 20210611 ALL SOL

Pagina 1

1 of 5 Orbital Mechanics Academic Year 2020-2021 Lecturer: Camilla Colombo Exam 11 June 2021 Duration: 1.5 h All solution sheets have to be written in clear form in pen. Do not write in pencil. 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 must be reported. Please report the number of the answers from the text of the exercise. Numerical results need to have proper units of measure. Last digit of Person Code (Codice Persona) 0 or 1 2 or 3 4 or 5 6 or 7 8 or 9 Exam Version 1 2 3 4 5 PART 1 (16 PT) Exercise 1 – Orbital manoeuvre A probe is sent to Mars for an exploration mission. After an interplanetary transfer, the probe is inserted in a hyperbolic trajectory around Mars (Orbit 1), lying on the Mars equatorial plane, with the infinite and perigee velocities, 𝑣∞ and 𝑣𝑝. Once the probe arrives at the perigee of the hyperbolic trajectory, a braking manoeuvre is performed to close the orbit. The orbit after this manoeuvre (Orbit 2) lies on the Mars equatorial plane and has an apocenter radius of 12500 km. Assume that the braking manoeuvre is performed tangentially to the manoeuvring point in the Mars equatorial plane. Now that the probe is on Orbit 2, an apse line rotation manoeuvre is req uired by the scientific mode of the mission, to move the prove on Orbit 3. The apse line rotation manoeuvre consists of a delta-v of 𝐷𝑉, given with a positive angle of 7° with respect to the transversal direction of the local horizon of the radial-transversal-normal Version 1 2 3 4 5 Infinite velocity: 𝑣∞ 0.35 km/s 0.38 km/s 0.40 km/s 0.42 km/s 0.46 km/s Perigee velocity: 𝑣𝑝 4.97 km/s Delta-V 𝐷𝑉 0.08 km/s 0.10 km/s 0.15 km/s 0.2 km/s 0.3 km/s S/C cross section area:…