Exam 20210630 ALL SOL

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1 of 5 Orbital Mechanics Academic Year 2020-2021 Lecturer: Camilla Colombo Exam 30 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. Second to 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 Earth Data: • 𝜇𝐸 = 398600 km3/s2 • 𝑅𝐸 = 6378.16 km • 𝐽2 = 0.0010826 Part 1/2) A satellite, named servicer, is designed to perform maintenance and repairs of two different satellites in Low Earth Orbit (LEO), namely SAT -1 and SAT -2. To perform the repair and servicing tasks, the servicer shall reach SAT-1 and SAT-2 orbits, in that order. The servicer is injected into a circular orbit with position and velocity equal Version 1 2 3 4 5 Δθ 40° 50° 60° 70° 80° 𝑟0 [ 4478.9 1608.3 5638.2 ] 𝑘𝑚 𝑣0 [ −5.5240 −1.1389 4.7131 ] 𝑘𝑚/𝑠 ℎ0 [ 14001 −52255 3783 ] 𝑘𝑚2/𝑠 ΔΩ 10° 20° 30° 40° 50° 2 of 5 to 𝒓0, 𝒗0 and 𝒉0 (see the table). The first satellite to be serviced, SAT -1, lies on the same orbit as the servicer injection orbit, but with an argument of latitude (anomaly of perigee + true anomaly) of 𝜃1 = 𝜃𝑠 + Δθ, with Δθ (see the table). The servicer is required to perform an in -plane phasing manoeuvre sequence to reach SAT -1 in two revolutions of both satellites. 1. Compute the Keplerian orbital elements of the servicer injection orbit. a. The semi-major axis of the servicer injection orbit [Output in km with 1 decimal digits] b.…