Exam 20210129 ALL SOL

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1 of 2 Orbital Mechanics Academic Year 2020-2021 Lecturer: Camilla Colombo Exam 29 January 2021 Duration: 3 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. PART 1 – EARTH TO SATURN MISSION EX 1 – Orbital Manoeuvre Part 1/2 Consider a refueling mission around the Earth. The satellite (spacecraft A) is injected by the launcher on a parking orbit (Orbit 1) with the following characteristics: Eccentricity: 𝑒𝑒1 = 0 Orbit Altitude: ℎ1 = 763 km Inclination: 𝑖𝑖1 = 10° RAAN: Ω1 = 120° The spacecraft A shall reach a new orbit (Orbit 2) to refuel a spacecraft B, part of a constellation mission. The orbit 2 has the following characteristics: Eccentricity: 𝑒𝑒2 = 0 Orbit Altitude: ℎ2 = 3642 km Inclination: 𝑖𝑖2 = 20° RAAN: Ω2 = 120° The spacecraft A begins the transfer when it is at the ascending node of Orbit 1 and performs a Hohmann transfer with a change of plane to reach the Orbit 2. The transfer orbit lies on the plane of Orbit 2. Constants R_earth = 6378.15 km; 2 of 2 𝜇𝜇_earth = 398600 km^3/s^2; Q1) Characterise the transfer orbit in terms of Keplerian elements {𝑎𝑎, 𝑒𝑒, 𝑖𝑖, Ω, 𝜔𝜔}𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 Q2) Compute the modulus of the delta-v that the satellite A should provide to pass form Orbit 1 to the transfer orbit. Q3) Compute the components of the delta-v at question Q2) in the {𝑟𝑟, 𝜃𝜃, ℎ} frame of Orbit 1. Q4) Compute the delta-v that the satellite A should provide to pass from the transfer orbit to the Orbit 2. Part 2/2 Now that…