Exam 20220622 Sol

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Orbital Mechanics Academic Year 2021-2022 Exam 22 June 2022 1 of 12 PART 1 (15 PT) Data for Part 1 Last digit of Person Code (Codice Persona) 1 or 6 2 or 7 3 or 8 4 or 9 5 or 0 Exam Version 1 2 3 4 5 Note that the DATA section reports the numerical data for the whole exercise. Read the whole exercise till the end before proceeding into its solution. Pay attention to the units of the numerical data and results. DATA: Earth radius: 𝑅𝑅𝐸𝐸= 6378.15 km Earth gravitational constant: 𝜇𝜇𝐸𝐸= 398600 km3s−2 Correction factors for apparent and mean time: Correction factor on Day 1 𝐸𝐸1 = 13 min 25 sec Correction factor on Day 1 +1 𝐸𝐸2 = 13 min 53 sec Table 1 Input data table for Part 1 Version 1 2 3 4 5 Maximum radial velocity of orbit 1: 𝑣𝑣𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚 (km/s) 1.263273 1.362014 1.464403 1.570918 1.6821121 Perigee altitude of orbit 1: ℎ𝑝𝑝 (km) 19757.330 18706.455 17655.330 16603.955 15552.330 Semi aperture angle of the antenna: 𝛼𝛼𝑔𝑔𝑔𝑔 (deg) 8.00 9.75 11.50 13.25 15.00 Orbit 2 radius of perigee: 𝑟𝑟𝑝𝑝2 (km) 6578.15 6603.15 6628.15 6653.15 6678.15 Orbit 2 radius of apogee: 𝑟𝑟𝑎𝑎2 (km) 58672.520 59733.395 60794.520 61855.895 62917.520 Apse line rotation: 𝜂𝜂 (deg) 18.00 20.25 22.50 24.75 27.00 Latitude: 𝜙𝜙𝑔𝑔𝑔𝑔 (deg) 33.00 N 35.75 N 38.50 N 41.25 N 44.00 N Longitude: 𝜆𝜆𝑔𝑔𝑔𝑔 (deg) 112 W 119 W 126 W 133 W 140 W Azimuth: 𝐴𝐴𝐴𝐴 (deg) 230.3867 243.9106 251.1847 257.6572 262.71694 Elevation: 𝐸𝐸𝐸𝐸 (deg) 11.89278 13.61583 15.42917 17.17556 19.8525 LCT (hh mm ss) 3 h 47 min 0 s 3 h 47 min 0 s 3 h 47 min 0 s 3 h 47 min 0 s 3 h 47 min 0 s Orbital Mechanics Academic Year 2021-2022 Exam 22 June 2022 2 of 12 SOLUTION FOR VERSION 1 Exercise 1 : Earth observation mission for artic tundra regions. PART 1 A spacecraft is flying in an elliptical orbit for the monitoring and observation of the tundra region close…