Aerospace Engineering - Orbital Mechanics

Full exam

Part 1 Exercise 1 -- Orbital Manoeuvre Branch 1 Q1) on Orbit 1: th_I = 150.0 deg, th_II = 330.0 deg on Orbit 2: th_I = 210.0 deg, th_II = 30.0 deg Q2) DV = 0.04039 km/s Q3) DV = 0.02162 km/s Q4) n = 4.064480e-04 rad/s Q4) th plume = 0.102 rad // = 5.827 deg Q4) Dt in the plume = 8.340 min Q5) No. Particles = 3.579677e+06 Branch 2 Q1) on Orbit 1: th_I = 147.5 deg, th_II = 327.5 deg on Orbit 2: th_I = 212.5 deg, th_II = 32.5 deg Q2) DV = 0.04293 km/s Q3) DV = 0.02143 km/s Q4) n = 3.491868e-04 rad/s Q4) th plume = 0.143 rad // = 8.165 deg Q4) Dt in the plume = 13.604 min Q5) No. Particles = 7.285239e+06 Branch 3 Q1) on Orbit 1: th_I = 145.0 deg, th_II = 325.0 deg on Orbit 2: th_I = 215.0 deg, th_II = 35.0 deg Q2) DV = 0.04544 km/s Q3) DV = 0.02131 km/s Q4) n = 3.042126e-04 rad/s Q4) th plume = 0.184 rad // = 10.557 deg Q4) Dt in the plume = 20.190 min Q5) No. Particles = 1.298184e+07 Branch 4 Q1) on Orbit 1: th_I = 142.5 deg, th_II = 322.5 deg on Orbit 2: th_I = 217.5 deg, th_II = 37.5 deg Q2) DV = 0.04793 km/s Q3) DV = 0.02123 km/s Q4) n = 2.681269e-04 rad/s Q4) th plume = 0.227 rad // = 12.992 deg Q4) Dt in the plume = 28.191 min Q5) No. Particles = 2.119779e+07 Branch 5 Q1) on Orbit 1: th_I = 140.0 deg, th_II = 320.0 deg on Orbit 2: th_I = 220.0 deg, th_II = 40.0 deg Q2) DV = 0.05038 km/s Q3) DV = 0.02119 km/s Q4) n = 2.386511e-04 rad/s Q4) th plume = 0.270 rad // = 15.464 deg Q4) Dt in the plume = 37.697 min Q5) No. Particles = 3.251631e+07 ======================================================= Exercise 2 -- Time Measurements and Spherical Geometry Branch 1 Q1) th = 128.43 deg Q1) Dt = 42.320 h Q2) delta = -52.954 deg, alpha = 203.075 deg Q3) h_mean sun = 1.937 h Q4) LST = 19.937 h Q5) Az = 319.362 deg, h = 23.073 deg Branch 2 Q1) th = 124.66 deg Q1) Dt = 38.233 h Q2) delta = -52.954 deg, alpha = 203.075 deg Q3) h_mean sun = 2.523 h Q4) LST = 20.523 h Q5) Az = 322.116 deg, h = 18.442 deg Branch 3 Q1) th = 121.61 deg Q1) Dt = 35.165 h Q2) delta = -52.954 deg, alpha = 203.075 deg Q3) h_mean sun = 3.249 h Q4) LST = 21.249 h Q5) Az = 326.106 deg, h = 13.136 deg Branch 4 Q1) th = 119.07 deg Q1) Dt = 32.753 h Q2) delta = -52.954 deg, alpha = 203.075 deg Q3) h_mean sun = 4.269 h Q4) LST = 22.269 h Q5) Az = 332.743 deg, h = 6.649 deg Branch 5 Q1) th = 116.92 deg Q1) Dt = 30.793 h Q2) delta = -52.954 deg, alpha = 203.075 deg Q3) h_mean sun = 0.710 h Q4) LST = 18.710 h Q5) Az = 315.136 deg, h = 33.488 deg Part 2 Codice Persona (last digit) h_park [km] RAAN_V [deg] DV_pfb [km/s] Intersection with Venus Q1) DV escape [km/s] Q2) Earth longitude at escape [deg] Q3) Day from Spring Equinox at escape [days] Q4) Time to next encounter [days] Q5) v_inf_r [km/s] Q5) v_inf_th [lm/s] Q5) v_inf_h [km/s] 0 300 57 6 2 3.340710177 57 240.1795286 182.6641044 0 -0.0521089 -1.760914 1 340 61 6.1 1 3.331587452 61 244.2387309 182.6641044 0 -0.0521089 -1.760914 2 380 65 6.2 2 3.32254826 65 248.2979333 182.6641044 0 -0.0521089 -1.760914 3 420 69 6.3 1 3.313591361 69 252.3571356 182.6641044 0 -0.0521089 -1.760914 4 460 73 6.4 2 3.304715543 73 256.4163379 182.6641044 0 -0.0521089 -1.760914 5 500 77 6.5 1 3.295919619 77 260.4755402 182.6641044 0 -0.0521089 -1.760914 6 540 81 6.6 2 3.287202423 81 264.5347426 182.6641044 0 -0.0521089 -1.760914 7 580 85 6.7 1 3.278562817 85 268.5939449 182.6641044 0 -0.0521089 -1.760914 8 620 89 6.8 2 3.269999682 89 272.6531472 182.6641044 0 -0.0521089 -1.760914 9 660 93 6.9 1 3.261511923 93 276.7123495 182.6641044 0 -0.0521089 -1.760914 Codice Persona (last digit) Q9) DV_fb [km/s] Q10) e_fb Q10) rp_fb [km] Q10) Delta_fb [km] Q12) theta_inter FIRST [deg] Q12) theta_inter SECOND [deg]2 Q13) lat_V(0) FIRST [deg] Q13) lon_V(0) FIRST [deg] Q13) lat_V(0) SECOND [deg]2 Q13) lon_V(0) SECOND [deg] 0 0.10421781 33.8077508 4212220.07 4338711.82 250.929723 109.0703 -3.34893 261.0622 -0.99169 196.991 1 0.10421781 33.8077508 4212220.07 4338711.82 249.995457 110.0045 -2.27787 317.8165 -3.37128 263.9695 2 0.10421781 33.8077508 4212220.07 4338711.82 249.086459 110.9135 0.746401 12.70509 -1.64522 330.9952 3 0.10421781 33.8077508 4212220.07 4338711.82 248.201475 111.7985 3.097634 66.00486 2.080918 37.83528 4 0.10421781 33.8077508 4212220.07 4338711.82 247.339339 112.6607 2.99858 117.833 3.278529 104.7503 5 0.10421781 33.8077508 4212220.07 4338711.82 246.498966 113.501 0.701625 168.0688 0.504638 171.4489 6 0.10421781 33.8077508 4212220.07 4338711.82 245.679342 114.3207 -2.03377 216.8329 -2.87347 237.925 7 0.10421781 33.8077508 4212220.07 4338711.82 244.879522 115.1205 -3.37353 264.3436 -2.80003 304.3446 8 0.10421781 33.8077508 4212220.07 4338711.82 244.098618 115.9014 -2.57616 310.5752 0.610741 10.3672 9 0.10421781 33.8077508 4212220.07 4338711.82 243.335802 116.6642 -0.26854 355.4618 3.292068 76.17899