Demonstrate targeting
Start with an initial orbit and impulsive burn, then numerically optimize so that the location of the Moon is the final condition and the magnitude of the burn is minimized. The dynamical model is the 3 body problem, but functions exist also for the CRTBP and the full 4 body problem.
Contents
See also
LowEnergyTransferInCRTBP Targeting4BP
%-------------------------------------------------------------------------- % Copyright (c) 2018 Princeton Satellite Systems, Inc. % All rights reserved. %-------------------------------------------------------------------------- % Since 2018.1 %-------------------------------------------------------------------------- % Initialize the Earth-Moon-Sun system id = PlanetId({'sun' 'earth' 'moon'}); PlanetPositionEMBarycenter('initialize',id); % Orbital elements elements = [7585.9 1.8086e-06 2.4524 2.4589 0.000833 3.1416]; % Initial velocity change dV1 = 2.988; % Time of trajectory dT = 8.6675e+06; % Graviational constant of the moon muMoon = 4902.7933840088; % Starting Julian Date jD = 2451546; % Plot the initial trajectory PlotLET3BP(elements,dV1,dT,jD); % Update the elements [elementsNew,dV1EphNew] = Targeting3BP2(elements,dV1,dT,0,muMoon,jD); % Plot the new elements PlotLET3BP(elementsNew,dV1EphNew,dT,jD); %--------------------------------------
Iteration Func-count min f(x) Procedure
0 1 3.11606
1 5 3.11606 initial simplex
2 7 3.06064 expand
3 8 3.06064 reflect
4 10 3.007 expand
5 11 3.007 reflect
6 13 2.89035 expand
7 14 2.89035 reflect
8 16 2.74766 expand
9 17 2.74766 reflect
10 19 2.4777 expand
11 20 2.4777 reflect
12 22 2.13328 expand
13 23 2.13328 reflect
14 25 1.57448 expand
15 26 1.57448 reflect
16 28 0.909496 expand
17 29 0.909496 reflect
18 31 0.255263 expand
19 32 0.255263 reflect
20 34 0.213276 reflect
21 35 0.213276 reflect
22 37 0.213276 contract outside
23 39 0.213276 contract inside
24 41 0.213276 contract inside
25 43 0.213276 contract inside
26 45 0.213276 contract inside
27 47 0.211073 contract inside
28 49 0.209444 contract inside
29 51 0.209444 contract inside
30 53 0.207384 contract inside
31 54 0.207384 reflect
32 56 0.207161 contract inside
33 58 0.206849 contract inside
34 60 0.20678 reflect
35 62 0.206527 contract inside
36 64 0.206527 contract inside
37 66 0.206243 reflect
38 68 0.206019 reflect
39 70 0.206007 contract inside
40 72 0.205282 expand
41 74 0.204489 expand
42 76 0.20362 expand
43 77 0.20362 reflect
44 79 0.200792 expand
45 80 0.200792 reflect
46 82 0.19868 expand
47 84 0.19531 expand
48 86 0.19001 expand
49 87 0.19001 reflect
50 89 0.18314 expand
51 91 0.170621 expand
52 92 0.170621 reflect
53 93 0.170621 reflect
54 95 0.167684 reflect
55 97 0.156252 expand
56 99 0.144369 expand
57 100 0.144369 reflect
58 102 0.144369 contract inside
59 104 0.122392 expand
60 105 0.122392 reflect
61 107 0.107766 expand
62 108 0.107766 reflect
63 109 0.107766 reflect
64 111 0.101156 reflect
65 113 0.0854941 reflect
66 115 0.0854941 contract inside
67 117 0.0852961 reflect
68 119 0.0846716 reflect
69 121 0.0846716 contract inside
70 123 0.064083 expand
71 125 0.064083 contract inside
72 126 0.064083 reflect
73 127 0.064083 reflect
74 129 0.0592255 expand
75 130 0.0592255 reflect
76 132 0.0499678 reflect
77 134 0.0499678 contract outside
78 135 0.0499678 reflect
79 136 0.0499678 reflect
80 138 0.0304419 expand
81 139 0.0304419 reflect
82 140 0.0304419 reflect
83 142 0.0304419 contract inside
84 144 0.0304419 contract outside
85 145 0.0304419 reflect
86 147 0.0261073 reflect
87 148 0.0261073 reflect
88 150 0.0155074 expand
89 152 0.0155074 contract inside
90 154 0.0155074 contract inside
91 155 0.0155074 reflect
92 157 0.0119127 expand
93 159 0.0119127 contract inside
94 161 0.0117321 reflect
95 162 0.0117321 reflect
96 163 0.0117321 reflect
97 165 0.0116092 contract inside
98 167 0.0116092 contract inside
99 169 0.0105409 contract inside
100 170 0.0105409 reflect
101 172 0.00731474 expand
102 173 0.00731474 reflect
103 175 0.00731474 contract inside
104 176 0.00731474 reflect
105 178 0.00731474 contract outside
106 180 0.00467096 expand
107 181 0.00467096 reflect
108 182 0.00467096 reflect
109 184 0.00467096 contract inside
110 186 0.00405597 expand
111 187 0.00405597 reflect
112 189 0.00299447 reflect
113 191 0.00137517 expand
114 193 0.00137517 contract inside
115 194 0.00137517 reflect
116 195 0.00137517 reflect
117 197 0.00137517 contract inside
118 199 0.00137517 contract inside
119 201 0.000587283 expand
120 202 0.000587283 reflect
121 203 0.000587283 reflect
122 205 0.000539435 contract outside
123 207 0.000539435 contract inside
124 209 0.000539435 contract inside
125 211 0.000295594 reflect
126 213 0.000295594 contract inside
127 215 0.000295594 contract inside
128 217 0.000284119 reflect
129 219 0.000284119 contract inside
130 220 0.000284119 reflect
131 222 0.000284119 contract inside
132 224 0.000231563 expand
133 226 0.000231563 contract outside
134 227 0.000231563 reflect
135 229 0.000231563 contract inside
136 231 0.000231563 contract inside
137 233 0.000231563 contract inside
138 235 0.000227704 contract inside
139 237 0.000226036 contract inside
140 238 0.000226036 reflect
141 240 0.000225986 contract inside
142 242 0.000225765 contract inside
143 244 0.000224909 contract inside
144 246 0.000224468 contract inside
145 248 0.000224032 contract inside
146 250 0.000224032 contract inside
147 252 0.000224032 contract outside
148 254 0.000223886 contract inside
149 256 0.000223865 contract inside
150 258 0.000223776 contract inside
151 260 0.000223776 contract inside
152 262 0.000223774 contract inside
153 264 0.000223738 contract inside
154 266 0.000223738 contract inside
155 268 0.000223723 contract outside
156 270 0.000223717 contract inside
157 272 0.000223717 contract inside
Optimization terminated:
the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-04
and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-03
