List of Tables. Table 3.1 Determination efficiency for circular orbits - Sample problem 1 41

Transcription

1 List of Tables Table 3.1 Determination efficiency for circular orbits - Sample problem 1 41 Table 3.2 Determination efficiency for elliptical orbits Sample problem 2 42 Table 3.3 Determination efficiency for hyperbolic orbits - Sample problem 3 43 Table 3.4 Determination efficiency for heliocentric orbits - Sample problem 4 44 Table 3.5 Comparison of Lambert problem solutions with variation in semi major axis 45 Table 3.6 Comparison of Lambert problem solutions with variation in eccentricity 46 Table 3.7 Comparison of Lambert problem solutions with variation in inclination 47 Table 3.8 Comparison of Lambert problem solutions with variation in transfer angle 48 Table 3.9 Comparison of Lambert problem solutions in the singularity region (r1=r2) 49 Table 4.1. Typical lunar transfer trajectory characteristics and comparison 71 Table 5.1 Solutions of non impact transfer trajectories 99 Table 5.2 Characteristics of non impact approach trajectories 100 Table 5.3 Target parameters achieved after numerical propagation 101 Table 5.4 Comparisons of transfer trajectory characteristics of different algorithms 102 Table 6.1 Impulse requirements to achieve the target orbit for different LOI altitudes 124 Table 6.2 Circular frozen orbit inclinations for different gravity models 124 Table 6.3 Circular frozen orbit inclinations for different orbit sizes 125 Table 6.4 Influence of number of zonal terms on analytical circular frozen orbit Table 6.5 inclination Stability of analytical solution with different force models Table 6.6 Minimum periapsis altitude in two years of orbit evolution for different RAANs 127 Table 6.7 Frozen orbit inclinations for different RAANs for 100 km circular orbit 128 vii

2 " 15 Table 7.1 Sensitivity of the target parameters for the deviations in the TLI parameters 162 Table 7.2 Effect of force models on the lunar transfer trajectory propagation 163 Table 7.3 Precise transfer trajectory design using GAAB and comparison with biased non impact algorithm 164 Table 8.1 Initial conditions of precise GAAB solution for lunar gravity assist trajectory 180 Table 8.2 Transfer trajectory parameters under different force models and the resulting targets on propagation 181 viii

3 List of Figures Figure 1.1 Ways of transfer 4 Figure 1.2 Geometry of ways of transfers to the moon 6 Figure 3.1 Geometry of Lambert's problem 28 Figure 3.2 Geometry of the transformation 29 Figure 4.1 Interplanetary transfer trajectory phases 52 Figure 4.2 Lunar transfer trajectory phases 53 Figure 4.3 Geometry of parking orbit orientation 60 Figure 4.4 TLilocation variation with respect to the sweep back duration 72 Figure 4.5 Parking orbit orientations with respect to the sweep back duration 73 Figure 4.6 Deviation in arrival time on reaching the target 74 Figure 4.7 Deviation from target distance at the specified arrival time 75 Figure 4.8 Differences (Pseudo - Lambert) in the departure characteristics 76 Figure 4.9 Differences (Pseudo - Lambert) in the arrival characteristics 77 Figure 5.1 Approach trajectory characteristics (method 1) 83 Figure 5.2 Target / Arrival B-plane coordinates 84 Figure 5.3 Approach trajectory characteristics (method 2) 86 Figure 5.4 Schematic illustration of periapsis of approach trajectory 87 Figure 5.5 Schematic illustration of non impact pseudostate algorithm 91 Figure 5.6 Impact of sweep-back duration on target.periapsis time 103 Figure 5.7 Variation of optimal sweep-back duration with departure epoch 104 Figure 5.8 Differences (impact-non impact) in departure and arrival characteristics 105 Figure 6.1 Moon's radial distance from the Earth in one lunar cycle 129 IX

4 o PI Figure 6.2 Moon's right ascension in one lunar cycle 129 Figure 6.3 Moon's declination in one lunar cycle 129 Figure 6.4 Variation of impulse requirement at TLI in one lunar cycle 130 Figure 6.5 Variation of right ascension of ascending node at TLI in one lunar cycle 131 Figure 6.6 Variation of argument of latitude at TLI in one lunar cycle 131 Figure 6.7 Variation of LOI impulse for circularization 132 Figure 6.8 Variation of right ascension of ascending node at LOI in one lunar cycle 132 Figure 6.9 Variation of argument of periapsis at LOI in one lunar cycle 133 Figure 6.10 Variations of impulse requirements at TLI and for LOI with flight duration 133 Figure 6.11 Variation of right ascension of ascending node of EPO and LPO with flight duration 134 Figure 6.12 Variation of argument of periapsis of EPO and LPO with flight duration 134 Figure 6.13 Impulse variation with EPO perigee altitude 135 Figure 6.14 Impulse variations with EPO inclination 135 Figure 6.15 Variation of TLI angles with EPO inclination 136 Figure 6.16 Variation of LOI angles with EPO inclination 136 Figure 6.17 Variation of TLI argument of latitude with LOI altitude 137 Figure 6.18 Variation of TLilongitude of ascending node with LOI altitude 137 Figure 6.19 Variation of LOI impulse with LOI altitude 138 Figure 6.20 Variation of LOI angles with LOI altitude 138 Figure 6.21 Variation of TLI angles with LOI inclination 139 Figure 6.22 Variation of LOI angles with LOI inclination 139 Figure 6.23 Frozen orbit eccentricity using zonals of Bills-Ferrari Gravity Model 140 Figure 6.24 Frozen orbit eccentricity with different gravity models 140 x

5 Figure 6.25 Frozen orbit eccentricity with different orbit sizes 141 Figure 6.26a Frozen orbit solutions with different number of zonal terms 141 Figure 6.26b Frozen orbit solutions with different number of zonal terms 142 Figure 6.26c Frozen orbit solutions with different number of zonal terms 142 Figure 6.27a Evolution of frozen orbit for different values of RAAN (i=95.3 deg) 143 Figure 6.27b Evolution of frozen orbit for different values of RAAN (i=95.3 deg) 143 Figure 6.27c Evolution of frozen orbit for different values of RAAN (i=95.3 deg) 144 Figure 6.28 Minimum periapsis altitude in two years of orbit evolution (Numerical integration) 144 Figure 6.29 Variation of orbital life time with lunar parking orbit inclination 145 Figure 6.30a Contribution of harmonics to the orbit evolution (i= 11 deg) 145 Figure 6.30b Contribution of harmonics to the orbit evolution (i= 11 deg) 146 Figure 6.31a Contribution of harmonics to the orbit evolution (i= 11 deg) 146 Figure 6.31b Contribution of harmonics to the orbit evolution (i= 11 deg) 147 Figure 6.32 Variation of periapsis altitude for orbits of polar and frozen inclinations 147 Figure 6.33 Evolution of periapsis altitude for different frozen combinations (Inc,RAAN) 148 Figure 6.34 Periapsis / Apoapsis profiles in two years (Frozen orbit) 148 Figure 6.35 Semi major axis variation in two years (Frozen orbit) 149 Figure 6.36 Eccentricity profile in two years (Frozen orbit) 149 Figure 6.37 Inclination profile in two years (Frozen orbit) 150 xi

6 Figure 7.1 Comparison of convergence pattern for achieved LOI altitude for different population sizes 165 Figure 7.2 Comparison of convergence pattern for achieved LOI inclination for different population sizes 166 Figure 7.3 Convergence with different adaptation sizes 167 Figure 8.1 Declination profile of the moon during January Figure 8.2 Right ascension profile of the moon during January Figure 8.3 Comparison of convergence pattern for GSO altitude 184 Figure 8.4 Comparison of convergence pattern for GSO altitude 185 Figure 8.5 Adaptation process of GAAB 186 Figure 8.6 Typical lunar gravity assist trajectory 187 XlI