A MATLAB Script for Interplanetary Gravity-Assist Trajectory Design

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sma (km) eccentricity inclination (deg) argper (deg)1.5035042760e+008 6.3393225612e-001 5.5914450567e+000 3.4463100237e+002raan (deg) true anomaly (deg) arglat (deg) period (days)3.2101153351e+002 1.7689713379e+002 1.6152813616e+002 3.6801651656e+002rx (km) ry (km) rz (km) rmag (km)-1.32035535104875e+008 +2.06286564188419e+008 +7.56463416445357e+006 +2.45040308490532e+008vx (kps) vy (kps) vz (kps) vmag (kps)-1.25554330370226e+001 -6.42410502897611e+000 -1.26219743232339e+000 +1.41598434500046e+001heliocentric orbital elements and state vector of the arrival planet(Earth mean ecliptic and equinox of J2000)------------------------------------------sma (km) eccentricity inclination (deg) argper (deg)2.2794303068e+008 9.3339698745e-002 1.8488884443e+000 2.8655654868e+002raan (deg) true anomaly (deg) arglat (deg) period (days)4.9525430962e+001 1.4654795300e+002 7.3104501675e+001 6.8698900475e+002rx (km) ry (km) rz (km) rmag (km)-1.32035535104823e+008 +2.06286564188446e+008 +7.56463416445518e+006 +2.45040308490528e+008vx (kps) vy (kps) vz (kps) vmag (kps)-1.94898388601497e+001 -1.10025325185690e+001 +2.48040863295955e-001 +2.23823829135022e+001MISSION SUMMARY===============total delta-vtotal energytotal mission duration9668.864451 meters/second47.491611 (km/sec)^2352.203773 daysSOI ENTRANCE CONDITIONS=======================calendar date01-Jun-2009TDB time 09:20:50.414TDB julian date 2454983.889472planet-centered orbital elements and state vector of the spacecraft(Earth mean ecliptic and equinox of J2000)------------------------------------------sma (km) eccentricity inclination (deg) argper (deg)-5.9511194428e+003 1.0019817403e+000 1.0559791033e+002 2.5301742495e+002raan (deg) true anomaly (deg) arglat (deg)4.8428235360e+001 1.8363883174e+002 7.6656256698e+001rx (km) ry (km) rz (km) rmag (km)+2.15002405199960e+005 -5.80447119474411e+002 +5.77556169508621e+005 +6.16277129299877e+005vx (kps) vy (kps) vz (kps) vmag (kps)-2.60506164952600e+000 +3.56938712688937e-003 -6.98968640927275e+000 +7.45936157042463e+000CLOSEST APPROACH CONDITIONS===========================calendar date02-Jun-2009page 6
TDB time 07:32:25.674TDB julian date 2454984.814186planet-centered orbital elements and state vector of the spacecraft(Earth mean ecliptic and equinox of J2000)------------------------------------------sma (km) eccentricity inclination (deg) argper (deg)-5.9498812099e+003 1.0022338972e+000 1.0680931836e+002 2.5437461831e+002raan (deg) true anomaly (deg) arglat (deg)5.4097508623e+001 3.8269451705e-009 2.5437461832e+002rx (km) ry (km) rz (km) rmag (km)-5.09774429484303e+000 -7.29173162413977e-001 -1.22532951219458e+001 +1.32914232398901e+001vx (kps) vy (kps) vz (kps) vmag (kps)+1.10971923691395e+002 +1.82671608612068e+002 -5.70381859380036e+001 +2.21217176312752e+002b-plane coordinates at closest approach(Earth mean ecliptic and equinox of J2000)------------------------------------------b-magnitudeb dot rb dot tb-plane anglev-infinityr-periapsisdecl-asymptoterasc-asymptoteflight path angle397.921400 kilometers-223.051763 kilometers-329.528985 kilometers214.093307 degrees7389.125383 meters/second13.291423 kilometers-69.561169 degrees179.940202 degrees0.000000 degreesAfter the solution is displayed, the software will ask the user if he or she would like to create a graphicsdisplay of the transfer trajectory with the following prompt:would you like to plot this trajectory (y = yes, n = no)?If the user’s response is y <strong>for</strong> yes, the script will request a plot step size withplease input the plot step size (days)?A plot step size between 5 and 10 days is recommended.The following is the graphics display <strong>for</strong> this example. This plot is a north ecliptic view where we arelooking down on the ecliptic plane from the north celestial pole. The vernal equinox direction is thelabeled line pointing to the right, the launch planet is labeled with an L, the flyby planet is labeled withan F and the arrival planet is labeled with an A. The location of the launch, flyby and arrival planets atthe launch time is marked with an asterisk. Please note that the axes are labeled in Astronomical Units.page 7
Page 1 and 2: A MATLAB Script for Interplanetary
Page 3 and 4: please select the arrival planet? 4
Page 5: -plane coordinates of incoming hype
Page 9: Lambert’s ProblemLambert’s prob
Page 12 and 13: prpve 1/cos 1 1a 2where is the
Page 14 and 15: The arrival asymptote unit vector
Page 16 and 17: The sphere-of-influence objective f
Page 18 and 19: SNOPT algorithm implementationThis
Page 20 and 21: Algorithm resources“Gravity-Assis
Page 22: theta = orientation of the b-plane

A MATLAB Script for Interplanetary Gravity-Assist Trajectory Design

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