ROSETTA : EVASION DE LA TERRE LE 13/01/2003

ROSETTA AU DEPART DE LA TERRE

La mission Rosetta est l'une des grandes aventures spatiales des 15 années à venir, consistant à aller se poser sur la comète WIRTANEN pour étudier in situ ses caractéristiques et faire ainsi progresser les connaissances sur l'origine du système solaire.

Evénements importants	Date prévue	Orbite
TIR ( injection en libération terrestre)	13 Janvier 2003
AVANT TREMPLIN SUR MARS, APRES PLUS D'UN TOUR COMPLET	26 Août 2005	C1
AVANT PREMIER TREMPLIN SUR LA TERRE	28 Novembre 2005	C2
APRES TREMPLIN SUR TERRE ET AVANT SURVOL DE OTAWARA LE :	11 Juillet 2006 à 0 h 56 mn	C3
APRES SURVOL DE OTAWARA ET AVANT DEUXIEME TREMPLIN SUR LA TERRE LE :	28 Novembre 2007	C3*
APRES TREMPLIN TERRE ET AVANT SURVOL DE SIWA LE :	24 Juillet 2008 à 20 h 49 mn	C4
RENDEZ-VOUS	29 novembre 2011	C4*

Les documents exploités dans cet exercice, proviennent des sites ( accessibles au public en décembre 2000):

http://planetary.so.estec.esa.nl/RSOC ou http://solarsystem.estec.esa.nl/RSOC/trajectory_data.html

Les tableaux que vous rencontrerez dans ce document donnent :

Colonne 1: La date en jour julien modifié, avec origine le 1/1/2000 à 0 h. Donc pour obtenir la date julienne classique il faut enlever 0.5 jj

Colonnes 2 à 4: Les composantes sur les axes X, Y, Z du rayon vecteur en km

Colonnes 5 à 7: Les composantes sur les axes X, Y, Z du vecteur vitesse en km/s

ROUTINES UTILES :

DATE_CAL.EXE pour convertir une date julienne en date classique du calendrier

DATEJULI.EXE pour convertir une date calendaire en date julienne

LAMBERT1.EXE pour les paramètres orbitaux d'une hyperbole joignant 2 points donnés pendant un intervalle de temps donné.

VECTFOND.EXE pour calculer pour les orbites terrestres les vecteurs fondamentaux h, e, n.

QUESTIONS

Exploitation des documents Internet enregistrés sous Evasion terre.txt et Rosetta0.txt

I TIR D'EVASION VU DE LA TERRE : voir plus loin

"The Ariane-5 rocket lifts off from Kourou. After burnout of the lower stage, the spacecraft and upper stage remain in Earth parking orbit (4000 km x 200 km) for about two hours. Ariane's upper stage then ignites to boost Rosetta onto its interplanetary trajectory, before separating from the spacecraft."

m_T= 39.86 10⁴km³s^-2

1°) La date du tir d'évasion ( fin de la combustion du moteur ) est le jour MJD= 1108.0918727

a) Quels sont la date calendaire et le jour julien nouveau?

b) Le rayon de la sphère d'influence terrestre est d'environ 900 000 km. Combien dure la traversée de la sphère d'influence de la Terre? Vous pourrez éventuellement traiter le fichier de données dans un tableur. Voir evasion terre.xls

c) Calculer la norme du rayon vecteur de départ, celle de la vitesse, le moment cinétique réduit h, l'énergie spécifique E, le demi-grand axe, la constante des aires K, l'excentricité e, l'inclinaison i du plan orbital de l'hyperbole d'évasion de la Terre.

d) Donner l'altitude du périgée de l'hyperbole de départ, le demi angle d'ouverture F des asymptotes de l'hyperbole.

2°) Par un examen judicieux du tableau, donner la vitesse à l'infini Vinf et la constante C3 du vol. Ariane 5ECA est capable de 5200 kg en évasion de C3=18 km²/s², précisément développé pour les missions martiennes.

3°) Quel a été le DV minimal fourni par le moteur d'évasion? Est-ce dans les possibilités du lanceur Ariane 5

4°) a) En prenant les deux dates t = 1108.0918727 et t = 1108.1918727 à 0.1 jour d'écart exactement et les positions précises à ces deux dates, lancez le programme LAMBERT1.EXE pour retrouver la trajectoire hyperbolique et ses paramètres orbitaux. Confirmez le périgée.

DONNEES

ATTENTION AUX DATES Voir Rosetta0.txt

Evasion de l'attraction terrestre, en axes J2000, équateur moyen

Colonne 1: Date MJD, Colonnes 2-3-4 : Rayon vecteur, colonnes 5-6-7 : Vitesse

1108.0918727 -3133.836 6822.853 1062.687 -10.786049 -0.790297 0.703883

1108.0960394 -6806.722 6209.680 1260.508 -9.591611 -2.425167 0.416348

1108.1002061 -10053.743 5180.516 1376.120 -8.488221 -3.192335 0.241152

1108.1043727 -12949.157 3960.760 1442.461 -7.637461 -3.538310 0.135948

1108.1085394 -15577.726 2655.699 1478.628 -6.995104 -3.690614 0.069768

1108.1127061 -18003.449 1314.405 1495.340 -6.501819 -3.750517 0.025890

1108.1168727 -20271.601 -39.225 1498.864 -6.113717 -3.764284 -0.004573

1108.1210394 -22414.349 -1393.068 1493.060 -5.801130 -3.754274 -0.026541

1108.1252061 -24455.055 -2740.838 1480.426 -5.544093 -3.731895 -0.042883

1108.1293727 -26411.105 -4079.289 1462.646 -5.328933 -3.703234 -0.055354

1108.1335394 -28295.751 -5406.821 1440.899 -5.146059 -3.671648 -0.065076

1108.1377061 -30119.308 -6722.755 1416.032 -4.988579 -3.639035 -0.072788

1108.1418727 -31889.962 -8026.934 1388.671 -4.851428 -3.606473 -0.078999

1108.1460394 -33614.315 -9319.497 1359.290 -4.730806 -3.574576 -0.084064

1108.1502061 -35297.774 -10600.750 1328.251 -4.623808 -3.543680 -0.088241

1108.1543727 -36944.819 -11871.088 1295.840 -4.528177 -3.513959 -0.091718

1108.1585394 -38559.210 -13130.950 1262.281 -4.442134 -3.485487 -0.094636

1108.1627061 -40144.134 -14380.790 1227.756 -4.364254 -3.458278 -0.097101

1108.1668727 -41702.314 -15621.060 1192.413 -4.293387 -3.432314 -0.099198

1108.1710394 -43236.101 -16852.200 1156.370 -4.228592 -3.407551 -0.100991

1108.1752061 -44747.535 -18074.635 1119.729 -4.169089 -3.383938 -0.102532

1108.1793727 -46238.401 -19288.767 1082.573 -4.114230 -3.361417 -0.103860

1108.1835394 -47710.272 -20494.979 1044.971 -4.063471 -3.339928 -0.105010

1108.1877061 -49164.536 -21693.632 1006.984 -4.016349 -3.319412 -0.106009

1108.1918727 -50602.432 -22885.065 968.660 -3.972472 -3.299810 -0.106878

1108.1960394 -52025.065 -24069.598 930.045 -3.931501 -3.281068 -0.107637

1108.2002061 -53433.426 -25247.531 891.173 -3.893144 -3.263134 -0.108299

1108.2043727 -54828.412 -26419.145 852.079 -3.857150 -3.245958 -0.108879

1108.2085394 -56210.831 -27584.706 812.789 -3.823296 -3.229495 -0.109387

1108.2127061 -57581.418 -28744.462 773.328 -3.791389 -3.213703 -0.109832

1108.2168727 -58940.844 -29898.648 733.716 -3.761259 -3.198541 -0.110222

1108.2210394 -60289.720 -31047.482 693.974 -3.732755 -3.183972 -0.110564

1108.2252061 -61628.606 -32191.174 654.116 -3.705742 -3.169962 -0.110862

1108.2293727 -62958.019 -33329.918 614.157 -3.680103 -3.156479 -0.111124

1108.2335394 -64278.432 -34463.899 574.111 -3.655730 -3.143494 -0.111351

1108.2377061 -65590.284 -35593.290 533.988 -3.632527 -3.130978 -0.111550

1108.2418727 -66893.981 -36718.257 493.798 -3.610409 -3.118907 -0.111721

1108.2460394 -68189.900 -37838.954 453.551 -3.589298 -3.107256 -0.111870

1108.2502061 -69478.388 -38955.529 413.255 -3.569124 -3.096003 -0.111997

1108.2543727 -70759.773 -40068.121 372.916 -3.549823 -3.085128 -0.112105

1108.2585394 -72034.359 -41176.864 332.541 -3.531337 -3.074611 -0.112197

1108.2627061 -73302.427 -42281.882 292.136 -3.513613 -3.064434 -0.112273

1108.2668727 -74564.246 -43383.295 251.706 -3.496604 -3.054581 -0.112336

1108.2710394 -75820.062 -44481.217 211.256 -3.480264 -3.045035 -0.112386

1108.2752061 -77070.111 -45575.756 170.790 -3.464554 -3.035782 -0.112425

1108.2793727 -78314.613 -46667.013 130.311 -3.449436 -3.026808 -0.112455

1108.2835394 -79553.773 -47755.089 89.823 -3.434876 -3.018100 -0.112475

1108.2877061 -80787.787 -48840.076 49.329 -3.420843 -3.009646 -0.112488

1108.2918727 -82016.839 -49922.064 8.833 -3.407306 -3.001435 -0.112493

1108.2960394 -83241.103 -51001.137 -31.665 -3.394239 -2.993456 -0.112491

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1108.3043727 -85675.918 -53150.866 -112.652 -3.369417 -2.978154 -0.112471

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1108.3127061 -88093.448 -55289.874 -193.617 -3.346196 -2.963665 -0.112430

1108.3168727 -89296.077 -56355.535 -234.088 -3.335137 -2.956705 -0.112404

1108.3210394 -90494.788 -57418.724 -274.548 -3.324420 -2.949925 -0.112374

1108.3252061 -91689.699 -58479.502 -314.996 -3.314031 -2.943316 -0.112340

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1108.3752061 -105769.423 -71040.844 -799.168 -3.210108 -2.875298 -0.111774

1108.3793727 -106923.752 -72075.070 -839.397 -3.202860 -2.870422 -0.111718

1108.3835394 -108075.504 -73107.560 -879.606 -3.195791 -2.865650 -0.111662

1108.3877061 -109224.742 -74138.350 -919.794 -3.188893 -2.860976 -0.111606

1108.3918727 -110371.527 -75167.475 -959.962 -3.182160 -2.856399 -0.111548

1108.3960394 -111515.916 -76194.969 -1000.109 -3.175585 -2.851916 -0.111490

1108.4002061 -112657.967 -77220.865 -1040.235 -3.169164 -2.847523 -0.111432

1108.4043727 -113797.732 -78245.196 -1080.340 -3.162891 -2.843217 -0.111374

1108.4085394 -114935.265 -79267.991 -1120.424 -3.156760 -2.838996 -0.111315

1108.4127061 -116070.616 -80289.283 -1160.487 -3.150767 -2.834858 -0.111257

1108.4168727 -117203.833 -81309.099 -1200.529 -3.144906 -2.830799 -0.111198

1108.4210394 -118334.964 -82327.467 -1240.549 -3.139174 -2.826818 -0.111139

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1108.4293727 -120591.145 -84359.972 -1320.527 -3.128076 -2.819078 -0.111021

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1108.4377061 -122839.505 -86387.008 -1400.419 -3.117442 -2.811622 -0.110903

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1108.4835394 -135079.135 -97446.264 -1838.322 -3.066036 -2.775021 -0.110265

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1108.4918727 -137283.697 -99442.124 -1917.672 -3.057795 -2.769067 -0.110152

1108.4960394 -138383.779 -100438.463 -1957.317 -3.053785 -2.766161 -0.110097

1108.5002061 -139482.431 -101433.765 -1996.942 -3.049847 -2.763301 -0.110041

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1108.5168727 -143863.226 -105404.917 -2155.243 -3.034767 -2.752300 -0.109822

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1108.7377061 -200338.817 -156848.860 -4226.572 -2.901343 -2.651352 -0.107459

1108.7418727 -201382.987 -157803.102 -4265.251 -2.899605 -2.649993 -0.107424

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1108.7710394 -208675.133 -164469.445 -4535.649 -2.887963 -2.640865 -0.107180

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1108.7793727 -210753.322 -166369.968 -4612.795 -2.884798 -2.638374 -0.107113

1108.7835394 -211791.569 -167319.561 -4651.350 -2.883240 -2.637147 -0.107080

1108.7877061 -212829.257 -168268.715 -4689.892 -2.881699 -2.635932 -0.107047

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1114.3418727 -1491583.342 -1350573.266 -54756.951 -2.594856 -2.420603 -0.108167

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1117.0918727 -2103039.724 -1924014.921 -81107.561 -2.551825 -2.406025 -0.113383

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1117.1752061 -2121408.051 -1941336.503 -81924.380 -2.550488 -2.405524 -0.113511

1117.2168727 -2130588.603 -1949995.934 -82333.132 -2.549819 -2.405271 -0.113574

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1117.3418727 -2158115.789 -1975968.720 -83560.732 -2.547807 -2.404502 -0.113759

1117.3835394 -2167286.688 -1984624.459 -83970.372 -2.547136 -2.404242 -0.113819

1117.4252061 -2176455.167 -1993279.260 -84380.228 -2.546464 -2.403981 -0.113879

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1117.5085394 -2194784.862 -2010586.023 -85200.579 -2.545118 -2.403453 -0.113996

1117.5502061 -2203946.074 -2019237.973 -85611.070 -2.544444 -2.403186 -0.114054

1117.5918727 -2213104.859 -2027888.959 -86021.767 -2.543770 -2.402917 -0.114111

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1117.6752061 -2231415.143 -2045188.015 -86843.772 -2.542420 -2.402375 -0.114223

1117.7168727 -2240566.638 -2053836.073 -87255.075 -2.541744 -2.402101 -0.114278

1117.7585394 -2249715.699 -2062483.140 -87666.575 -2.541068 -2.401825 -0.114333

1117.8002061 -2258862.324 -2071129.212 -88078.269 -2.540391 -2.401548 -0.114386

1117.8418727 -2268006.511 -2079774.281 -88490.156 -2.539713 -2.401268 -0.114439

1117.8835394 -2277148.260 -2088418.340 -88902.232 -2.539036 -2.400987 -0.114492

1117.9252061 -2286287.567 -2097061.382 -89314.495 -2.538357 -2.400703 -0.114543

1117.9668727 -2295424.432 -2105703.400 -89726.942 -2.537679 -2.400418 -0.114594

1118.0085394 -2304558.853 -2114344.388 -90139.571 -2.536999 -2.400131 -0.114644

1118.0502061 -2313690.828 -2122984.337 -90552.380 -2.536320 -2.399841 -0.114694

1118.0918727 -2322820.355 -2131623.242 -90965.365 -2.535640 -2.399550 -0.114742

1119.0918727 -2541191.262 -2338624.053 -100923.019 -2.519214 -2.391929 -0.115685

1120.0918727 -2758137.878 -2544911.025 -110942.487 -2.502698 -2.383008 -0.116168

1121.0918727 -2973660.000 -2750368.219 -120983.207 -2.486269 -2.372715 -0.116176

1122.0918727 -3187772.693 -2954876.396 -131004.248 -2.470100 -2.361043 -0.115716

1123.0918727 -3400505.316 -3158317.764 -140966.158 -2.454347 -2.348030 -0.114813

1124.0918727 -3611899.308 -3360579.329 -150832.410 -2.439131 -2.333746 -0.113509

1125.0918727 -3822005.181 -3561554.894 -160570.386 -2.424540 -2.318276 -0.111852

1126.0918727 -4030879.206 -3761145.742 -170151.819 -2.410621 -2.301706 -0.109894

1127.0918727 -4238580.249 -3959260.112 -179552.691 -2.397388 -2.284109 -0.107680

1128.0918727 -4445167.231 -4155811.687 -188752.629 -2.384829 -2.265537 -0.105248

1129.0918727 -4650697.533 -4350717.500 -197733.961 -2.372923 -2.246015 -0.102623

1130.0918727 -4855226.440 -4543895.678 -206480.609 -2.361645 -2.225543 -0.099816

1131.0918727 -5058807.511 -4735263.463 -214977.041 -2.350981 -2.204103 -0.096830

1132.0918727 -5261493.567 -4924735.728 -223207.406 -2.340928 -2.181659 -0.093656

1133.0918727 -5463337.943 -5112224.086 -231154.933 -2.331501 -2.158172 -0.090280

1134.0918727 -5664395.705 -5297636.508 -238801.579 -2.322725 -2.133598 -0.086688

1135.0918727 -5864724.621 -5480877.268 -246127.857 -2.314636 -2.107895 -0.082861

1136.0918727 -6064385.802 -5661847.010 -253112.751 -2.307275 -2.081021 -0.078782

1137.0918727 -6263444.043 -5840442.711 -259733.606 -2.300687 -2.052933 -0.074431

1138.0918727 -6461967.997 -6016557.358 -265965.903 -2.294916 -2.023580 -0.069784

1139.0918727 -6660030.429 -6190079.224 -271782.828 -2.290012 -1.992903 -0.064810

1140.0918727 -6857708.900 -6360890.726 -277154.607 -2.286039 -1.960826 -0.059472

1141.0918727 -7055087.257 -6528867.030 -282047.646 -2.283082 -1.927257 -0.053719

1142.0918727 -7252258.281 -6693874.820 -286423.649 -2.281265 -1.892093 -0.047493

1143.0918727 -7449327.575 -6855771.850 -290238.998 -2.280761 -1.855233 -0.040731

1144.0918727 -7646418.342 -7014407.971 -293444.772 -2.281805 -1.816599 -0.033374

1145.0918727 -7843676.172 -7169628.122 -295987.692 -2.284679 -1.776159 -0.025382

1146.0918727 -8041272.659 -7321277.177 -297812.081 -2.289698 -1.733946 -0.016742

1147.0918727 -8239406.849 -7469205.932 -298862.552 -2.297177 -1.690065 -0.007474

1148.0918727 -8438304.147 -7613277.106 -299086.938 -2.307407 -1.644683 0.002369

1149.0918727 -8638213.030 -7753370.318 -298438.918 -2.320629 -1.598022 0.012706

1150.0918727 -8839400.459 -7889385.472 -296880.009 -2.337029 -1.550327 0.023437

1151.0918727 -9042146.855 -8021244.499 -294380.794 -2.356733 -1.501858 0.034453

1152.0918727 -9246741.298 -8148891.737 -290921.494 -2.379816 -1.452874 0.045642

1153.0918727 -9453477.275 -8272293.344 -286492.010 -2.406307 -1.403620 0.056893

1154.0918727 -9662649.070 -8391436.048 -281091.603 -2.436197 -1.354325 0.068101

1155.0918727 -9874548.818 -8506325.452 -274728.292 -2.469445 -1.305196 0.079167

1156.0918727 -10089464.197 -8616984.050 -267418.062 -2.505991 -1.256418 0.090006

1157.0918727 -10307676.798 -8723449.077 -259183.925 -2.545756 -1.208147 0.100542

1158.0918727 -10529461.152 -8825770.353 -250054.931 -2.588656 -1.160518 0.110711

1159.0918727 -10755084.359 -8924008.287 -240065.187 -2.634604 -1.113642 0.120459

1160.0918727 -10984806.194 -9018232.166 -229252.984 -2.683518 -1.067614 0.129743

1161.0918727 -11218879.519 -9108518.809 -217660.070 -2.735321 -1.022515 0.138526

1162.0918727 -11457550.792 -9194951.589 -205331.086 -2.789941 -0.978416 0.146777

1163.0918727 -11701060.513 -9277619.730 -192313.151 -2.847311 -0.935381 0.154469

1164.0918727 -11949643.499 -9356617.746 -178655.522 -2.907367 -0.893468 0.161581

1165.0918727 -12203528.971 -9432044.853 -164409.260 -2.970043 -0.852729 0.168092

1166.0918727 -12462940.525 -9504004.181 -149626.819 -3.035275 -0.813201 0.173991

1167.0918727 -12728096.175 -9572601.667 -134361.462 -3.102998 -0.774911 0.179271

1168.0918727 -12999208.760 -9637944.554 -118666.468 -3.173159 -0.737862 0.183938

SOLUTION

I TIR D'EVASION VU DE LA TERRE :

1°) a) Quels sont la date calendaire et le jour julien nouveau?

MJD= 1108.0918727 donne avec date_cal.exe la date 13 janvier 2003 à 2 h 12mn 18 s et JJ=1107.5918727

b) Combien dure la traversée de la sphère d'influence de la Terre?

La lecture sur le fichier excel du rayon vecteur donne une date de sortie égale à MJD=1110.758539 soit le 15 janvier 2003 à 18 h 12 mn 18 s c'est à dire 2 jours et 16 h après l'injection . Voir evasion terre.xls

Le tableau Excel donne Ro = 7583 km soit à 1205 km du sol terrestre.

La vitesse d'évasion est alors de norme Vo = 10.8378 km/s.

L'énergie spécifique vaut E = 6.143 km²/s² et correspond à un demi grand axe a = 32331.3 km

Le moment cinétique réduit obtenu par VECTFOND.EXE vaut h = ( 5642.33 //-9256.32 //76068.31 ) donnant une constante des aires K= 76836.86 km²/s

Le calcul de l'excentricité , classique avec E et K ou avec VECTFOND.EXE donne e = 1.20753 et donc un demi angle d'ouverture F des asymptotes donné par cosF = 1/e ===> F = 34°.1

L'inclinaison est donnée par cosi = h(3)/h = 76068.31/76836.86 = 0.9899976 et vaut i= 8°.11

d) Altitude du périgée de l'hyperbole de départ, le demi angle d'ouverture des asymptotes de l'hyperbole.

Rp = a(e-1) = 6710 km soit à 332 km du sol terrestre. Ceci laisse supposer que la mise à feu du moteur assurant l'évasion a eu lieu au passage au périgée à 200 km et s'est terminé vers 400 km environ.

NB : i= 8°.11, c'est une inclinaison orbitale de travail du lanceur Ariane 5, ce qui laisse supposer que l'incrément de vitesse supplémentaire a été délivré probablement colinéairement à la vitesse sur le parking.

2°) Vitesse à l'infini et la constante C3 du vol.

Lorsque Rosetta arrive à une distance de l'ordre de 900 000 km de la terre, sa vitesse est Vinf = 3.63 km/s et correspond à C3 = Vinf ² = 13.18 km²/s².

3°) Quel a été le DV minimum fourni par le moteur d'évasion? Est-ce dans les possibilités du lanceur Ariane 5

Primitivement sur une orbite 4000/200 km, la vitesse au périgée se calcule classiquement par :

a = 8478 km, E= -23.508 km²/s², Vp=(2*E+2*m/R)^0.5 = 8.613 km/s

L'incrément de vitesse est au moins DV = 10.838 - 8.613 = 2.225 km/s

4°) a) ) Avec les deux dates t = 1108.0918727 et t = 1108.1918727 à 0.1 jour d'écart exactement et les positions précises à ces deux dates LAMBERT1.EXE donne :

******************************************************************************

* ............... ROSETTA : EVASION TERRESTRE DU 13/01/2003 .................*

******************************************************************************

------------------- CONDITIONS DE VOL CHOISIES --------------------------

VOL COURT AVEC BALAYAGE ANGULAIRE FINAL < 180°

DUREE CHOISIE DE CE VOYAGE : 8640.0 secondes = 0.1 jour

-----------------------------------------------------------------------------

--------------------- LES POINTS A RELIER -----------------------------------

POINT DE DEPART P1 ( Coordonnées en km ) : à t=1108.0918727 mjd

X en km, X = -3133.84 km

Y en km, Y = 6822.85 km

Z en km, Z = 1062.69 km

POINT D'ARRIVEE P2 ( Coordonnées en km ) : à t=1108.198727 mjd

X en km, X = -50602.43 km

Y en km, Y = -22885.07 km

Z en km, Z = 968.66 km

-----------------------------------------------------------------------------

*-*-*-*-*-*-*-*-*-*-*-* RESULTATS DU CALCUL *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

Distance départ R1 en km, X = 7582.98 km

Distance arrivée R2 en km, X = 55545.21 km

Duree minimale d'un voyage elliptique , X = 10695.2 secondes

VOTRE VOYAGE SERA HYPERBOLIQUE

Rayon vecteur périgée Rp= 6710 km

Anomalie excentrique départ fi1= 0.211 sans dimension

Anomalie excentrique arrivée fi2= 1.451 sans dimension

------------------------- PARAMETRES ORBITAUX -------------------------- -----

VOYAGE HYPERBOLIQUE: CAS DE VOL N° 11

Demi grand-axe a = 32331.71 km

Excentricité e = 1.20752

Longitude Vernale W = 31.365 degrés

Argument Nodal du périgée w= 45.504 degrés

Inclinaison i= 8.111 degrés

Anomalie vraie du départ Téta1 = 37.867 degrés

------------------ VITESSES ABSOLUES DEPART-ARRIVEE -------------------------

DEPART

Sur I : V1X = -10.7860 km/s

Sur J : V1Y = -0.7903 km/s

Sur K : V1Z = 0.7039 km/s

NORME DE LA VITESSE ABSOLUE V1 = 10.8378 km/s

ARRIVEE

Sur I : V2X = -3.9725 km/s

Sur J : V2Y = -3.2998 km/s

Sur K : V2Z = -0.1069 km/s

NORME DE LA VITESSE ABSOLUE V2 = 5.1653 km/s

--------------------------------------------------------

DESCRIPTION DU CAS DE VOL HYPERBOLIQUE N° 11

Ce qui confirme parfaitement tous les calculs précédents, notamment le périgée à 6710 km du centre de la Terre.

Guiziou Robert janvier 2003