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L'altimétrie Planétaire

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L'altimétrie Planétaire 1 / xx L’altimétrie planétaire G. Balmino , CNES-GRGS 7ème Ecole d’ été du GRGS Saint-Pierre d’Oléron " Altimétrie spatiale " 1-5 Septembre 2014 LE BUT Connaissance précise de : - la forme globale (moyenne) d’un corps - ses variations détaillées de forme : topographie Noyau de C-G (Rosetta, 23 juillet 2014) Pourquoi ? Comment ? Principales missions Pourquoi ? LES GRANDES QUESTIONS Formation Evolution Structure interne ... ... des corps du système solaire en particulier ceux dits de "type terrestre" … sont abordées avec les outils de : la mécanique céleste la géodésie spatiale la géologie la géophysique … et les données : - des télescopes : au sol, en orbite (HST) - des missions spatiales Structure ⇔ Histoire thermique DIFFERENCIATION D' UNE PLANETE, D' UN SATELLITE Existence, taille et nature de : noyau manteau Champ de gravité croûte CHRONOLOGIE DES EVENEMENTS EN SURFACE Caractères physiographiques et géologiques Distribution des cratères (type, taille, fréquence) Topographie → âges ~ relatifs "CLIMAT" Rotation, obliquité Atmosphère : Terre, Vénus, Mars, Titan... ⇔ Eau ? Océans : Terre, Europe, Encelade… Vie ??? Notre connaissance de la structure interne des planètes et satellites naturels provient essentiellement : de la mesure de la topographie (incluant forme globale et taille) du champ de gravité (dont la masse) Gouvernent la forme de la rotation globale des observations "géologiques" (imagerie multi-spectrale) PROPRIETES GLOBALES - Taille + Forme ⇒ Volume Masse volumique - Mouvement orbital + 3ème loi de Képler ⇒ Masse (densité) - Forme ⇒ Centre de figure - Centre de masse Écart ? (déterminé via un objet en orbite autour du corps) (structure interne) - Rotation propre : vitesse angulaire - Masse Aplatissement - Taille moyenne (rayon) dynamique - Coef. zonal J2 du potentiel de gravitation Moment d’inertie - Coef. J 2 polaire moyen - Constante de précession < 0.4 ? - Moment d’inertie polaire moyen Aplatissement - Vitesse angulaire de rotation hydrostatique Forme globale et potentiel gravitationnel (U ) : le problème direct Forme globale et potentiel gravitationnel (U ) : le problème inverse Stratification : surfaces limites ? sauts de densité ? ⇒ INVERSION : CHAMP DE DENSITE r0 A PARTIR DU CHAMP DE GRAVITE r 1 F(U) = ρ ∗ F(1/ r) r 2 ρ2 ρ0 ρ1 Observation Densité distance ρ : pas de solution unique (problème inverse singulier) F(U) + autres données (vitesses sismiques, ...) Mais : + hypothèses physico-chimiques ρ(r) + contraintes (relatives) sur ρ (sur Δρ) Exemples de modèles Problèmes régionaux / locaux Champ de gravité + topographie 1. Isostasie densité d ⇒ Etude des propriétés ex : modèle d'Airy 0 de la croûte (lithosphère) et du manteau supérieur d > d0 2. Flexure (visco-) élastique d1 d0 Vénus : les "pancakes" d > d0 EXEMPLE D'INVERSION D'UN PROBLEME REGIONAL Recherche des variations de densité Mesures - gravité (g) ou potentiel (U )en surface (ou en orbite), ou F(g,U) ...... (1) - vitesses sismiques VP , VS (avec λ , µ donnés) - cas de la Terre ...... (2) orbite mesure : F(g) g topo. discrétisée ρij décomposition en éléments finis Equations d'observation : correspondant à (1), (2) Inéquations de contrainte : ρ1 < ρij < ρ2 ; Δρ1 < ρij − ρi−n, j− p < Δρ2 Résolution : méthode des moindres carrés avec inégalités … mais problème récurrent Champ de gravité (g) + topographie (t) Inadéquation: résolution (g) vs. (t) (g) ç observ. des (t) ç photogram. perturbations altimétrie (D) orbitales 2 Klm ~ A / l S uˆ . Δρ ~0.05 – 0.1 mm/s r D T λmin ~ altitude station O TERRE è résolution ~200 km è résolution : ~ ou < km ! (MGS, ODY) ex : MOLA-MGS Comment ? Observations télescopiques terrestres Ex : La Lune - diamètres des cratères - altitude des reliefs (mesure des ombres) Obs. de Meudon, 1966 Observations télescopiques en orbite Vesta Observations radar depuis la Terre Goldstone – Mojave, USA, 1959 Pluton complex Yevpatoria, URSS, 1960 D Puissance du signal retour en 1/D4 Dist. max. détection ~ √taille de l’objet Observations radar depuis la Terre Radio-télescope d’Arecibo (Porto Rico, 1960-63), D = 305 m 20 TW @ 2380 MHz, 2.5 TW @ 430 MHz, et 300 MW @ 47 MHz Venus, 1974 Quelques "premières" radar d’Arecibo Maxwell Mt. images 216 Kleopatra, nov.1999 Mercure, pôle N, 1999 modèle Observations radar (ou autres) en orbite Navigation précise ⇒ radio-sciences : - champ de gravité - topographie imagerie altitudes nature du sol Observations en orbite S Il faut : uˆû - la position de S / (R) r D - l’attitude ⇒ û / (R) - mesurer D T surface du corps GO (R) lié au corps Alternative : on ne mesure pas de distances directement, mais : Ak, Bk dans Rk {xk, yk, zk} ûk , Rk dans (R) AB dans (R): (stéréo)-photogrammétrie O1O2 dans (R) z z1 2 x O1 2 O2 y1 y2 x1 û1 û2 (R) ⇒ Problème global de géodésie spatiale planétaire Réf: S quasars û T G obs. = f ( GS ou OS, û ) = F [ GS(t0 ), t , param.), û ] • O OS (t0 ) référentiels Terre ( & cinématique) déformations dynamique (forces) La précision dépend beaucoup de la finesse du traitement global ! Corps perturbateur ∼ SST-hl Mouvement de Plasma solaire & interplanétaire Mouvement de l'axe de rotation l'axe de rotation de la Terre du corps observé Station "Deep space" Orbite du corps observé Orbite Observation de la trajectoire de la Effets relativistes (retard, courbure) Terre • Position-vitesse de l'orbiteur (navigation) • Paramètres des modèles de perturbations : • Taille et forme de la planète ; topographie - gravitation : statique, marées solides, (+ océans) + - atmosphère (frottement), redistribution de masses • Paramètres rotationnels : (ex : océan/atmosphère/calottes polaires) angle ("temps") sidéral - pression solaire directe + albedo (surface, nuages) coord. du pôle (α,δ) et variations • Si lander, rover, ballon… : position (t) Géodésie dynamique Un altimètre mesure D … S uˆ r D T surface du corps O (R) lié au corps Différents types d’instruments Altimètre radar conventionnel, "pulse limited" Retour de l’impulsion Altimètre laser ~ few 100 meters Signal retour : D = c Δt / 2 Δt small Laser pulse Counts ~power sent from s/c footprint Essai d’un prototype de MOLA (altimètre laser pour les missions martiennes) Navette "Endeavour" (janvier 1996) Profil sur Mauna Kea SAR (radar à ouverture synthétique) Longueur "synthétique" du SAR L (1) Imagerie Développé dans les années 70 pour des besoins militaires de surveillance Le processeur stocke tous les signaux retours, amplitude et phase, pendant le temps T correspondant au déplacement de A en D. On reconstruit alors le signal qui aurait été obtenu par une antenne de longueur L = vT (v : vitesse du satellite) ⇒ résolution beaucoup plus grande Construction (théorique) pas à pas du (2) Mode altimètre signal retour (pour un faisceau unique). = "Delay Doppler/SAR altimeter" En mode altimètre on traite chaque cellule le long de la trace (tant qu’elle est illuminée). Chaque cellule est vue par une plus grande portion du lobe d’antenne que dans l’altimétrie classique ("pulse limited") ⇒ plus d’information Avantages : - utilisation optimale de la puissance du signal Contrairement à l’altimétrie radar classique, - résolution accrue la surface illuminée n’est pas un anneau de surface constante mais seulement une partie - mesure de distance le long ⇒ Forme plus « pointue » de l’écho. de la trace et orthogonalement ( et plusieurs faisceaux sont utilisés simultanément Les altimètres planétaires sont en majorité de type laser. Avantages : - très grande précision - pas de grande antenne - puissance requise bien adaptée Mais : - empreinte au sol petite - difficultés d’estimation des pentes (sauf instrument multi-faisceaux) - utilisation des écarts aux intersections de profils (X-overs) plus délicate (pentes topographiques de la surface solide : très variables) B C B 5 • A • 1 4 • t • 2 1 2 3 4 5 3 • • 3 X-O • 4 •2 C 1 D • 5 • D A 1 2 3 4 5 t Principales missions Lune Venus Mars Mercure Saturne (Titan) … et la Terre TERRE SRTM (Shuttle Radar Topography Mission) 11-22 fév. 2000 Navette : Endeavour (STS 99) Alt. ~233 km, I = 57° Résolution : 30 m (grilles à 30 m, 90 m, 900 m) Précision : planimétrique ~ 50 m altimétrique ~ 15 m 60 m Interférométrie radar 2 radards : bande C SAR bande X SRTM - Couverture : 60° N – 56° S Paris et sa région Ouest du Tibet Bali Tanzanie Volcan Meru Région de Los Angeles La LUNE Apollo 15, 16, 17 Clementine Chang’E 1, 2 Selene - Kaguya LRO (Lunar Reconnaissance Orbiter) (+ GRAIL) Apollo 15, 16, 17 A-15 : 26 juillet – 7 août 1971 A-16 : 16 avril – 27 avril 1972 A-17 : 7 déc. – 19 déc. 1972 + radar imageur (SAR) sur A- 17 Caractéristiques des altimètres laser d’Apollo 15, 16, 17 Faisceau pulsé à 694.3 nm (rubis) Flashes de 200 nJ pendant 10 ns Résolution ~2 m Distance entre mesures : 30 à 43 km Erreur absolue ~25 à 400 m Précision relative (le long de la même orbite) ~10 m Caractéristiques orbitales h(péri- h(apo- Incl. Période N.bre Lune) Lune) révol. Apollo 15 107 km 315 km 168.0° 120 mn 64 Apollo 16 101 km 120 km 23.0° 87 mn 72 Apollo 17 170 km 170 km 28.5° 108 mn 74 Apollo 15 : I = 168° (12° rétrogr.) Apollo 16 : I = 23° Apollo 15 Apollo 15 rev Apollo 17 Quelques profils sur la face cachée Apollo 17 Altimètre laser Face visible ⇒ Face cachée ⇒ Les apports des altimètres Apollo Recalage des altitudes de la face visible obtenues par photos télescopiques et les Lunar Orbiters H( "mers" ) < plusieurs km aux "highlands" environnantes Altitudes de la face cachée Face cachée : plus haute et plus rugueuse que la face visible Offset centre de masse / centre de figure : 2.5 km, direction 24°E Terre Cf. épaisseurs de croûte modélisées ultérieurement
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