Low-cost travels within the Solar system
Celletti, Alessandra
La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana, Tome 7 (2014), p. 157-180 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

Modern space mission designs are often based on merging advanced notions of Celestial Mechanics and Dynamical Systems theory. In particular, the special configurations known as collinear equilibrium points are used to compute low-energy orbits, which allow us to let the spacecraft travel along natural dynamical routes, without requiring too much fuel consumption (hence minimizing the total cost of the mission). The overall astrodynamical strategy comes over the centuries, thanks to the works of Euler, Lagrange and Conley. Nowadays, several space missions exploit the potentiality of the collinear points, allowing low-cost travels within the Solar system.

Le progettazioni delle moderne missioni spaziali sono spesso basate su una fusione di concetti avanzati della Meccanica Celeste e della teoria dei Sistemi Dinamici. In particolare, alcune configurazioni speciali note come punti di equilibrio collineari sono usate per calcolare orbite a bassa energia, le quali consentono di far si che la sonda percorra delle traiettorie naturali, senza richiedere troppo consumo di carburante (e quindi minimizzando la spesa della missione). L’attuale strategia usata in Astrodinamica ci giunge attraverso i secoli, grazie ai lavori di Eulero, Lagrange e Conley. Numerose missioni spaziali sono state lanciate sfruttando le potenzialità dei punti collineari, che consentono viaggi a basso costo nel sistema solare.

Publié le : 2014-08-01
@article{RIUMI_2014_1_7_2_157_0,
     author = {Alessandra Celletti},
     title = {Low-cost travels within the Solar system},
     journal = {La Matematica nella Societ\`a e nella Cultura. Rivista dell'Unione Matematica Italiana},
     volume = {7},
     year = {2014},
     pages = {157-180},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RIUMI_2014_1_7_2_157_0}
}

Celletti, Alessandra. Low-cost travels within the Solar system. La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana, Tome 7 (2014) pp. 157-180. http://gdmltest.u-ga.fr/item/RIUMI_2014_1_7_2_157_0/

[1] Bucciarelli, S., Ceccaroni, M., Celletti, A., Pucacco, G., Qualitative and analytical results of the bifurcation thresholds to halo orbits, accepted for publication in Annali di Matematica Pura ed Applicata (2015). | MR 3476685 | Zbl 1344.70021

[2] Celletti, A., Stability and Chaos in Celestial Mechanics, Springer-Verlag, Berlin; published in association with Praxis Publishing Ltd., Chichester, ISBN: 978-3-540-85145-5 (2010). | MR 2571993 | Zbl 1203.70001

[3] Celletti, A., Pucacco, G., Stella, D., Lissajous and Halo orbits in the restricted three-body problem, accepted for publication in J. Nonlinear Science (2015). | MR 3318799 | Zbl 1344.70022

[4] Conley, C.C., Low energy transit orbits in the restricted three-body problem, SIAM J. Appl. Math.16, n. 4, 732-746 (1968). | MR 233535 | Zbl 0197.21105

[5] Conley, C.C., On the ultimate behavior of orbits with respect to an unstable critical point. I. Oscillating, asymptotic, and capture orbits, J. Diff. Eq.5, 136-158 (1969). | MR 251301 | Zbl 0169.11402

[6] Conley, C.C., Isolated Invariant Sets and the Morse Index, CBMS Regional Conference Series in Mathematics38, American Mathematical Society, Rhode Island (1978). | MR 511133 | Zbl 0397.34056

[7] Euler, L., Considerationes de motu corporum coelestium. Novi commentarii academiae scientiarum Petropolitanae10, 544-558 (1764) (read at Berlin in 1762). See also: Opera Omnia, s. 2, 25, 246-257.

[8] Farquar, R.W., The control and use of libration-point satellites, Ph.D. dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford CA, USA (1968).

[9] Farquar, R.W., Kamel, A.A., Quasi-periodic orbits about the translunar libration point, Cel. Mech.7, 458 (1973). | Zbl 0258.70011

[10] Gómez, G., Barrabés, E., Space Manifold Dynamics, in ``Celestial Mechanics'', A. Celletti ed., EOLSS-UNESCO publ., ISBN 978-1-78021-519-8 (2015).

[11] Gómez, G., Jorba, À., Masdemont, J., Simó, C., Study refinement of semi-analytical Halo orbit theory, ESOC Contract 8625/89/D/MD(SC), Final Report (1991).

[12] Gómez, G., Mondelo, J.M., The dynamics around the collinear equilibrium points of the RTBP, Physica D157, 283-321 (2001). | MR 1862865 | Zbl 0990.70009

[13] Henrard, J., Periodic orbits emanating from a resonant equilibrium, Cel. Mech.1, 437- 466 (1970). | MR 260240 | Zbl 0193.25302

[14] Hohmann, W., Die Erreichbarkeit der Himmelskörper, Verlag Oldenbourg, München (1925).

[15] Jorba, À., Masdemont, J., Dynamics in the center manifold of the collinear points of the restricted three body problem, Physica D, 132, 189-213 (1999). | MR 1705705 | Zbl 0942.70012

[16] Kepler, J., Astronomia nova seu physica coelestis tradita commentariis de motibus stellæ, Heidelberg, Voegelin (1609).

[17] Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D., Heteroclinic connections between periodic orbits and resonance transitions in Celestial Mechanics, Chaos10, n. 2, 427- 469 (2000). | MR 1765636 | Zbl 0987.70010

[18] Lagrange, J.-L., Essai sur le problème des trois corps, Prix de l'Académie royale des sciences de Paris, tome IX (1772).

[19] Moser, J., On the generalization of a theorem by A. Liapounoff, Comm. Pure Appl. Math.XI, 257-271 (1958). | MR 96021 | Zbl 0082.08003

[20] Murray, C.D., Dermott, S.F., Solar system dynamics, Cambridge University Press (1999). | MR 1747818 | Zbl 0957.70002

[21] NASA/JPL Keplerian elements, available on http://ssd.jpl.nasa.gov/txt/p_elem_t1.txt

[22] Richardson, D.L., Analytic construction of periodic orbits about the collinear points, Celestial Mechanics22, 241-253 (1980). | MR 590496 | Zbl 0465.34028