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Some orbital characteristics of lunar artificial satellites. (English) Zbl 1223.70075
Summary: In this paper we present an analytical theory with numerical simulations to study the orbital motion of lunar artificial satellites. We consider the problem of an artificial satellite perturbed by the non-uniform distribution of mass of the Moon and by a third-body in elliptical orbit (Earth is considered). Legendre polynomials are expanded in powers of the eccentricity up to the degree four and are used for the disturbing potential due to the third-body. We show a new approximated equation to compute the critical semi-major axis for the orbit of the satellite. Lie-Hori perturbation method up to the second-order is applied to eliminate the terms of short-period of the disturbing potential. Coupling terms are analyzed. Emphasis is given to the case of frozen orbits and critical inclination. Numerical simulations for hypothetical lunar artificial satellites are performed, considering that the perturbations are acting together or one at a time.
MSC:
70M20Orbital mechanics (general mechanics)
References:
[1]Abad A., Elipe A., Tresaco E.: Analytical model to find frozen orbits for a lunar orbiter. J. Guid. Control Dyn. 32(3), 888–898 (2009) · doi:10.2514/1.38350
[2]Breiter S.: Second-order solution for the zonal problem of satellite theory. Celest. Mech. Dyn. Astron. 67, 237–249 (1997) · Zbl 0900.70369 · doi:10.1023/A:1008234420951
[3]Breiter S., Elipe A.: Critical inclination in the main problem of a massive satellite. Celest. Mech. Dyn. Astron. 95, 287–297 (2006) · Zbl 1152.70314 · doi:10.1007/s10569-005-5911-x
[4]Broucke R.A.: The Double Averaging of the Third Body Perturbations; Classnotes. Austin-Texas University, USA (1992)
[5]Broucke R.A.: Long-term third-body effects via double averaging. J. Guid. Control Dyn. 26(1), 27 (2003) · doi:10.2514/2.5041
[6]Brouwer D.: Solution of the problem of an artificial satellite, theory without drag. Astron. J. 64(9), 378–397 (1959) · doi:10.1086/107958
[7]Carvalho, J.P.dos S., Vilhena de Moraes, R., Prado, A.F.B.A.: Moon artificial satellites: Lunar oblateness and earth perturbations. In: ICNPAA-2008, 2009, Genoa. Proceedings of the ICNPAA 2008, pp. 1095–1106. Cambrige Scientific, Cambridge (2009a)
[8]Carvalho J.P.dos S., Vilhena de Moraes R., Prado A.F.B.A.: Nonsphericity of the Moon and near Sun-synchronous polar lunar orbits. Math. Probl. Eng. 2009, 1–25 (2009b) · Zbl 1188.70052 · doi:10.1155/2009/740460
[9]Cayley A.: Tables of the developments of functions in theory of elliptic motion. Mem. Roy. Astron. Soc. 29, 191–306 (1861)
[10]D’Avanzo P., Teofilatto P., Ulivieri C.: Long-terms effects on lunar orbiter. Acta Astronaut. 40(1), 13–20 (1997) · doi:10.1016/S0094-5765(97)00010-6
[11]De Saedeleer B., Henrard J.: The combined effect of J 2 and C 22 on the critical inclination of a lunar orbiter. Adv. Space Res. 37, 80–87 (2006) · doi:10.1016/j.asr.2005.06.052
[12]De Saedeleer B.: Analytical theory of a lunar satellite with third body perturbations. Celest. Mech. Dyn. Astron. 95, 407–423 (2006) · Zbl 1219.70066 · doi:10.1007/s10569-006-9029-6
[13]Domingos R.C., Moraes R.V., Prado A.F.B.A.: Third-body perturbation in the case of elliptic orbits for the disturbing body. Adv. Appl. Stat. Sci. 130, 1571–1578 (2008)
[14]Elipe A., Lara M.: Frozen orbits about Moon. J. Guid. Control Dyn. 26(2), 238–243 (2003) · doi:10.2514/2.5064
[15]Ely T.A., Lieb E.: Constellations of elliptical inclined lunar orbits providing polar and global coverage. J. Astronaut. Sci. 54(1), 53–67 (2006) · doi:10.1007/BF03256476
[16]Ferrer S., San-Juan J.F., Abad A.: A note on lower bounds for relative equilibria in the main problem of artificial satellite theory. Celest. Mech. Dyn. Astron. 99, 69–83 (2007) · Zbl 1162.70327 · doi:10.1007/s10569-007-9091-8
[17]Folta, D., Quinn, D.: Lunar Frozen Orbits, Paper AIAA 2006-6749, Aug (2006)
[18]Giacaglia G.E.O., Murphy J., Felsentreger T.: A semi-analytic theory for the motion of a lunar satellite. Celest. Mech. 3, 3–66 (1970) · Zbl 0213.51605 · doi:10.1007/BF01230432
[19]Hori G.I.: Theory of general perturbations with unspecified canonical variables. Publ. Astr. Soc. Jpn. 18(4), 287–296 (1966)
[20]Hori G.I.: A new approach to the solution of the main problem of the lunar theory. Astr. J. 68, 125–146 (1963) · doi:10.1086/108930
[21]Knežević Z., Milani A.: Orbit maintenance of a lunar polar orbiter. Planet Space Sci. 46(11/12), 1605–1611 (1998) · doi:10.1016/S0032-0633(98)00021-X
[22]Kovalevsky J.: Introduction to Celestial Mechanics. Lib. Armand Colin, Paris (1967)
[23]Kozai Y.: Secular perturbations of asteroids with high inclination and eccentricity. Astron. J. 67(9), 591 (1962) · doi:10.1086/108790
[24]Lara, M., Palacián, J.F., Russell, R.P.: Mission design through averaging of perturbed keplerian systems: The paradigm of an Enceladus orbiter. Celest. Mech. Dyn. Astron. 108, 1–22 (2010)
[25]Meyer, W.K., Buglia, J.J., Desai, P.N.: Lifetimes of Lunar Satellite Orbits. NASA STI/Recon Technical Report N-TP-3394 94, 27771 (1994)
[26]Morando B.: Mouvement d’um Satellite Artificiel de la Terre. Gordon and Breach, Paris (1974)
[27]Murray C.D., Dermott S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999)
[28]Oesterwinter C.: The motion of a lunar satellite. Celest. Mech. 1, 368–436 (1970) · Zbl 0185.52405 · doi:10.1007/BF01231142
[29]Palacián J.F.: Dynamics of a satellite orbiting a planet with an inhomogeneous field. Celest. Mech. Dyn. Astron. 98, 219–249 (2007) · Zbl 1136.70316 · doi:10.1007/s10569-007-9078-5
[30]Park S.Y., Junkins J.L.: Orbital mission analysis for a lunar mapping satellite. J. Astronaut. Sci. 43(2), 207–217 (1995)
[31]Prado A.F.B.A.: Third-body perturbation in orbits around natural satellites. J. Guid. Control Dyn. 26(1), 33–40 (2003) · doi:10.2514/2.5042
[32]Radwan M.: Analytical approach to the motion of a lunar artificial satellite. Astrophys. Space Sci. 283(2), 133–150 (2003)
[33]Solórzano, C.R.H.: Third-Body Perturbation Using a Single Averaged Model. Master Dissertation, National Institute for Space Research (INPE), São José dos Campos, SP, Brazil (2002)
[34]Szebehely V.: Adventures in Celestial Mechanics. University of Texas Press, Austin (1989)
[35]Tzirti S., Tsiganis K., Varvoglis H.: Quasi-critical orbits artificial lunar satellites. Celest. Mech. Dyn. Astron. 104(3), 227–239 (2009) · Zbl 1223.70101 · doi:10.1007/s10569-009-9207-4
[36]Wang X., Liu L.: Another mechanism of restricting the lifetimes of orbiting satellites. Chin. Astron. Astrophys. 26, 489–496 (2002) · doi:10.1016/S0275-1062(02)00100-5
[37]Winter O.C., Mourão D.C., Melo C.F., Macau E.N., Ferreira J.L., Carvalho J.P.dos S.: Controlling the eccentricity of polar lunar orbits with low-thrust propulsion. Math. Probl. Eng. 2009, 1–10 (2009) · Zbl 1184.70012 · doi:10.1155/2009/159287