Abstract
In this paper, we study the invariant manifold and its application in transfer trajectory problem from a low Earth parking orbit to the Sun-Earth \(L_{1}\) and \(L_{2}\)-halo orbits with the inclusion of radiation pressure and oblateness. Invariant manifold of the halo orbit provides a natural entrance to travel the spacecraft in the solar system along some specific paths due to its strong hyperbolic character. In this regard, the halo orbits near both collinear Lagrangian points are computed first. The manifold’s approximation near the nominal halo orbit is computed using the eigenvectors of the monodromy matrix. The obtained local approximation provides globalization of the manifold by applying backward time propagation to the governing equations of motion. The desired transfer trajectory well suited for the transfer is explored by looking at a possible intersection between the Earth’s parking orbit of the spacecraft and the manifold.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alexander, S., Antonio, F.B., Prado, A.: Celest. Mech. Dyn. Astron. 90(3–4), 331–354 (2004)
Baoyin, H., McInnes, C.: Celest. Mech. Dyn. Astron. 94, 155–171 (2006)
Barden, B.T.: Using stable manifolds to generate transfers in the circular restricted problem of three bodies. MS Thesis, Purdue University (1994)
Bettis, D.G., Szebehely, V.: Astrophys. Space Sci. 31, 388–405 (1971)
Betts, J.T.: J. Guid. Control Dyn. 21(2), 193–207 (1998)
Canalias, E., Gomez, G., Marcote, M., Masdemont, J.J.: Assessment of mission design including utilization of libration points and weak stability boundaries, ESA-ESTEC ARIADNA, 03/4103 (2004)
Di Donato, P.F.A., Masdemont, J.J., Paglione, P., de Almeida Prado, A.F.B.: In: Proceedings of COBEM 2007, 19th International Congress of Mechanical Engineering, November 5–9, 2007, Brasília, DF (2007)
Fitzpatrick, R.: An Introduction to Celestial Mechanics. Cambridge University Press, New York (2012)
Folta, D.C., Beckman, M., Marr, G.C., Mesarch, M., Cooley, S., Leete, S.J.: Servicing and deployment of national resources in Sun-Earth libration point orbit. IAC Paper 02-Q.6.08 (2002)
Gomez, G., Jorba, A., Masdemont, J., Simo, C.: Celest. Mech. Dyn. Astron. 56, 541–562 (1993)
Heiligers, J., McInnes, C.: Novel solar sail mission concepts for space weather for fixed point recasting. In: 24th AAS/AIAA Space Flight Mechanics Meeting, Santa Fe, NM (2014)
Howell, K.C., Kakoi, M.: Acta Astronaut. 59, 367–380 (2006)
Howell, K.C., Barden, B., Lo, M.: J. Astronaut. Sci. 45(2), 161–178 (1997)
Lei, H., Xu, B.: J. Eng. Math. 98(1), 163–186 (2016)
Lei, H., Xu, B.: Astrophys. Space Sci. 362(4), 75 (2017)
Lei, H., Xu, B., Hou, X., Sun, Y.: Celest. Mech. Dyn. Astron. 117(4), 349–384 (2013)
Mains, D.L.: Transfer trajectories from Earth parking orbits to L1 halo orbits. MS Thesis, Purdue University (1994)
Martin, T.O.: A low-thrust transfer strategy to Earth-Moon collinear libration point orbits. MS Thesis, Purdue University (2006)
Masdemont, J.J.: Dyn. Syst. 20, 59–113 (2005)
McInnes, C.R.: Solar Sailing: Technology, Dynamics and Mission Applications. Springer, Berlin (1999)
Mireless, J.D.: The State Transition Matrix and Method of Differential Corrections. Rutgers University Press, New Brunswick (2006)
Moore, A., Ober-Blobaum, S., Marsden, J.E.: Optimization of spacecraft trajectories: a method combining invariant manifold techniques and discrete mechanics optimal control, AAS, 09-257 (2010)
Nath, P., Ramanan, R.V.: Adv. Space Res. 57, 202–217 (2016)
Parrish, N.L., Parker, J.S., Hughes, S.P., Heiligers, J.: Low-thrust transfers from distant retrograde orbits to L2 halo orbits in the Earth-Moon system. In: International Conference on Astrodynamics Tools and Techniques, 6th, Darmstadt, Germany, 14–17 Mar. 2016
Patterson, C.E.: Representations of invariant manifolds for applications in system-to-system transfer design. MS Thesis, Purdue University (2005)
Perozzi, E., Mello, S.F.: Space Manifold Dynamics: Novel Spaceways for Science and Exploration. Springer, Berlin (2010)
Rausch, R.R.: Earth to halo orbit transfer trajectories. MS Thesis, Purdue University (2005)
Seetha, S., Megala, S.: Curr. Sci. 113(4), 610–612 (2017)
Shang, H., Shuai, W., Pingyuan, C.: Chin. J. Aeronaut. 27(2), 338–348 (2014)
Srivastava, V.K., Kumar, J., Kushvah, B.S.: Acta Astronaut. 129, 389–399 (2016)
Srivastava, V.K., Kumar, J., Kushvah, B.S.: Astrophys. Space Sci. 362, 49 (2017)
Szebehely, V.: Theory of Orbits. The Restricted Problem of Three Bodies. Academic Press, San Diego (1967)
Tiwary, R.D., Kushvah, B.S.: Astrophys. Space Sci. 357, 73 (2015)
Vallado, D.A.: Fundamental of Astrodynamics and Applications, 4th edn. Microcosm, Hawthorne (2013)
Verrier, P., Waters, W., Sieber, J.: Celest. Mech. Dyn. Astron. 120(4), 373–400 (2014)
Waters, T.J., McInnes, C.R.: J. Guid. Control Dyn. 30(3), 687–693 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Srivastava, V.K., Kumar, J. & Kushvah, B.S. Halo orbit transfer trajectory design using invariant manifold in the Sun-Earth system accounting radiation pressure and oblateness. Astrophys Space Sci 363, 17 (2018). https://doi.org/10.1007/s10509-017-3235-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-017-3235-4