Abstract
We discuss the existence, location, and stability of the collinear equilibrium points of a generalized Hill problem with radiation of the primary (the Sun) and oblateness of the secondary (the planet), and present some remarkable fractals created as basins of attraction of Newton’s method applied for their computation in several cases of the parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
AbdulRaheem, A., Singh, J.: Astron. J. 131, 1880 (2006)
Chernikov, Y.A.: Sov. Astron. AJ 14, 176 (1970)
Douskos, C.N., Markellos, V.V.: Astron. Astrophys. 446, 357 (2005)
Hill, G.W.: Acta Math. 8, 1 (1886)
Kroustalloudi, M., Kalvouridis, T.: Planet. Space Sci. 55, 53 (2006)
Kunitsyn, A.L., Polyakhova, E.N.: Astron. Astrophys. Trans. 6, 283 (1995)
Markakis, M.P., Perdiou, A.E., Douskos, C.N.: Astrophys. Space Sci. 315, 297 (2008)
Markellos, V.V., Roy, A.E., Velgakis, M.J., Kanavos, S.S.: Astrophys. Space Sci. 271, 293 (2000)
Markellos, V.V., Roy, A.E., Perdios, E.A., Douskos, C.N.: Astrophys. Space Sci. 278, 295 (2001)
Oberti, P., Vienne, A.: Astron. Astrophys. 397, 353 (2003)
Schuerman, D.W.: Astrophys. Space Sci. 19, 351 (1972)
Schuerman, D.W.: Astrophys. J. 238, 337 (1980)
Schwehm, G.: In: Elsasser, H., Fechtig, H. (eds.) Lecture Notes in Physics, vol. 48, p. 459. Springer, Berlin (1976)
Sharma, R.K.: Astrophys. Space Sci. 135, 271 (1987)
Sharma, R.K., Subba Rao, P.V.: Celest. Mech. 12, 189 (1975)
Sharma, R.K., Subba Rao, P.V.: Celest. Mech. 13, 137 (1976)
Simmons, J.F.L., McDonald, A.J.C., Brown, J.C.: Celest. Mech. 35, 145 (1985)
Szebehely, V.G.: Theory of Orbits. Academic Press, New York (1967)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Douskos, C.N. Collinear equilibrium points of Hill’s problem with radiation and oblateness and their fractal basins of attraction. Astrophys Space Sci 326, 263–271 (2010). https://doi.org/10.1007/s10509-009-0213-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-009-0213-5