Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T18:55:44.917Z Has data issue: false hasContentIssue false
  • English
  • Français

Lommel Functions in some Drag-Perturbed Problems

Published online by Cambridge University Press:  12 April 2016

Sławomir Breiter  and
Albert A. Jackson
Sławomir Breiter
Affiliation:
Astronomical Observatory of the A. Mickiewicz University, Słoneczna 36, PL 60-286 Poznań, Poland. E-mail:breiter@phys.amu.edu.pl
Albert A. Jackson
Affiliation:
Lunar and Planetary Institute, 3600 Bay Area Blvd. Houston, TX 77058, USA.

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let us consider the orbital problem in which a particle is subject to the force (per unit mass)

The force consists of the Newtonian two body attraction term and a drag part which is linear in both components of velocity (radial vr and transverse vt). Depending on a physical interpretation of the parameters μ and α, as well as on the particular choice of the dimensionless constant γ, the model (1) can match various two body problems with dissipation. They include the classical Poynting-Robertson effect (Robertson, 1936) with γ = 1, Poynting’s (1903) version with γ = ½ and the two body drag cases recently studied by Mittleman and Jezewski (1982) and by Mavraganis and Michalakis (1994) under the name of Danby’s drag.

Type
Extended Abstracts
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 437 - 438
Copyright
Copyright © Kluwer 1999

References

Breiter, S., Jackson, A.A.: 1998, ‘Unified analytical solutions to two-body problems with drag’, MNRAS, 299, 237–243.CrossRefGoogle Scholar
Klačka, J., Kaufmannová, J.: 1992, ‘Poynting-Robertson Effect: “Circular” Orbit’, Earth, Moon and Planets, 59, 97–102.CrossRefGoogle Scholar
Mavraganis, A.G., Michalakis, D.G.: 1994, ‘The Two-Body Problem with Drag and Radiation Pressure’, tCelest. Mech. & Dynam. Astron., 58, 393–403.CrossRefGoogle Scholar
Mittleman, D., Jezewski, D.: 1982, ‘An Analytic Solution to the Classical Two-Body Problem with Drag’, Celest. Mech., 28, 401–413.CrossRefGoogle Scholar
Poynting, J.H.: 1903, ‘Radiation in the Solar System: its Effect on Temperature and its Pressure on Small Bodies’, Phil. Trans. Roy. Soc., A 202, 525–552.Google Scholar
Robertson, H.P.: 1937, ‘Dynamical Effects of Radiation in the Solar System’, MNRAS, 97, 423–438.CrossRefGoogle Scholar
Watson, G.N.: 1958 A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, Cambridge.Google Scholar
Wyatt, S.P., Whipple, F.L.: 1950, ‘The Poynting-Robertson Effect on Meteor Orbits’, ApJ, 111,558–565.CrossRefGoogle Scholar