Skip to main content
SpringerLink
Log in

Secular orbit variation due to solar radiation effects: a detailed model for BYORP

  • Original Article
  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

A detailed derivation of the effect of solar radiation pressure on the orbit of a body about a primary orbiting the Sun is given. The result is a set of secular equations that can be used for long-term predictions of changes in the orbit. Solar radiation pressure is modeled as a Fourier series in the body’s rotation state, where the coefficients are based on the shape and radiation properties of the body as parameters. In this work, the assumption is made that the body is in a synchronous orbit about the primary and rotates at a constant rate. This model is used to write explicit variational equations of the energy, eccentricity vector, and angular momentum vector for an orbiting body. Given that the effect of the solar radiation pressure and the orbit are periodic functions, they are readily averaged over an orbit. Furthermore, the equations can be averaged again over the orbit of the primary about the Sun to give secular equations for long-term prediction. This methodology is applied to both circular and elliptical orbits, and the full equations for secular changes to the orbit in both cases are presented. These results can be applied to natural systems, such as the binary asteroid system 1999 KW4, to predict their evolution due to the Binary YORP effect, or to artificial Earth orbiting, nadir-pointing satellites to enable more precise models for their orbital evolution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Brouwer D., Clemence G.: Methods of Celestial Mechanics. Academic Press, New York (1961)

    Google Scholar 

  • Cheng M., Ries J., Tapley B.: Assessment of the solar radiation model for grace orbit determination. Adv. Astronautical Sci. 129, 501–510 (2008)

    Google Scholar 

  • Ćuk M.: Formation and destruction of small binary asteroids. Astrophys. J. 659, L57–L60 (2007)

    Article  ADS  Google Scholar 

  • Ćuk M., Burns J.: Effects of thermal radiation on the dynamics of binary neas. Icarus 176, 418–431 (2005)

    Article  ADS  Google Scholar 

  • Gladman B., Michel P., Froeschlé Ch.: The near-earth object population. Icarus 146, 176–189 (2000)

    Article  ADS  Google Scholar 

  • Goldreich P., Sari R.: Tidal evolution of rubble piles. Astrophys. J. 691, 54–60 (2009)

    Article  ADS  Google Scholar 

  • Hudson J., Scheeres D.: Reduction of low-thrust continuous controls for trajectory dynamics. J. Guid. Control. Dyn. 32(3), 780–787 (2009)

    Article  Google Scholar 

  • Lucchesi D.: Reassessment of the error modelling of non-gravitational perturbations on lageos ii and their impact in the lense-thirring determination. Part i. Planet. Space Sci. 49, 447–463 (2001)

    Article  ADS  Google Scholar 

  • Lucchesi D.M., Iafolla V.: The non-gravitational perturbations impact on the BepiColombo Radio Science Experiment and the key rôle of the ISA accelerometer: direct solar radiation and albedo effects. Celest. Mech. Dyn. Astron. 96, 99–127 (2006)

    Article  MATH  ADS  Google Scholar 

  • Margot J.L. et al.: Binary asteroids in the near-earth object population. Science 296, 1445–1448 (2002)

    Article  ADS  Google Scholar 

  • Mazarico E., Zuber M., Lemoine F., Smith D.: Effects of self-shadowing on nonconservative force modeling for mars-orbiting spacecraft. J. Spacecr. Rockets 46(3), 662–669 (2009)

    Article  ADS  Google Scholar 

  • McMahon, J., Scheeres, D.: A new navigation force model for solar radiation pressure. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, number AAS 09-346. Pittsburgh, PA, August 10–13 (2009)

  • Paddack S.J.: Rotational bursting of small celestial bodies: effects of radiation pressure. J. Geophys. Res. 74(17), 4379–4381 (1969)

    Article  ADS  Google Scholar 

  • Scheeres D.: The dynamical evolution of uniformly rotating asteroids subject to YORP. Icarus 188, 430–450 (2007)

    Article  ADS  Google Scholar 

  • Scheeres D.J., Mirrahimi S.: Rotational dynamics of a solar system body under solar radiation torques. Celest. Mech. Dyn. Astron. 101, 69–103 (2008)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Taff L.: Celestial Mechanics; A Computational Guide for the Practitioner. Wiley, New York (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aerospace Engineering Sciences, University of Colorado-Boulder, 431 UCB, University of Colorado, Boulder, CO, 80309-0431, USA

    Jay McMahon

  2. Aerospace Engineering Sciences, University of Colorado-Boulder, 429 UCB, University of Colorado, Boulder, CO, 80309-0429, USA

    Daniel Scheeres

Authors
  1. Jay McMahon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Scheeres
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jay McMahon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

McMahon, J., Scheeres, D. Secular orbit variation due to solar radiation effects: a detailed model for BYORP. Celest Mech Dyn Astr 106, 261–300 (2010). https://doi.org/10.1007/s10569-009-9247-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-009-9247-9

Keywords

Search

Navigation