Skip to main content
SpringerLink
Log in
Book cover

Fundamentals of Spacecraft Attitude Determination and Control pp 365–402Cite as

Orbital Dynamics

  • Chapter

  • 9565 Accesses

Part of the book series: Space Technology Library ((SPTL,volume 33))

Abstract

The study of bodies in orbit has attracted the world’s greatest mathematicians in the past, and remains a flourishing subject area in the present. In fact many useful mathematical concepts, such as Bessel functions and nonlinear least squares, can be directly traced back to the study of orbital motion. Here the basic equations and concepts of orbital dynamics are introduced. More details can be found in the references herein.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    The generalization to any other central body is straightforward; we choose the Earth for specificity.

  2. 2.

    We use λ′ for latitude to avoid confusion with the geodetic latitude of Sect. 2.6.3.

  3. 3.

    Equation (10.90) is the well-known Rodrigues equation for the Legendre polynomials.

  4. 4.

    We follow Vallado’s notation [21]. Montenbruck and Gill [14] and Abramowitz and Stegun [1] denote these functions by Pnm and define \(P_n^m=(-1)^mP_{nm}\).

  5. 5.

    The format is also described in http://en.wikipedia.org/wiki/Two-line_element_set.

  6. 6.

    The lack of precise agreement with Eq. (10.129) is due to higher-order zonal perturbations.

  7. 7.

    In discussing the Sun/Earth Lagrange points, “Earth” means the system of the Earth and the Moon, the Sun is the first body, and the mass and location of the second body are the summed Earth/Moon mass and the location of the Earth/Moon center of mass.

  8. 8.

    This labeling convention is not universally followed.

References

  1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Applied Mathematics Series - 55. National Bureau of Standards, Washington, DC (1964)

    Google Scholar 

  2. Arfken, G.B., Weber, H.J., Harris, F.E.: Mathematical Methods for Physicists: A Comprehensive Guide, 7th edn. Academic Press, Waltham (2013)

    MATH  Google Scholar 

  3. Bate, R.R., Mueller, D.D., White, J.E.: Fundamentals of Astrodynamics. Dover Publications, New York (1971)

    Google Scholar 

  4. Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics and Astronautics, New York (1987)

    MATH  Google Scholar 

  5. Borderies, N., Longaretti, P.: A new treatment of the albedo radiation pressure in the case of a uniform albedo and of a spherical satellite. Celestial Mech. Dyn. Astron. 49(1), 69–98 (1990)

    Article  Google Scholar 

  6. Brouwer, D.: Solution of the problem of artificial satellite theory without drag. Astron. J. 64(1274), 378–397 (1959)

    Article  MathSciNet  Google Scholar 

  7. Colwell, P.: Solving Kepler’s Equation over Three Centuries. Willmann-Bell, Richmond (1993)

    Google Scholar 

  8. Danby, J.M.A.: Fundamentals of Celestial Mechanics, 2nd edn., 3rd Printing. Willman-Bell, Richmond (1992)

    Google Scholar 

  9. Farquhar, R.W.: Fifty Years on the Space Frontier: Halo Orbits, Comets, Asteroids, and More. Outskirts Press, Parker (2011)

    Google Scholar 

  10. Hoots, F.R., Schumacher Jr., P.W., Glover, R.A.: History of analytical orbit modeling in the U.S. space surveillance system. J. Guid. Contr. Dynam. 27(2), 174–185 (2004)

    Article  Google Scholar 

  11. Kolenkiewicz, R., Carpenter, L.: Stable periodic orbits about the Sun perturbed Earth-Moon triangular points. AIAA J. 6(7), 1301–1304 (1968)

    Article  Google Scholar 

  12. Kozai, Y.: The motion of a close Earth satellite. Astron. J. 64(1274), 367–377 (1959)

    Article  MathSciNet  Google Scholar 

  13. Markley, F.L., Jeletic, J.F.: Fast orbit propagator for graphical display. J. Guid. Contr. Dynam. 14(2), 473–475 (1991)

    Article  Google Scholar 

  14. Montenbruck, O., Gill, E.: Satellite Orbits: Models, Methods, and Applications. Springer, Berlin/Heidelberg/New York (2000)

    Book  Google Scholar 

  15. Morena, L.C., James, K.V., Beck, J.: An introduction to the RADARSAT-2 mission. Can. J. Rem. Sens. 30(3), 221–234 (2004)

    Article  Google Scholar 

  16. Roy, A.E.: Orbital Motion, 4th edn. IOP Publishing, Bristol (2005)

    MATH  Google Scholar 

  17. Schaub, H., Junkins, J.L.: Analytical Mechanics of Aerospace Systems, 2nd edn. American Institute of Aeronautics and Astronautics, New York (2009)

    MATH  Google Scholar 

  18. Scheffer, L.K.: Conventional forces can explain the anomalous acceleration of Pioneer 10. Phys. Rev. D67(8), 8402-1–8402-11 (2003)

    Google Scholar 

  19. Tapley, B.D., Lewallen, J.M.: Solar influence on satellite motion near the stable Earth-Moon libration points. AIAA J. 2(4), 728–732 (1964)

    Article  Google Scholar 

  20. Turyshev, S.G., Toth, V.T., Kinsella, G., Lee, S.-C., Lok, S.M., Ellis, J.: Support for the thermal origin of the Pioneer anomaly. Phys. Rev. Lett. 108(24), 241101 (2012)

    Article  Google Scholar 

  21. Vallado, D.A.: Fundamentals of Astrodynamics and Applications, 3rd edn. Microcosm Press, Hawthorne and Springer, New York (2007)

    Google Scholar 

  22. Vallado, D.A., Crawford, P., Hujsak, R., Kelso, T.S.: Revisiting Spacetrack Report #3: Rev 2. In: AIAA/AAS Astrodynamics Specialist Conference. Keystone (2006)

    Google Scholar 

  23. Vallado, D.A., Finkleman, D.: A critical assessment of satellite drag and atmospheric density modelling. In: AIAA/AAS Astrodynamics Specialist Conference. Honolulu (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Attitude Control Systems Engineering Branch, NASA Goddard Space Flight Center, Greenbelt, MA, USA

    F. Landis Markley

  2. Mechanical and Aerospace Engineering, University at Buffalo State University of New York, Amherst, NY, USA

    John L. Crassidis

Authors
  1. F. Landis Markley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John L. Crassidis
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Markley, F.L., Crassidis, J.L. (2014). Orbital Dynamics. In: Fundamentals of Spacecraft Attitude Determination and Control. Space Technology Library, vol 33. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0802-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-0802-8_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4939-0801-1

  • Online ISBN: 978-1-4939-0802-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation