Abstract
The equations of motion describe the path that a spacecraft, planet, satellite, molecule, electromagnetic wave or any body will follow. In space, the path that a spacecraft follows is called a trajectory and for a planet it is called an ephemeris. For the purpose of navigation, a planet is defined as any object that orbits the sun and thus, includes comets and asteroids. A satellite is any body that orbits a planet. Flight operations are generally conducted using solutions of Newton’s equation of motion obtained by numerical integration. Analytic solutions of Newton’s equation of motion provide some insight into trajectory design and navigation analysis, but these solutions are seldom used in the conduct of flight operations. For spacecraft near the Sun and Jupiter, and for the planet ephemerides, Newton’s equations of motion are augmented with terms from the n-body solution of General Relativity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Bate, R. R., Mueller, D. D., and White, J. E., Fundamentals of Astrodynamics, Dover Publications, New York, 1971.
Davies, M. E., V. K. Abalakin, M. Bursa, T. Lederle, J. H. Lieske, R. H. Rapp, P. K. Seidelmann, A. T. Sinclair, V. G. Teifel, Y. S. Tjuflin 1986. Report of the IAU/IAG/COSPAR Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: Celest. Mech. 39, 103–113., 1985.
Greenwood D. T. 1965, Principles of Dynamics, Prentice-Hall Inc., Englewood Cliffs, NJ.
Hellings, R. W., “Relativistic Effects in Astronomical Timing Measurements,” The Astronomical Journal, vol. 91, no. 3, pp. 650–659, March 1986.
Ichinose, S. and Y. Kaminaga, “Inevitable ambiguity in perturbation around flat space-time,” Physical Review, Vol 40, N 12, pp 3997–4010, 15 December 1989.
Lass, H., Vector and Tensor Analysis, McGraw-Hill, New York, 1950.
Llanos, P. J., Miller, J. K. and Hintz, G. R., “Trajectory Dynamics of Gas Molecules and Galaxy Formation”, Paper AAS 13-863. AAS/AIAA 2013 Astrodynamics Specialist Conference, Hilton Head, SC, January 2013.
Lieske, J. H., “Improved Ephemerides of the Galilean Satellites”, Astronomy Astrophysics, Vol. 82, pp. 340–348, 1980.
McVittie, G. C., General Relativity and Cosmology, The University of Illinois Press, Urbana, 1965.
Miller, J, K. and S. G. Turyshev, “The Trajectory of a Photon”, AAS03-255, 13th AAS/AIAA Space Flight Mechanics Meeting, Ponce, Puerto Rico, February 9, 2003.)
Misner, C. W., Thorne, K. S., Wheeler, J. A., Gravitation, W. H. Freeman, New York, 1972.
Moyer, T. D., “Transformation from Proper Time on Earth to Coordinate Time in Solar System Barycentric Space-Time Frames of Reference: Parts 1 and 2,” Celestial Mechanics, vol. 23, pp. 33–08, January 1981.
Moyer, T. D., Mathematical Formulation of the Double-Precision Orbit Determination Program, JPL Technical Report 32–1527, Jet Propulsion Laboratory, Pasadena, California, May 15, 1971.
Richter, G. W. and Matzner, R. A., “Second-order contributions to relativistic time delay in the parameterized post-Newtonian formalism,” Physical Review, Vol. 28, N 12, 15 December 1983.
Sokolnikoff, I. S., Tensor Analysis Theory and Applications to Geometry and Mechanics of Continua, John Wiley and Sons, New York, 1964.
Standish, E. M., E. M. Keesey, and X. X. Newhall, “JPL Development Ephemeris Number 96,” Technical Report 32–1603, Jet Propulsion Laboratory internal document, Pasadena, California, 1976.
Van De Kamp, P., Elements of Astromechanics, W. H. Freeman and Company, San Francisco, 1964.
Weeks, C. J., J. K. Miller, B. G. Williams, “Calibration of Radiometric Data for Relativity and Solar Plasma During a Solar Conjunction”, Journal of the Astronautical Sciences, Vol. 49, No. 4, pp. 615–628, October-December, 2001.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Miller, J. (2019). Equations of Motion. In: Planetary Spacecraft Navigation. Space Technology Library, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-78916-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-78916-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78915-6
Online ISBN: 978-3-319-78916-3
eBook Packages: EngineeringEngineering (R0)