Abstract
The aim of this chapter is to determine a preliminary orbit of Mars. The method of Herget is used and adapted slightly to obviate the need for a numerical differentiation. Lagrange’s f and g functions are introduced. A method is borrowed from Escobal to calculate sector triangle ratios without the use of continued fractions or hypergeometric functions. Time is introduced via Kepler’s equation. A Fortran program is given to calculate a preliminary orbit from a set of fifteen observations. The use of more than three observations enables the calculation of preliminary orbits when the orbit is almost coplanar with that of the Earth.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boulet, D., 1991, Methods of Orbit Determination for the Microcomputer, Willmann-Bell, ISBN 0943396344.
Gauss, C. F, 1809, Work cited.
Bauschinger, J., 1906, Die Bahnbestimmung der Himmelskörper; mit 84 Figuren im Text, Wilhelm Engelmann, available online, in German, at https://diglib.uibk.ac.at/ulbtirol/content/pageview/360713.
Karimi, R. R. & Mortari, D.,2010, Orbit Determination Using Prescribed Orbits, AAS 10-236, AAS/AIAA Space Flight Mechanics Meeting Conference, San Diego, CA, February 14-18, 2010.
Karimi, R.R. and Mortari, D., 2009, On Preliminary Orbit Determination: A New Approach, Paper AAS 09-106 of the 2009 AAS/AIAA Space Flight Mechanics Meeting Conference, Savannah, GA, February 9-12, 2009.
Karimi, R.R. and Mortari, D., 2010, Initial Orbit Determination Using Multiple Observations, Celestial Mechanics and Dynamical Astronomy, Vol. 109, No. 2, 2010, pp.167–180.
Karimi, R.R. and Mortari, D., 2012 Orbit Determination Based on Variation of Orbital Error, Paper AAS 12-201 of the 2012 AAS/AIAA Space Flight Mechanics Meeting Conference, Charleston, SC, Jan 29 –Feb 2, 2012
Karimi, R.R. and Mortari, D., 2011, On Laplace’s Orbit Determination Method: Some Modifications, Paper AAS 11-121 of the 2011 AAS/AIAA Space Flight Mechanics Meeting Conference, New Orleans, LA, February 13-17, 2011.
Karimi, R.R. and Mortari, D., 2013, A Performance Based Comparison of Angle-only Initial Orbit Determination Methods, AAS 13-823, 2013 AAS/AIAA Astrodynamics Specialist Conference, Hilton Head, SC, August 11-15, 2013.
Herget, P., 1965, Computation of Preliminary Orbits, Astronomical Journal, 70,1–3
https://en.wikipedia.org/wiki/International_Celestial_Reference_Frame
Clark, J. D., 2009, Work Cited, Chapter 4 shows the observational evidence for this phenomenon.
Murray, C.D. and Dermott, S.F., 1999, Solar System Dynamics, Work Cited
Danby, J.M.A., 1988, Work Cited, p.146.
Herget, P., 1948, The Computation of Orbits, Privately Published.
Escobal, P. R., 1976, Methods of Orbit Determination, Robert E. Krieger Publishing Co., Malabar, FL.
Givens, W., 1958, Computation of Plain Unitary Rotations Transforming a General Matrix to Triangular Form, Journal of the Society for Industrial and Applied Mathematics, 6(1), 26–50.
Escobal, P. R., Work Cited, §3.7.1, pp. 96–98
Hamilton, W. R., 1845, Proc. R. Irish Acad., III, Appendix p. 36.
Danby, J. M. A., Work Cited, p. 28
Newton, I., 1687, Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), later Editions 1713 and 1726, Translated by I. Bernard Cohen and Anne Whitman, preceded by A Guide to Newton’s Principia by I. Bernard Cohen, University of California Press, 1999, ISBN 978-0-520-08817-7
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Clark, J. (2021). First Shot at the Orbit of Mars. In: Calculate the Orbit of Mars!. Springer, Cham. https://doi.org/10.1007/978-3-030-78267-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-78267-2_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-78266-5
Online ISBN: 978-3-030-78267-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)