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Lena Strömberg
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Journal of Physics and Astronomy Research

A model for non-circular orbits derived from a two-step linearisation of the Kepler laws

Lena Strömberg

Previously Department of Solid Mechanics, Royal Institute of Technology (KTH), Stockholm, Sweden 

Accepted 29 September, 2014.

Citation: Strömberg L (2014). A model for non-circular orbits derived from a two-step linearisation of the Kepler laws. Journal of Physics and Astronomy Research 1(2): 013-014. 

Copyright: © 2014 Strömberg L. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.


In the Solar System most orbits are circular, but there are some exceptions. The paper addresses results from a two-step linearisation of the Kepler laws, to model non-circular orbits, at Newtonian gravity and other interactions with adjacent bodies. The orbit will then be characterised by a generalised eccentricity and a secondary frequency denoted L-frequency, ωL (and considered proportional to the angular velocity). The path will be that of a circle, superimposed by small vibrations with the L-frequency. Hereby, the amplitude corresponds to an eccentricity, such that the radius varies, with time. When the ratio between the L-frequency and angular velocity is a non-integer, ‘perihelion’ moves. Bounds are derived and resulting orbits are generated and visualized.

For the integer ratio 2, results are compared with an ellipsoidal, and a tidal wave. For a non-integer ratio, the orbit is related to data for Mercury. Methods for detecting and measuring the secondary frequency are discussed, in terms of transfer orbits in Spaceflight dynamics.

Keywords: Kepler laws, planetary orbit, linearization, L-frequency, eccentricity, inertia refinement, perihelion, detection, Mercury, Mars