Long term orbital inclination and eccentricity oscillations of the planets in our solar system
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2016
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Not published
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University of Cape Town
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University of Cape Town
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Abstract
The orbits of the planets in our solar system are not in the same plane, therefore natural torques stemming from Newton’s gravitational forces exist to pull them all back to the same plane. This causes the inclinations of the planet orbits to oscillate with potentially long periods and very small damping, because the friction in space is very small. Orbital inclination changes are known for some planets in terms of current rates of change, but the oscillation periods are not well published. They can however be predicted with proper dynamic simulations of the solar system.
A three-dimensional dynamic simulation was developed for our solar system capable of handling 12 objects, where all objects affect all other objects. Each object was considered to be a point mass which proved to be an adequate approximation for this study. Initial orbital radii, eccentricities and speeds were set according to known values. The validity of the simulation was demonstrated in terms of short term characteristics such as sidereal periods of planets as well as long term characteristics such as the orbital inclination and eccentricity oscillation periods of Jupiter and Saturn. A significantly more accurate result, than given on approximate analytical grounds in a well-known solar system dynamics textbook, was found for the latter period.
Empirical formulas were developed from the simulation results for both these periods for three-object solar type systems. They are very accurate for the Sun, Jupiter and Saturn as well as for some other comparable systems.
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Reference:
Mouton HD, Long term orbital inclination and eccentricity oscillations of the planets in our solar system