Force function of a slightly elliptical Gaussian ring and its generalization to a nearly coplanar system of rings |
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| Authors: | M A Vashkovyak S N Vashkovyak |
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| Institution: | 1.Keldysh Institute of Applied Mathematics,Moscow,Russia;2.Sternberg Institute for Astronomy,Moscow State University,Moscow,Russia |
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| Abstract: | An analytical expression of the force function of a slightly elliptical Gaussian ring is proposed. The obtained power expansion
of ellipse eccentricity contains the terms up to the third power inclusive. The coefficients of this expansion depend on the
coordinates of the sampling point and semi-major axis of the ellipse. In the advanced application to the system of the major
moons of Uranus for the investigation into secular mutual perturbations, the generalization of the force function is performed
for the case of a nearly coplanar system of rings. The force function obtained in this work is more accurate than the earlier
known ones and includes the terms up to the third power inclusive with respect to the eccentricities and equatorial inclinations
of the moons’ orbits. |
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