Comparison of three methods for computing the gravitational attraction of tesseroids at satellite altitude

We consider the linear stability of a thin differentially rotating gaseous disc with reflecting boundaries against non-axisymmetric perturbations. We assume the unperturbed disc to be in centrifugal equilibrium with the gravitational attraction of a central mass M, and consider discs whose mass can be neglected relative to M. We discuss the relevant conservation laws for the energy and angular momentum of linear non-axisymmetric modes in a thin rotating disc without self-gravity and illustrate the basic mode amplification mechanisms with help of some of our numerical solutions [1].

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Estimative of the gravity-gradient data from vertical component of gravitational attraction by using the equivalent-layer and fast Fourier transform techniques

10.22564/16cisbgf2019.235 ◽

2019 ◽

Author(s):

Larissa Piauilino ◽

Valéria Barbosa ◽

Vanderlei Olivera Jr

Keyword(s):

Fourier Transform ◽

Fast Fourier Transform ◽

Vertical Component ◽

Gravity Gradient ◽

Gravitational Attraction ◽

Equivalent Layer

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On the possible ellipticity of Saturn's ring

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1924.0086 ◽

1924 ◽

Vol 106 (739) ◽

pp. 526-552 ◽

Cited By ~ 1

Keyword(s):

Nineteenth Century ◽

The Other ◽

Gravitational Attraction ◽

History Of Astronomy ◽

Small Oscillations ◽

First Approximation ◽

Elliptical Ring ◽

Single Ring ◽

History Of ◽

Concentric Circles

Clerk Maxwell’s investigation into the constitution and stability of Saturn’s Ring was based upon the fundamental supposition that the rings were composed of particles arranged in concentric circles. Although the particles could perform small oscillations about their mean positions, it is evident that the outline of the ring would be to all appearances circular. A line in Clerke’s ‘Popular History of Astronomy in the Nineteenth Century’ (page 299) suggests that some observers have regarded the outline of the ring as elliptical. It is therefore of interest to enquire under what conditions an elliptical ring could exist. The ellipse is a more general form than a circle. If, therefore, it can be shown that an elliptic ring is possible, any explanation of the origin of the rings must take account of this fact. In this paper a single ring of particles is examined. The actual Ring of Saturn probably consists of numerous rings, one within the other. By their gravitational attraction, each will affect the motions of the others. As a first approximation, however, it is sufficient to consider the case of a single ring.

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