Research Article
Equilibrium Positions in a Gravitational Field Generated by an Elongated Asteroid with Density of Order 4
El Haj El Ourabi*
,
Mohammed Bennai
Issue:
Volume 12, Issue 1, March 2025
Pages:
1-8
Received:
26 November 2024
Accepted:
10 December 2024
Published:
7 January 2025
DOI:
10.11648/j.ajaa.20251201.11
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Views:
Abstract: Calculating the gravitational potential generated by non-spherical mass distributions is an old problem that has been tackled by astronomical researchers. The majority of small celestial objects have an elongated shape with a non-uniform mass distribution. Early work in this field modelled these elongated bodies as segments with a uniform mass distribution. In a previous work, we established the analytical form of the potential generated by an asteroid modelled by a linear and inhomogeneous repair whose mass density is a polynomial of order four. We have studied the dynamic behavior of a test particle in the vicinity of this asteroid, which is assumed to be at rest, and have extracted periodic orbits under certain conditions. Every celestial object has an angular momentum due to its own rotation. This result in competition between gravitational attraction and centrifugal repulsion in the synodic reference frame linked to the object. This led us to focus our research on the existence of relative equilibrium positions. We calculated the Jacobi integral analytically and used the zero velocity curves numerically to extract four equilibrium positions, two isosceles and two equilateral.
Abstract: Calculating the gravitational potential generated by non-spherical mass distributions is an old problem that has been tackled by astronomical researchers. The majority of small celestial objects have an elongated shape with a non-uniform mass distribution. Early work in this field modelled these elongated bodies as segments with a uniform mass dist...
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