Detection by MEGNO of the gravitational resonances between a rotating ellipsoid and a point mass satellite

Research output: Contribution to journalArticle

Abstract

Nowadays the scientific community considers that more than a third of the asteroids are double. The study of the stability of these systems is quite complex, because of their irregular shapes and tumbling rotations, and requires a full body-full body approach. A particular case is analysed here, when the secondary body is sufficiently small and distant from the primary to be considered as a point mass satellite. Gravitational resonances (between the revolution of the satellite and the rotation of the asteroid) of a small body in fast or slow rotation around a rigid ellipsoid are studied. The same model can be used for the motion of a probe around an irregular asteroid. The gravitational potential induced by the primary body is modelled by the MacMillan potential. The stability of the satellite is measured thanks to the MEGNO indicator (Mean Exponential Growth Factor of Nearby Orbits). We present stability maps in the plane (b/d,c/d) where d, b, and c are the three semi-axes of the ellipsoid shaping the asteroid. Special stable conic-like curves are detected on these maps and explained by an analytical model, based on a simplification of the MacMillan potential for some specific resonances (1 : 1 and 2 : 1). The efficiency of the MEGNO to detect stability is confirmed.
Original languageEnglish
JournalCelestial Mechanics and Dynamical Astronomy
Volume112
Publication statusPublished - 2012

Fingerprint

ellipsoids
asteroid
asteroids
satellite rotation
simplification
gravitational fields
probe
detection
orbits
probes
curves

Keywords

  • Gravitational resonance - MEGNO - Satellite of asteroid - Binary asteroid - 1:1 Resonance - Synchronous case

Cite this

@article{038cf4069ceb41be88f65463b69cc930,
title = "Detection by MEGNO of the gravitational resonances between a rotating ellipsoid and a point mass satellite",
abstract = "Nowadays the scientific community considers that more than a third of the asteroids are double. The study of the stability of these systems is quite complex, because of their irregular shapes and tumbling rotations, and requires a full body-full body approach. A particular case is analysed here, when the secondary body is sufficiently small and distant from the primary to be considered as a point mass satellite. Gravitational resonances (between the revolution of the satellite and the rotation of the asteroid) of a small body in fast or slow rotation around a rigid ellipsoid are studied. The same model can be used for the motion of a probe around an irregular asteroid. The gravitational potential induced by the primary body is modelled by the MacMillan potential. The stability of the satellite is measured thanks to the MEGNO indicator (Mean Exponential Growth Factor of Nearby Orbits). We present stability maps in the plane (b/d,c/d) where d, b, and c are the three semi-axes of the ellipsoid shaping the asteroid. Special stable conic-like curves are detected on these maps and explained by an analytical model, based on a simplification of the MacMillan potential for some specific resonances (1 : 1 and 2 : 1). The efficiency of the MEGNO to detect stability is confirmed.",
keywords = "Gravitational resonance - MEGNO - Satellite of asteroid - Binary asteroid - 1:1 Resonance - Synchronous case",
author = "Audrey Compere and Anne Lema{\^i}tre and Nicolas Delsate",
year = "2012",
language = "English",
volume = "112",
journal = "Celest. Mech & Dyn. Astron.",
issn = "0923-2958",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Detection by MEGNO of the gravitational resonances between a rotating ellipsoid and a point mass satellite

AU - Compere, Audrey

AU - Lemaître, Anne

AU - Delsate, Nicolas

PY - 2012

Y1 - 2012

N2 - Nowadays the scientific community considers that more than a third of the asteroids are double. The study of the stability of these systems is quite complex, because of their irregular shapes and tumbling rotations, and requires a full body-full body approach. A particular case is analysed here, when the secondary body is sufficiently small and distant from the primary to be considered as a point mass satellite. Gravitational resonances (between the revolution of the satellite and the rotation of the asteroid) of a small body in fast or slow rotation around a rigid ellipsoid are studied. The same model can be used for the motion of a probe around an irregular asteroid. The gravitational potential induced by the primary body is modelled by the MacMillan potential. The stability of the satellite is measured thanks to the MEGNO indicator (Mean Exponential Growth Factor of Nearby Orbits). We present stability maps in the plane (b/d,c/d) where d, b, and c are the three semi-axes of the ellipsoid shaping the asteroid. Special stable conic-like curves are detected on these maps and explained by an analytical model, based on a simplification of the MacMillan potential for some specific resonances (1 : 1 and 2 : 1). The efficiency of the MEGNO to detect stability is confirmed.

AB - Nowadays the scientific community considers that more than a third of the asteroids are double. The study of the stability of these systems is quite complex, because of their irregular shapes and tumbling rotations, and requires a full body-full body approach. A particular case is analysed here, when the secondary body is sufficiently small and distant from the primary to be considered as a point mass satellite. Gravitational resonances (between the revolution of the satellite and the rotation of the asteroid) of a small body in fast or slow rotation around a rigid ellipsoid are studied. The same model can be used for the motion of a probe around an irregular asteroid. The gravitational potential induced by the primary body is modelled by the MacMillan potential. The stability of the satellite is measured thanks to the MEGNO indicator (Mean Exponential Growth Factor of Nearby Orbits). We present stability maps in the plane (b/d,c/d) where d, b, and c are the three semi-axes of the ellipsoid shaping the asteroid. Special stable conic-like curves are detected on these maps and explained by an analytical model, based on a simplification of the MacMillan potential for some specific resonances (1 : 1 and 2 : 1). The efficiency of the MEGNO to detect stability is confirmed.

KW - Gravitational resonance - MEGNO - Satellite of asteroid - Binary asteroid - 1:1 Resonance - Synchronous case

M3 - Article

VL - 112

JO - Celest. Mech & Dyn. Astron.

JF - Celest. Mech & Dyn. Astron.

SN - 0923-2958

ER -