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

Compère, Audrey; Lemaître, Anne; Delsate, N.

doi:10.1007/s10569-011-9384-9

Cited by 19 publications

(21 citation statements)

References 27 publications

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“…These numerical results agree well with those of Tricarico & Sykes (2010) and with the analytical study. Compère et al (2012) studied the evolution of a small body in rotation around a rigid ellipsoidal asteroid in constant rotation. Simulations were made with NIMASTEP using the MacMillan (1958) potential for the influence of the shape of the asteroid on the small body and the chaos indicator MEGNO.…”

Section: Comparison With Results Of Analytical Studiesmentioning

confidence: 99%

“…This indicator has been successfully used in some papers, for instance, Breiter et al (2005), Cincotta & Simó (2000), Goździewski et al (2001Goździewski et al ( , 2008 and Hinse et al (2008Hinse et al ( , 2010. For the results concerning the MEGNO implemented into NIMASTEP we refer the reader to Valk et al (2009a) and Compère et al (2012).…”

Section: Megno: Mean Exponential Growth Factor Of Nearby Orbitsmentioning

confidence: 99%

“…NIMASTEP was initially developed to numerically integrate the motion of an artificial satellite orbiting a telluric planet (Delsate et al 2010;Valk et al 2009a) 1 . Later on this software was extended to calculate the motion of one or several artifical (Delsate 2011a) or natural satellites (Compère et al 2012) orbiting a (dwarf-)planet or an asteroid of the solar system. In the current version of the software, several forces are still neglected.…”

Section: Introductionmentioning

confidence: 99%

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NIMASTEP: a software to modelize, study, and analyze the dynamics of various small objects orbiting specific bodies

Delsate

Compère

2012

A&A

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NIMASTEP is a dedicated numerical software developed by us, which allows one to integrate the osculating motion (using Cartesian coordinates) in a Newtonian approach of an object considered as a point-mass orbiting a homogeneous central body that rotates with a constant rate around its axis of smallest inertia. The code can be applied to objects such as particles, artificial or natural satellites, or space debris. The central body can be either any terrestrial planet of the solar system, any dwarf-planet, or even an asteroid. In addition, very many perturbations can be taken into account, such as the combined third-body attraction of the Sun, the Moon, or the planets, the direct solar radiation pressure (with the central body shadow), the non-homogeneous gravitational field caused by the non-sphericity of the central body, and even some thrust forces. The simulations were performed using different integration algorithms. Two additional tools were integrated in the software package; the indicator of chaos MEGNO and the frequency analysis NAFF. NIMASTEP is designed in a flexible modular style and allows one to (de)select very many options without compromising the performance. It also allows one to easily add other possibilities of use. The code has been validated through several tests such as comparisons with numerical integrations made with other softwares or with semi-analytical and analytical studies. The various possibilities of NIMASTEP are described and explained and some tests of astrophysical interest are presented. At present, the code is proprietary but it will be released for use by the community in the near future. Information for contacting its authors and (in the near future) for obtaining the software are available on the web site http://www.fundp.ac.be/en/research/projects/ page_view/10278201/

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Section: Comparison With Results Of Analytical Studiesmentioning

confidence: 99%

Section: Megno: Mean Exponential Growth Factor Of Nearby Orbitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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NIMASTEP: a software to modelize, study, and analyze the dynamics of various small objects orbiting specific bodies

Delsate

Compère

2012

A&A

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“…The MEGNO map is a fast chaos indicator which has proven to be reliable in a broad number of dynamical systems (Cincotta et al 2003;Goździewski et al 2001Goździewski et al , 2008Breiter et al 2005;Compère et al 2012;Frouard & Compère 2012). The MEGNO is a characterisation of the divergence rate of two nearby orbits and is based on the numerical integration of a tangent vector defined for the orbits.…”

Section: Chaos Indicators and Numerical Methodsmentioning

confidence: 99%

A possible mechanism to explain the lack of binary asteroids among the Plutinos

Compère

Farrelly

Lemaître

et al. 2013

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Context. Binary asteroids are common in the solar system, including in the Kuiper belt. However, there seems to be a marked disparity between the binary populations in the classical part of the Kuiper belt and the part of the belt in the 3:2 resonance with Neptune -i.e., the region inhabited by the Plutinos. In particular, binary Plutinos are extremely rare. Aims. We study the impact of the 3:2 resonance on the formation of Kuiper belt binaries, according to the Nice model, in order to explain such phenomenon. Methods. Numerical simulations are performed within the 2 + 2 body approximation (Sun/Neptune + binary partners). The MEGNO chaos indicator is used to map out regular and chaotic regions of phase space. Residence times of test (binary) particles within the Hill sphere are compared inside and outside of the 3:2 resonance. The effect of increasing the heliocentric eccentricity of the centre of mass of the binary system is studied. This is done because mean-motion resonances between a planet and an asteroid usually have the effect of increasing the eccentricity of the asteroid. Results. The stable zones in the MEGNO maps are mainly disrupted in the resonant, eccentric case: the number of binary asteroids created in this case is significantly lower than outside the 3:2 resonance. Conclusions. In the 2 + 2 body approximation, the pumping of the eccentricity of the centre of mass of a potential binary destabilises the formation of binaries. This may be a factor in explaining the scarcity of binaries in the Plutino population.

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“…The C 30 term was found to create tiny chaotic layers around the separatrix but without significant influence on the resonance width. With the ellipsoid shape model (Compère et al 2012), MEGNO (Mean Exponential Growth factor of Nearby Orbits) was applied as an indicator to detect stable resonant periodic orbits and also 1:1 and 2:1 resonance structures under different combinations of the three semi-major axes of the ellipsoid. A 1-DOF resonant model parametrized by e and i was obtained with a truncated ellipsoidal potential up to degree and order 2.…”

Section: Introductionmentioning

confidence: 99%

1:1 Ground-track resonance in a uniformly rotating 4th degree and order gravitational field

Feng

Noomen

Hou

et al. 2016

Celest Mech Dyn Astr

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Using a gravitational field truncated at the 4th degree and order, the 1:1 groundtrack resonance is studied. To address the main properties of this resonance, a 1-degree of freedom (1-DOF) system is firstly studied. Equilibrium points (EPs), stability and resonance width are obtained. Different from previous studies, the inclusion of non-spherical terms higher than degree and order 2 introduces new phenomena. For a further study about this resonance, a 2-DOF model which includes a main resonance term (the 1-DOF system) and a perturbing resonance term is studied. With the aid of Poincaré sections, the generation of chaos in the phase space is studied in detail by addressing the overlap process of these two resonances with arbitrary combinations of eccentricity (e) and inclination (i). Retrograde orbits, near circular orbits and near polar orbits are found to have better stability against the perturbation of the second resonance. The situations of complete chaos are estimated in the e − i plane. By applying the maximum Lyapunov Characteristic Exponent (LCE), chaos is characterized quantitatively and similar conclusions can be achieved. This study is applied to three asteroids 1996 HW1, Vesta and Betulia, but the conclusions are not restricted to them.

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

Cited by 19 publications

References 27 publications

NIMASTEP: a software to modelize, study, and analyze the dynamics of various small objects orbiting specific bodies

NIMASTEP: a software to modelize, study, and analyze the dynamics of various small objects orbiting specific bodies

A possible mechanism to explain the lack of binary asteroids among the Plutinos

1:1 Ground-track resonance in a uniformly rotating 4th degree and order gravitational field

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