Frequency modified fourier transform and its application to asteroids

Sidlichovsky, M.; Nesvorný, David

doi:10.1007/bf00048443

Cited by 153 publications

(95 citation statements)

References 3 publications

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“…To investigate possible indirect effects caused by the presence of other massive asteroids in the system we obtained the values of the proper frequencies of pericenter and longitude of the node precession g and s for (4) Vesta for simulations involving progressively all 51 asteroids in Baer et al (2011) paper 3 , using the frequency modified Fourier transform algorithm of Šidlichovský & Nesvorný (1997). We integrated our asteroids as massive bodies over 30 Myr, using SWIFT-SKEEL, the symplectic integrator using the Wisdom & Holman mapping (Wisdom & Holman 1991;Levison & Duncan 2000).…”

Section: Numerical Simulation Set-upmentioning

confidence: 99%

Chaotic diffusion caused by close encounters with several massive asteroids

Carruba

Huaman

Douwens

et al. 2012

A&A

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Context. Close encounters with massive asteroids are known to be a mechanism of dynamical mobility that can significantly alter proper elements of minor bodies, and they are the main source of dynamical mobility for medium-sized and large asteroids (D > 20 km, approximately). Aims. Orbital mobility caused by close encounters with (4) Vesta has been studied in the past and could be a viable mechanism to produce the current orbital location of some of the V-type asteroids currently outside the Vesta family. It is well known, however, that the proper frequencies of precession of pericenter g and longitude of the node s of terrestrial planets change when one or more of the other planets is not considered in the integration scheme. For instance, the g 4 and s 4 frequencies are different when the full solar system is considered or when only Mars and the Jovian planets are accounted for. In this work we consider the effect that including one or more (up to 51) massive asteroids in the integration scheme has on the Vesta orbit, and, indirectly on the statistics of changes in semi-major axis caused by close encounters with this massive asteroid. Methods. By using chaos indicators such as the maximum Lyapunov exponent, and integrations with symplectic integrators able to account for the interaction between a massive asteroid and a mass-less particle, we studied the problem of scattering caused by close encounters with (4) Vesta, when only (4) Vesta (and the eight planets) are considered, and when (4) Vesta and other massive main belt asteroids are also accounted for. Results. We find that (4) Vesta proper frequencies are dependent on the number of other massive asteroids considered in the integration scheme and that, as a result, the whole statistics of encounters with (4) Vesta is also affected. Variances of the change in proper a caused by the four most massive asteroids varied up to 36.3% in the five integration schemes that we used, and the number of encounters that caused the strongest changes in semi-major axis varied up to a factor 2. The indirect effect caused by the presence of other massive asteroids therefore introduces an additional source of uncertainty in estimating the long-term effect of close encounters with massive asteroids that was not accounted for in previous works on the subject, and that strongly affects estimates of its Hurst exponent.

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Section: Numerical Simulation Set-upmentioning

confidence: 99%

Chaotic diffusion caused by close encounters with several massive asteroids

Carruba

Huaman

Douwens

et al. 2012

A&A

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“…The frequency analysis FMFT algorithm (Šidlichovský & Nesvorný 1996) based on the frequency analysis algorithm (Laskar 2005) is then applied to the time series of the equinoctal elements k + ih and q + ip defined by…”

Section: Long-term Integrations Of the Jovian Irregular Satellitesmentioning

confidence: 99%

The long-term dynamics of the Jovian irregular satellites

Frouard

Vienne

Fouchard

2011

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Context. The dynamical region of the Jovian irregular satellites presents an interesting web of resonances that are not yet fully understood. Of particular interest is the influence of the resonances on the stochasticity of the individual orbits of the satellites, as well as on the long-term chaotic diffusion of the different families of satellites. Aims. We make a systematic numerical study of the satellite region to determine the important resonances for the dynamics, to search for the chaotic zones, and to determine their influences on the dynamics of the satellites. We also compare these numerical results to previous analytical works. Methods. Using extensive numerical integrations of the satellites along with an indicator of chaos (MEGNO), we show global and detailed views of the retrograde and prograde regions for various dynamical models of increasing complexity and indicate the appearance of the different types of resonances and the implied chaos. Results. Along with secular and mean motion resonances that shape the dynamical regions of the satellites, we report a number of resonances involving the Great Inequality, and which are present in the system thanks to the wide range of the values of frequencies of the pericenter available for the satellites. The chaotic diffusion of the satellites is also studied and shows the long-term stability of the Ananke and Carme families, in contrast to the Pasiphae family.

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“…In our paper we adopt a different approach based on the Frequency Map Analysis (hereinafter FMA; Laskar 1993a,b;Sidlichovský & Nesvorný 1997) that allows to estimate the diffusion rate of an orbit in the proper elements space. This method has been previously applied to study dynamical stability of minor bodies in the solar system (Nesvorny & Ferraz-Mello 1997;Melita & Brunini 2001;.…”

Section: Introductionmentioning

confidence: 99%

The MATROS project: Stability of Uranus and Neptune Trojans. The case of 2001 QR322

Marzari

Tricarico

Scholl

2003

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Abstract. We present in this paper an analysis of the long term stability of Trojan type orbits of both Uranus and Neptune. Employing the Frequency Map Analysis (hereinafter FMA) we measure the diffusion speed in the phase space for a large sample of Trojan orbits with short numerical integrations. High resolution diffusion maps are derived for different values of initial inclination. These maps outline where the most stable orbits can be found in the Trojan clouds of the two planets. The orbit of the newly discovered Neptune Trojan 2001 QR322 has been analysed in detail with the FMA method. In the phase space the body is located close to the border of a stable region for low inclination Neptune Trojans. Numerical integrations over 4.5 Gyr of clone orbits generated from the covariance matrix show that only 10% of the clones escape from the Trojan cloud. The proper frequencies of the Trojan motion computed with the FMA algorithm allow us to to derive a numerical secular theory. From this theory it is possible to locate in the phase space the main secular resonances that can perturb Trojan orbits of the two planets and lead to instability.

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Frequency modified fourier transform and its application to asteroids

Cited by 153 publications

References 3 publications

Chaotic diffusion caused by close encounters with several massive asteroids

Chaotic diffusion caused by close encounters with several massive asteroids

The long-term dynamics of the Jovian irregular satellites

The MATROS project: Stability of Uranus and Neptune Trojans. The case of 2001 QR322

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