Locations of stationary/periodic solutions in mean motion resonances according to the properties of dust grains

Pástor, P.

doi:10.1093/mnras/stw894

Cited by 24 publications

(6 citation statements)

References 36 publications

(63 reference statements)

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“…The periodic solutions exist at the universal eccentricity. The libration amplitude of the periodical solutions is zero (Pástor 2016). Using analytical theory from Gomes (1995) can be proved that the zero libration amplitude does not increase in contrary to the cases with the non-zero libration amplitude.…”

Section: Periodic Solutionsmentioning

confidence: 92%

“…These periodic solutions set maximal capture time in the exterior resonances theoretically to infinity. Their position in aeσ phase space can be obtained as points where a, e, and σ are constant after the averaging over the synodic period for a particle with given β (Pástor 2016). The periodic solutions exist at the universal eccentricity.…”

Section: Periodic Solutionsmentioning

confidence: 99%

“…In the conservative PCRTBP the periodic solutions in the mean motion resonances exist at various eccentricities. These periodic solutions can be obtained using the method in Pástor (2016) without the condition giving the universal eccentricity. Periodic solutions in the circular-planar, spatial-circular, elliptic-planar and spatial-elliptic restricted three-body problem with the PR effect were found to exist for the dust particles captured in the mean motion 1/1 resonance with the planet (Pástor 2014b;Lhotka & Celletti 2015).…”

Section: Periodic Solutionsmentioning

confidence: 99%

“…This method was used for stability tests of the stationary points in the PCRTBP with the PR effect also by Šidlichovský & Nesvorný (1994). In Pástor (2016) periodic motions in a reference frame rotating with the planet were found to exist at each of such stationary points obtained from the averaged resonant equations. Lhotka & Celletti (2015) found stationary points in the circular-planar, spatial-circular, elliptic-planar and spatial-elliptic restricted three-body problem with the PR effect for the dust particles captured in the mean motion 1/1 resonance with the planet (see also Pástor 2014b).…”

Section: Introductionmentioning

confidence: 99%

“…The same color in the plots denotes the sets of the periodic solutions emerging from the same σ as β increases from zero. Circles depict the frequencies of libration for the periodic solutions in the exact resonances(Pástor 2016).…”

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confidence: 99%

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Linearized averaged resonant equations and their solution for dust particles

Pastor

2015

Preprint

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The averaged resonant equations of motion for the planar circular restricted three-body problem are solved on the linearization basis taking into account also non-gravitational effects. The averaged resonant equations are derived from Lagrange's planetary equations with additional Gauss's terms caused by the non-gravitational effects. The time depending solution has the standard form with exponential, quadratic, linear and constant terms. The existence of a rotational symmetry in the action of the non-gravitational effects around the star determines the order of a characteristic equation of the linearized system. In the symmetrical case (order 3) the considered non-gravitational effects are the stellar electromagnetic radiation and the radial stellar wind (stellar radiation). In the asymmetrical case (order 4) the stellar radiation and interstellar gas flow are considered. It is investigated how well the linearization solution describes real solution obtained from an equation of motion by a comparison of the resonant libration frequency found analytically and numerically. It is found that from initial values of the evolving orbital parameters (semimajor axis, eccentricity, longitude of pericenter, and resonant angular variable) in the averaged phase space the linearization frequency depends most sensitively on the initial value of the resonant angular variable. For small libration amplitudes of the resonant angular variable the best match of the real libration frequency and the linearization frequency is located approximately at the solution of the resonant condition (da/dt = 0). If the initial averaged conditions are chosen close to the solution of resonant condition, then the linearization frequency for practically all simple oscillatory evolutions matches the real libration frequency and the linearization solution very well approximates the real evolution. The linearization results obtained for stationary solutions are tested. In the planar circular restricted Sun-Neptune-dust problem with the solar radiation and the interstellar gas flow the solutions of resonant condition are practically independent on the longitude of perihelion.

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Section: Periodic Solutionsmentioning

confidence: 92%

Section: Periodic Solutionsmentioning

confidence: 99%

Section: Periodic Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Linearized averaged resonant equations and their solution for dust particles

Pastor

2015

Preprint

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Charged dust close to outer mean-motion resonances in the heliosphere

Lhotka

Galeş

2019

Celest Mech Dyn Astr

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We investigate the dynamics of charged dust close to outer meanmotion resonances with planet Jupiter. The importance of the interplanetary magnetic field on the orbital evolution of dust is clearly demonstrated. New dynamical phenomena are found that do not exist in the classical problem of uncharged dust. We find changes in the orientation of the orbital planes of dust particles, an increased amount of chaotic orbital motions, sudden 'jumps' in the resonant argument, and a decrease in time of temporary capture due to the Lorentz force. Variations in the orbital planes of dust grain orbits are found to be related to the angle between the orbital angular momentum and magnetic axes of the heliospheric field and the rotation rate of the Sun. These variations are bound using a simplified model derived from the full dynamical problem using first order averaging theory. It is found that the interplanetary magnetic field does not affect the capture process, that is still dominated by the other non-gravitational forces. Our study is based on a dynamical model in the framework of the inclined circular restricted three-body problem. Additional forces include solar radiation pressure, solar wind drag, the Poynting-Robertson effect, and the influence of a Parker spiral type interplanetary magnetic field model. The analytical estimates are derived on the basis of Gauss' form of planetary equations of motion. Numerical results are obtained by simulations of dust grain orbits together with the system of variational equations. Chaotic regions in phase space are revealed by means of Fast Lyapunov Chaos Indicators.

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Mapping the circumsolar dust ring near the orbit of Venus

Jones

Bewsher

Brown

2017

Icarus

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Synoptic images obtained from the HI-2 instrument on STEREO-A and -B between 2007 and 2014 have been used to further investigate the circumsolar dust ring at the orbit of Venus that was reported by Jones, Bewsher, Brown (2013). The analysis is based on high signal-to-noise ratio photometry of the zodiacal light, using data acquired over 10-day intervals, followed by a process of extracting spatial variability on scales up to about 6.5• . The resulting images provide information about the structure of the ring at the location where it is viewed tangentially. We identify 65 usable data sets that comprise about 11 percent of the available HI-2 data. Analysis of these images show that the orientation of the ring appears to be different to that of the orbit of Venus, with an inclination of 2.1• and longitude of ascending node of 68.5• . We map the variation of ring density parameters in a frame of reference that is co-rotating with Venus and find a pattern suggestive of dust in a 3 : 2 orbital resonance.However, the location of the maxima of dust densities is not as expected from theoretical models, and there is some evidence that the dust density distribution in the ring has a pattern speed that differs from the mean motion of Venus.

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Locations of stationary/periodic solutions in mean motion resonances according to the properties of dust grains

Cited by 24 publications

References 36 publications

Linearized averaged resonant equations and their solution for dust particles

Linearized averaged resonant equations and their solution for dust particles

Charged dust close to outer mean-motion resonances in the heliosphere

Mapping the circumsolar dust ring near the orbit of Venus

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