Positions of equilibrium points for dust particles in the circular restricted three-body problem with radiation

Abstract

For a body with negligible mass moving in the gravitational field of a star and one planet in a circular orbit (the circular restricted three-body problem) five equilibrium points exist and are known as the Lagrangian points. The positions of the Lagrangian points are not valid for dust particles because in the derivation of the Lagrangian points is assumed that no other forces beside the gravitation act on the body with negligible mass. Here we determined positions of the equilibrium points for the dust particles in the circular restricted three-body problem with radiation. The equilibrium points are located on curves connecting the Lagrangian points in the circular restricted threebody problem. The equilibrium points for Jupiter are distributed in large interval of heliocentric distances due to its large mass. The equilibrium points for the Earth explain a cloud of dust particles trailing the Earth observed with the Spitzer Space Telescope. The dust particles moving in the equilibrium points are distributed in interplanetary space according to their properties.

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

“…Interesting result is that the existence of periodic motions in the reference frame orbiting with the planet results from the averaged theory. The existence of the periodical motions in the MMRs occurring in the planar CRTBP with radiation demonstrated by the existence of circular orbits for the 1/1 resonance (Pástor 2014b) would be nicely completed by the existence of the periodical motions in the exterior resonances. The stationary solution for a given dust particle captured in a given exterior MMR in the planar CRTBP with radiation would represent a core that is a periodic motion to which the eccentricity asymptotically approaches and around which the libration occurs.…”

“…Periodic solutions in 1/1 resonance were already found to exist (Liou, Zook & Jackson 1995;Pástor 2014b). The existence of secularly stationary solutions in the vicinity of the triangular Lagrangian equilibrium points in spatialcircular, planar-elliptic and spatial-elliptic restricted threebody problem with the PR effect was recently confirmed in Lhotka & Celletti (2015).…”

“…The MMRs in a circular restricted three-body problem (CRTBP) with a stellar electromagnetic radiation and a stellar wind include numerous aspects which are directly applicable to astrophysical systems, ranging from the resonant dust ring close to the Earth's orbit (e.g. Jackson & Zook 1989;Dermott et al 1994;Reach et al 1995;Reach 2010;Pástor 2014b) through dust in the Edgeworth-Kuiper belt zone (e.g. Liou & Zook 1999;Moro-Martín & Malhotra 2002;Holmes et al 2003;Kuchner & Stark 2010) to structures observed in debris disks (e.g.…”

Linearized averaged resonant equations and their solution for dust particles

“…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).…”

“…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). The stability of found stationary points was investigated using the linearization of the equations of motion written in Delaunay variables and averaged over the orbital period.…”