Astronomy and Astrophysics – Astrophysics
Scientific paper
Sep 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...289..972s&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 289, no. 3, p. 972-982
Astronomy and Astrophysics
Astrophysics
23
Capture Effect, Earth Orbits, Interplanetary Dust, Interplanetary Medium, Orbital Resonances (Celestial Mechanics), Poynting-Robertson Effect, Three Body Problem, Celestial Mechanics, Grain Size, Gravitational Fields, Libration, Orbital Mechanics, Radiation Pressure
Scientific paper
The orbital evolution of the dust grains of radius approximately 10 micrometers, close to the exterior resonances with the Earth is investigated. Especially resonances 6/7, 5/6 and 4/5 were studied as they are close enough to the Earth orbit and our numerical experiments proved their higher capture efficiency. Numerical simulations were compared to the semi-analytical approach of the circular restricted problem with Poynting-Robertson drag. The disturbing function has been averaged over the fast variable numerically. It was shown that due to convergence problems the disturbing function cannot be approximated by the usual truncated series. Even if the terms of the fourth order in eccentricity e are included, a qualitatively different picture is obtained. Using the semi-analytic approach we found stationary solutions where the resonance effect cancels the drag. Where there is capture in numerical simulations, the solution clearly approaches these stationary points. The amplitude of the resonant variable is, however, slowly increasing which has to lead eventually to close approach to the Earth, and the capture is only temporary. The particle may be trapped even for times of the order of 105 years in the circular case. The equations linearized numerically in the vicinity of stationary point were shown to lead to one real negative frequency and two complex conjugate frequencies with a positive real part for typical values of the parameters. This shows the instability of the stationary point. The beta-dependence of the stationary point positions is given. For beta approximately 0.1 and larger, these stationary points are much too close to the collision curve, where the averaging method fails and the particle will soon be removed by close approach to the Earth. Some inferences for the possible distribution of grains in the vicinity of the Earth orbit are made. The effect of other planets has been shortly discussed. It was shown that temporary trapping is still possible, only the time of capture is shorter.
Nesvorný David
Sidlichovský Miloš
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