Motion of space dust close to the equilateral Lagrange points is determined by the gravitational attraction of the central star and the perturbing planets, but is also subject to non-gravitational forces, mainly due to the central celestial body. In my study on the phenomenon of temporary capture of space dust inside the orbits of the planets I investigated two main effects: the solar wind and drag due to the Poynting-Robertson effect. The latter effect describes the interaction of dust grains with photons by means of special relativity. It causes a drag term in the equations of motion of the dust grain in its first order Newtonian approximation. The term depends on the velocity of the dust grain and reduces the orbital energy of the grain. The same holds true for the drag term induced by the interaction of the dust grain with stellar winds. As a consequence, dust grains in planetary systems spiral inwards, towards the central star on time-scales of the order of thousands of years, depending on the grain size and strength of stellar radiation. However, it is known that temporary capture of dust grains in mean motion resonances with the planets may prolong the orbital life-time significantly. While the stabilizing effect of the much weaker outer and inner resonances with the planets was already well understood, the effect of the much stronger 1:1 resonance remained unclear. With my study the scientific gap could be filled: stable motion for dust sized particles is not possible due to the Poynting-Roberston also in the equilateral configuration of the 1:1 resonance while temporary capture is possible for a wide range of system parameters. Much more important, the effect shifts the locations of the Lagrange points, and moreover may cause an asymmetry between the two Lagrange points L4 and L5 and may therefore also serve as an explanation for the observational evidence that the number of asteroids – if formed from dust in 1:1 resonance with a planet – is unequal between those two locations.
The figure was fist published in (1, 2) . It shows the phenomenon of temporary capture of space dust in 1:1 resonance with a planet that is located at 1 astronomical unit (see ordinate). One clearly sees the effect of temporary capture in terms of the oscillations around a mean value that defines the location of the resonance. While for extended celestial bodies the location lies also at 1 astronomical unit, the location is shifted to smaller values in semi-major axis due to the Poynting-Robertson effect. The stronger the effect the larger the shift, and the smaller the time of temporary capture.