Micrometer sized space dust falls in two distinct categories of origin: natural and man-made. While natural space dust is formed in interplanetary space by means of cometary activity and asteroid collision, the man-made counterpart is mainly found in the near Earth environment. The origin of micrometer-sized space dust in the latter case is due to fragmentation of larger particles into smaller ones. Fragmentation is caused by collision and erosion of artificial satellites that have been placed in Earth-orbit to fulfil civil and military missions for human mankind. Television and communication services rely on satellites in the geostationary orbit, where the orbital period of the satellite coincides with the rotation period of the Earth. In my work on the long-term stability of micro-meter sized space debris in the vicinity of the geostationary orbit I investigated the role of the so-called Poynting-Robertson effect on the orbital motion of micro-meter sized space debris: the relativistic interaction of photons with micron sized space dust causes loss of orbital energy of the particles. As a result the semi-major axes, i.e. the distance from the centre of the Earth shrinks with time too. As a consequence micro-meter sized space dust of large amounts is able to pollute lower regimes of motion in the near Earth environment with time. High velocity impacts of these sub-millimetre sized objects with space crafts or astronauts in extravehicular activity may cause severe problems, like drop outs of electronics or even damage of space-suits with fatal consequences. For this reason special care needs to be taken in the design and choice of materials that are used in space industry to prevent such catastrophic events. It is therefore also a mandatory and crucial task to provide engineers with precise estimates of the amount and long-term fate of sub-millimetre sized space dust in the different Earth environments.
The figure was first published in [I], [II] and shows the inward drift in semi-major axis due to the Poynting-Robertson effect on the abscissa versus the initial distance of a dust grain released in the vicinity of the geostationary resonance. The blue line provides the estimate on the basis of an analytical theory. Red circles and black crosses mark averaged drift rates based on numerical simulations including the effect of the Moon. We notice that temporary capture of dust grains inside the 1:1 resonance with the rotation of the Earth may prolong the orbital life-time of micron sized dust grains significantly (see also my study in the Lagrange problem). Outside resonance the theory perfectly predicts the averaged drifts rates obtain from numerical simulations.
Christoph Lhotka 