Interstellar dust grains approaching the Sun are influenced mainly by solar gravity, solar electromagnetic radiation and Lorentz force due to the existence of interplanetary magnetic field. These interactions together with the effect of the solar wind on dust grain and the effect of solar cycle are taken into account when modelling behaviour of interstellar dust in the vicinity of the Sun. As a consequence, nonspherical dust grains can be captured and survive in the solar system – they can orbit the Sun in sufficiently large distances from the Sun not to be thermally destroyed. On the other hand, captured spherical dust grains are practically all destroyed. Detailed numerical simulations showed an interesting behaviour of a quantity of the dimension of length cubed divided by time squared. The quantity behaves practically as an invariant of motion: it is a constant during the process when surviving captured interstellar grain is orbiting the Sun. The constancy is fulfilled with an accuracy better than 1%.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html