Moscow October 8-12, 2012 V. Sizenkov, V. Lupovka, V. Dmitriev, H. Hussmann, J. Oberst This work has been supported by a grant from the Ministry of Education and Science of the Russian Federation (Agreement 11.G dd. 30/11/2010). Numerical simulation of the formation of dust ring around Mars

MIIGAIK Extraterrestrial Laboratory Previous studies by Hamliton and Krivov (1997) and Burns et al. (2001) have constructed analytical models of dust rings around earth- type planets. Particles ejected from natural planet satellites by meteoroid impacts can be one of the sources of material for dust rings. In our work we study the possible existence of a ring along the Phobos orbit using of numerical methods. Problem statement

MIIGAIK Extraterrestrial Laboratory Simulation of ejecta 1/2 When the impact takes place, ejected particles start practically from the same position (crater), but with different velocities and under different ejection angles. It is interesting estimating if ejected particles can form rings for some initial conditions. Therefore, we consider the orbital evolution of a set of particles with stochastically modeled initial velocity vectors.

MIIGAIK Extraterrestrial Laboratory Simulation of ejecta 2/2 Phobos is considered as the particles parent body. The mean Phobos soil density is ± g/cm 3 and geometric albedo is ± [3]. Group 1 Group 2 CoordinatesPhobos at January 1, 1000 Velocity km/s in relation to Phobos km/s in relation to Phobos Mass 0.9 g Albedo Surface 78 mm 2

MIIGAIK Extraterrestrial Laboratory Integration of particle orbits was performed by the explicit Adams–Bashforth method [5] from January 1, 1000 to January 1, The integration was made in Cartesian coordinates. Perturbations: the Mars gravity field for up to 16x16; third body attraction (Sun, 4 planets and Moon); solar radiation pressure (cannonball model). Orbit integration

MIIGAIK Extraterrestrial Laboratory

General Results of Orbit Integration Initially 70 particles were launched. Just 49 modeled particles with initial velocities in between km/s to km/s from the orbital Phobos velocity formed a ring-similar structure along the Phobos orbit. From them 18 modeled particles with initial velocities km/s and 18 particles with initial velocities km/s. Particles that have large changes of velocity more than the 0.34 km/s escape from the orbit of Phobos and did not form a ring.

MIIGAIK Extraterrestrial Laboratory Particle positions at 1100

MIIGAIK Extraterrestrial Laboratory Particle positions at 1500

MIIGAIK Extraterrestrial Laboratory Particle positions at 2000

MIIGAIK Extraterrestrial Laboratory Particle positions at 2500

MIIGAIK Extraterrestrial Laboratory Final particle positions at 3000

MIIGAIK Extraterrestrial Laboratory EVOLUTION OF ORBITAL ELEMENTS Mars Mean Equator

MIIGAIK Extraterrestrial Laboratory Analysis of orbital evolution of ejecta from Phobos shows that dust ring formed by particles with some initial motion models resemble a belt, but not a disk. Depiction of possible ring structure

MIIGAIK Extraterrestrial Laboratory Summary Simulations of orbital evolution of ejecta from Phobos shows that for some initial conditions ejected particles can form ring-like structures According to our investigation this ring appears to have a stability for a minimum of two thousand years These studies will be continued to a larger number of particles, a larger mass range and longer time intervals Summary Simulations of orbital evolution of ejecta from Phobos shows that for some initial conditions ejected particles can form ring-like structures According to our investigation this ring appears to have a stability for a minimum of two thousand years These studies will be continued to a larger number of particles, a larger mass range and longer time intervals

MIIGAIK Extraterrestrial Laboratory References [1] Joseph A. Burns, Douglas P. Hamilton, Mark R. Showalter: Dusty rings and circumplanetary dust: observations and simple physics. In Interplanetary Dust (E. Grun, B. Gustafson, S. Dermott and H. Fechtig, Eds.), Springer, Berlin, pp. 641–725, [2] Alexander V. Krivov, Douglas P. Hamilton: Martian Dust Belts: Waiting for Discovery. ICARUS Vol. 128, pp. 335–353, [3] JPL's HORIZONS System [4] Acton, C.H.: Ancillary Data Services of NASA's Navigation and Ancillary Information Facility; Planetary and Space Science, Vol. 44, No. 1, pp , [5] Hussmann H.et al., Planet. Space Science, in press, [1] Joseph A. Burns, Douglas P. Hamilton, Mark R. Showalter: Dusty rings and circumplanetary dust: observations and simple physics. In Interplanetary Dust (E. Grun, B. Gustafson, S. Dermott and H. Fechtig, Eds.), Springer, Berlin, pp. 641–725, [2] Alexander V. Krivov, Douglas P. Hamilton: Martian Dust Belts: Waiting for Discovery. ICARUS Vol. 128, pp. 335–353, [3] JPL's HORIZONS System [4] Acton, C.H.: Ancillary Data Services of NASA's Navigation and Ancillary Information Facility; Planetary and Space Science, Vol. 44, No. 1, pp , [5] Hussmann H.et al., Planet. Space Science, in press, 2012.

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