Migration of dust particles ejected from the Earth and Mars

Introduction. Сollisions of large bodies with planets (mainly during planet formation) could produce ejection of bodies and dust particles. The probabilities of collisions of bodies ejected from the Earth with planets and the Moon were studied by Ipatov (2024a, 2025a). Ipatov (2024b-c, 2025b-c, 2926) presented shorter information about probabilities of collisions of bodies ejected from all terrestrial planets and the Moon with planets. Migration of dust particles was shortly discussed in (Ipatov, 2025c). Below I study the migration of dust ejected from the Earth and Mars. In each calculation variant (“run”), the motion of 250 ejected dust particles was studied for the fixed values of an ejection angle i_ej, a velocity v_ej of ejection, and one of three points of ejection. In different variants, i_ej equaled to 45^o, or 15^o, or 90^o, and v_ej varied from 11.3 to 20 km/s for the Earth and from 5.05 to 20 km/s for Mars. For points W and B, the particles started from the forward point on the planet's surface in the direction of the planet's motion and from the back point on the opposite side of the planet, respectively. The starting point F is located most far from the Sun. The gravitational influence of the Sun and all planets, radiation pressure, the Poynting-Robertson effect and the solar wind were taken into account. The evolution of orbits was studied during the dynamical lifetime T_end of all particles (until all particles left the Solar System or collided with the Sun or planets). Calculations were carried out for the ratio β of radiation pressure force to gravitational force equaled to 0.0004, 0.004, 0.04 and 0.4 (corresponding to silicate particle diameters of about 1 mm, 100, 10 and 1 micron).

Ejection from the Earth. At β=0.0004 the values of T_end (for a run with 250 particles) were typically between 0.5 and 10 Myr, but could exceed 100 Myr. For 8500 considered 1-mm particles, there were 35 collisions with Mercury, 43 with Venus and 40 with the Earth. For i_ej=45^o the fraction p_ej of ejected particles was 0 for all ejections from point B and for ejection at small v_ej from other points. At v_ej=20 km/s and i_ej=45^op_ej reached 0.3 for point F and 1 for point W.

At β=0.004 the values of T_end were between 0.006 and 10 Myr. For 8500 considered 100-micron particles, there were 2 collisions with Mercury, 7 with Venus, and 6 with the Earth. Most of particles collided with the Sun. Ejection of particles was in 7 among 34 runs. All particles were ejected from point W at v_ej=20 km/s and i_ej=45^o. For ejection from point F at v_ej=20 km/s and i_ej=45^o, p_ej equaled to 0.27.

At β=0.04 the values of T_end were between 0.003 and 5 Myr. Among 7750 considered 10-micron particles, there was only one collision with planets. The fraction of ejected particles was 0 in all calculations for ejection from point B and also for ejection from point W at i_ej=89^o. For ejection from point W at i_ej=45^o, p_ej varied from 0 at v_ej=11.5 km/s to 1 at v_ej=20 km/s. For ejection from point F at i_ej=45^o, p_ej varied from 0 at v_ej=11.3 km/s to 0.3 at v_ej=20 km/s.

At β=0.4, T_end was less than 0.4 Myr. For 8500 considered micron particles, there were no their collisions with planets. In most calculations at β=0.4, about a half of particles collided with the Sun, and other particles were ejected from the Solar System. For ejection from point W at v_ej≥14 km/s and i_ej≥45^o, all micron particles were ejected into hyperbolic orbits.

The estimated (based on arrays of orbital elements of migrating particles) ratio of probabilities of collisions of particles with the Earth and the Moon was between 20 and 65 (more often between 25 and 35).

Ejection from Mars. For each β, 4000 particles were considered at i_ej=45^o and different v_ej and ejection points. At β=0.0004, for 4000 particles there were 15 collisions with Mercury, 20 with Venus, 18 with Earth, and 4 with Mars. For considered series of calculations, T_end was between 0.0005 and 7 Myr. T_end equaled to 0.0005 Myr for ejection from point W at v_ej=20 km/s. The fraction of bodies collided with the Sun and the fraction p_ej of ejected particles varied from 0 to 1. At β=0.004, there were 5 collisions with Mercury, 4 with Venus, and 4 with Earth. Depending on v_ej and an ejection point, p_ej and the fraction of bodies collided with the Sun varied from 0 to 1, and 0.0005≤T_end≤5 Myr. At β=0.04, the values of p_ej were between 0 and 1, 0.0005≤T_end≤1.3 Myr, and there were no collisions of particles with planets. At β=0.4, there were no collisions of particles with planets, and in different runs p_ej varied from 0.5 to 1 (other particles collided with the Sun). The values of T_end were between 0.0004 and 0.45 Myr. For a few series of runs, the estimated ratio of probabilities of collisions with the Earth and the Moon was between 21 and 23 at β=0.4, between 30 and 50 at β=0.04, between 15 and 40 at β=0.004, and between 15 and 35 at β=0.0004.

Acknowledgements: The studies of delivery of material to the Moon were supported by the Russian Science Foundation, project 25-17-00051. Other studies were carried out under government-financed research project for the Vernadsky Institute.

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