The Fifth Moscow Solar System Symposium (5M-S 3 ) Moscow 2014 Formation of embryos of the Earth-Moon system as a result of a collision of two rarefied condensations S. I. Ipatov 1,2 , 1 Vernadsky Institute of Geochemistry and Analytical Chemistry of Russian Academy of Sciences, Kosygina 19, 119991, Moscow, Russia; 2 Space Research Institute of Russian Academy of Sciences, Profsoyuz- naya st. 84/32, Moscow, Russia. Contact: siipatov@hotmail.com Main Points of the Abstract: The angular momentum of the present Earth-Moon system could be acquired at the collision of two identical rarefied condensations with sizes of Hill spheres which total mass was about 0.1 of the mass of the Earth. Solid embryos of the Earth and the Moon could be originated as a result of contraction of the condensation formed at the collision. Depending on eccentricities of planetesimals that collided with solid embryos of the Earth and the Moon, the Moon could acquire 0.04-0.3 of its mass at the stage of accumulation of solid bodies while the mass of the growing Earth increased by a factor of ten. Introduction: Many authors (e.g., [1-3]) suppose that the Earth-Moon system formed as a result of collision of the solid Earth with a Mars-sized object. Galimov and Krivtsov [4] presented arguments that the giant impact concept has several weaknesses. It is considered that one of the weaknesses of the impact theory is that the Moon would consist almost exclusively of material from the impactor, but the rocks from the Moon and the Earth are similar. Ipatov [5] simulated the evolution of a disk of planetesimals initially divided into groups ac- cording to their distances from the Sun. He showed that the composition of large enough embryos in the terres- trial feeding zone could be similar due to mixing of planetesimals during planet formation. So in principle, it could be possible that composition of some impactors collided with the embryo of the Earth could not differ much from that of the embryo. Lyra et al. [8] showed that in the vortices launched by the Rossby wave instabil- ity in the borders of the dead zone, the solids quickly achieve critical densities and undergo gravitational col- lapse into protoplanetary embryos in the mass range 0.1M E -0.6M E (where M E is the mass of the Earth). Ipatov [6] and Nesvorny et al. [9] supposed that transneptunian satellite systems were formed from rarefied condensations. According to [6], the angular momenta acquired at collisions of condensations moved in circular heliocentric orbits could have the same values as the angular momenta of discovered transneptunian and asteroid binaries. Ipatov [7] obtained that the angular momenta used in [9] as initial data in calculations of the contrac- tion of condensations leading to formation of transneptunian binaries could be acquired at collisions of two con- densations moved in circular heliocentric orbits. Ipatov supposed that the number of collisions of condensations at which the formed condensation with mass equal to that of a solid body with diameter d>100 km got the angu- lar momentum needed for formation of a satellite system can be about the number of small bodies with d>100 km having satellites, i.e., the fraction of condensations formed at collisions leading to formation of satellite sys- tems among all condensations can be about 0.3 for solid primaries with d>100 km formed in the transneptunian belt. The model of collisions of condensations explains negative angular momenta of some observed binaries (e.g., 2000 CF105, 2001 QW322, 2000 QL251), as about 20 percent of collisions of condensations moving in circular heliocentric orbits lead to retrograde rotation. The Angular Momentum at a Collision of Two Condensations: Using the formulas presented in [6], we obtained that the angular momentum K EM of the Earth-Moon system equals to the angular momentum K s2 at a typical collision of two identical condensations with size of Hill spheres, which total mass equals 0.13M Е . For circular heliocentric orbits, the maximum value of K s2 is greater by a factor of 0.6 -1 than the above typical value [6]. In this case, the above total mass is 0.096M Е . Therefore, the angular momentum of the Earth-Moon system could be acquired at a collision of two condensations with a total mass not smaller than 0.1M Е . We suppose that solid proto-Earth and proto-Moon could form by contraction of a condensation (e.g., according to the models of contraction of a condensation presented in [4, 9]). Not all material of collided preplanetesimals could be left in the condensation formed at the collision. So the total mass of collided preplanetesimals could exceed 0.1M Е . Angular Velocities of Condensations Needed for Formation of Satellite Systems: In calculations of con- traction of condensations (of mass m and radius r equal to 0.6 of the Hill radius r H ) presented in [9], trans- Neptunian objects with satellites were formed at initial angular velocities ω о from the range 0.5Ω о –0.75Ω о , where Ω о =(Gm/r 3 ) 1/2 (G is the gravitational constant). In 3-D calculations of gravitational collapse of a conden- sation presented in [4], binaries were formed at ω о /Ω о from the range of 1-1.46. For smaller ω о /Ω о , satellites were not formed, and a considerable fraction of angular momentum could be in particles that left the formed condensation. The difference in results presented in [4] and [9] can be caused, in particular, by different chaotic velocities of particles/bodies constituting condensations and by different sizes of condensations. The sizes of condensations in calculations presented in [4] were smaller than Hill spheres. For example, in one of their calcu- lations (page 108 in [4]) the radius of the condensation exceeded the radius of the corresponding solid planet by a factor of 5.5, while the Earth radius is smaller by a factor more than 200 than the Hill radius.