ON FORMING ME MOON IN GEOCENTRIC ORBIT; DYNAMICAL EVOLUTION OF A CIRCUMTERRESTRIAL PLANETESIMAL SWARM; Floyd Herbert, University of Arizona, Tucson, and D.R. Davis and S.J. Weidenschilling, Planetary Science Institute, Tucson, AZ. The wclassicalv theories of lunar origin all have major difficulties that have prevented any of them from beinq generally accepted: the capture hypo- thesis is quite improbable, while the fission hypothesis suffers a larqe anqular momentum problem. New theories have, of course, sprouted to replace these -- tidal disruption/capture, accretion in geocentric orbit, and the qiant impact hypothesis. At a recent conference on the oriqin of the moon (October, 1984, Kona, HI), the qiant impact hypothesis, which holds that the moon formed as the result of a large (Mercury-to-Mars-sized) planetesimal impactinq the proto-Earth, emerqed as the current favored hypothesis, with co-formation in geocentric orbit a possible alternative. The latter model, which suqgests that the moon formed from planetesimals captured from helio- centric orbit and forminq a circumterrestrial disk, was criticized also as suffering an angular momentum deficit, based on our preliminary results (1). We present here additional results of studies of anqular momen-tum input to a circumterrestrial swarm by planetesimals arriving from heliocentric orbits. Such a target swarm could have formed initially by collisions among heliocentric planetesimals passing within Earth's sphere of influence. Such collisions have a siqnificant probability (tens of $1 of yieldinq capture into qeocentric orbit (2). We assume that the swarm is evolvinq due to collisions with the heliocentric planetesimal population as they pass close to the Earth. We calculate the mean angular momentum relative to the Earth that an incoming planetesimal would have as a function of distance from the Earth. The planar restricted three-body model (Sun-Earth-planetesimal system) is used to calculate numerically the trajectory of the planetesimal as it encounters the Earth. Rather than startinq the planetesimal far from Earth and pro- pagatinq motion forward in time -- an inefficient procedure due to the diffi- culty of finding initial conditions leading to Earth encounter -- we follow the procedure of Giuli (3) and start the particle near the Earth and integrate backward in time to find the initial heliocentric orbit of the particle. A small perturbation is made in the startinq conditions and the trajectory propagated forward until it encounters the Earth; this procedure is repeated until the particle does not encounter Earth. In this fashion, we construct an inventory of heliocentric orbit elements (a,e) that lead to encounters with Earth at speeds up to about 1.25 x the geocentric escape speed. For each trajectory, we compute the radial and tangential velocity components relative to the Earth at each of 15 qeocentric distances, yielding the anqular momentum energy that would input to the swarm by a collision at each location. Approximately 25,000 trajectories are inteqrated to construct the data base. We next combined several assumed distributions of surface density and orbital elements for the heliocentric population with the data base in order to find the anqular momentum delivered by the incominq planetesimals at different distances from Earth. Fiqure 1 gives the result of the calculations for 4 assumed orbit element distributions. Also shown is the size of the circular orbit that has the same anqular momentum as the averaae angular momentum brouqht in by the heliocentric population. We see that there is little to choose between the first three cases: the average anqular momentum delivered is proqrade, but small compared with that required to maintain an orbit about the Earth. Most material brouqht in would simply collapse onto the Earth in this case. The last case, however, delivers a significantly

O Lunar and Planetary Institute Provided by the NASA Astrophysics Data System ON FORMING THE MOON IN GEOCENTRIC ORBIT Herbert, F., et al. larger averaqe angular momentum than the previous ones due to the enhancement of the number of bodies arriving on nearly tangential orbits (i.e., they intersect the Earth's orbit near aphelion or perihelion of their orbit). Such orbits tend to deliver much more angular momentum on average than those coming in on orbits that are deep Earth crossers (4). This last distribution suggests that material captured into orbit at, large geocentric distances can bring with it enough angular momentum to remain in Earth orbit. For example, material captured at 40-60 Re would bring suf- ficient angular momentum to produce a final circular orbit at 2-4 R distance. Capture at even larger distances wou l d lead to even larger final orpits, thus providinq a way of placing material from heliocentric orbits into low, nearly circular geocentric orbits -- the type of orbit in which the moon may have formed. If the swarm is dominated by km-sized bodies, viscous transport of angular momentum is sufficient to maintain its outer edge at several tens of R , at the expense of some mass loss from its inner edge onto the Earth. #us, the angular momentum barrier to co-accretion does not appear insur- mountable. Fiaure 1: Mean angu lar momentum, normalized to the circular orbit angular mo- + mentum, (h/hc) delivered o Uniform by an impactcng population + e from .03 - .07 of heliocentric projectiles A e from 0-0.1 as a function of geocentric ' crossers distance ( in units of earth 0.4 radii). Earth has its pre- sent mass and size. Four hypothesized heliocentric orbit element distributions ,., are assumed: 1) uniform in both a and 3; 2) uniform h/h, in a but a triangular 2 distribution between 0.03 and 0.07; 3) same as 21, 0.2 -, except 2 is between 0 and 0.1; 4) a is depleted by a factor of 10 when the orbit is Earth-crossing and uni- form otherwise, while 2 is 0.1 - n the same as 2). Shown for 1 comparison is the assumed • A and Rusk01 (5) anqular momentum input by Safronov and Ruskol (5). Also shown are three circu- 0 lar orbit sizes that have the same angular momentum as the correspondinq fractional anqular momentum at larger geocentric d i stances. REFERENCES: (1) Herbert, F. and Davis, D.R. (1984). Lunar Origin Conf. ab- stracts, 53. (2) Weidenschilling, S.J. (1984). Lunar Origin Conf. abstracts, 54, 55. (3) Giuli, R.T. (1968). lcarus 8, 301. (4) Harris, A.W. (1977). lcarus 31, 168. (5) Safronov, V.S. and Ruskol, E.L. (1977). In Planetarv Satellites, J. Burns, Ed., University of Arizona Press, Tucson, 501-512.

O Lunar and Planetary Institute Provided by the NASA Astrophysics Data System