  Recent isotopic studies of Martian meteorites by Dauphas & Pourmond (2011)
have established that large (~ 3000 km radius) planetary embryos existed in the
solar nebula at the same time that chondrules - millimeter-sized igneous
inclusions found in meteorites - were forming. We model the formation of
chondrules by passage through bow shocks around such a planetary embryo on an
eccentric orbit. We numerically model the hydrodynamics of the flow, and find
that such large bodies retain an atmosphere, with Kelvin-Helmholtz
instabilities allowing mixing of this atmosphere with the gas and particles
flowing past the embryo. We calculate the trajectories of chondrules flowing
past the body, and find that they are not accreted by the protoplanet, but may
instead flow through volatiles outgassed from the planet's magma ocean. In
contrast, chondrules are accreted onto smaller planetesimals. We calculate the
thermal histories of chondrules passing through the bow shock. We find that
peak temperatures and cooling rates are consistent with the formation of the
dominant, porphyritic texture of most chondrules, assuming a modest enhancement
above the likely solar nebula average value of chondrule densities (by a factor
of 10), attributable to settling of chondrule precursors to the midplane of the
disk or turbulent concentration. We calculate the rate at which a planetary
embryo's eccentricity is damped and conclude that a single planetary embryo
scattered into an eccentric orbit can, over ~ 10e5 years, produce ~ 10e24 g of
chondrules. In principle, a small number (1-10) of eccentric planetary embryos
can melt the observed mass of chondrules in a manner consistent with all known
constraints.
