  It has been suggested that chondrules and calcium-aluminum-rich inclusions
(CAIs) were formed at the inner edge of the protoplanetary disk and then
entrained in magnetocentrifugal X-winds. We study trajectories of such solid
bodies with the consideration of the central star gravity, the protoplanetary
disk gravity, and the gas drag of the wind. The efficiency of the gas drag
depends on a parameter $\eta$, which is the product of the solid body size and
density. We find that the gravity of the protoplanetary disk has a
non-negligible effect on the trajectories. If a solid body re-enters the flared
disk, the re-entering radius depends on the stellar magnetic dipole moment, the
disk's gravity, the parameter $\eta$, and the initial launching angle. The
disk's gravity can make the re-entering radius lower by up to 30%. We find a
threshold $\eta$, denoted as $\eta_t$, for any particular configuration of the
X-wind, below which the solid bodies will be expelled from the planetary
system. $\eta_t$ sensitively depends on the initial launching angle, and also
depends on the mass of the disk. Only the solid bodies with a $\eta$ larger
than but very close to $\eta_t$ can be launched to a re-entering radius larger
than 1 AU. This size-sorting effect may explain why chondrules come with a
narrow range of sizes within each chondritic class. In general, the size
distributions of CAIs and chondrules in chondrites can be determined from the
initial size distribution as well as the distribution over the initial
launching angle.

Earth and Planetary Astrophysics;Solar and Stellar Astrophysics