Orbital evolution of planetesimals in gaseous disks

Abstract

Planets are formed from collisional growth of small bodies in a protoplanetary disk. Bodies much larger than approximately 1 m are mainly controlled by the gravity of the host star and experience weak gas drag; their orbits are mainly expressed by orbital elements: semimajor axes a, eccentricities e, and inclinations ̄, which are modulated by gas drag. In a previous study, a, ė, and ̄ were analytically derived for e蠐1 and i蠐H/a, where H is the scale height of the disk. Their formulae are valid in the early stage of planet formation. However, once massive planets are formed, e and ̄ increase greatly. Indeed, some small bodies in the solar system have very large e and ̄. Therefore, in this paper, I analytically derive formulae for a 蠑, ė, and ̄ 蠑 for 1-e 2蠐1 and i ̄蠐H/a and for iLtH/a. The formulae combined from these limited equations will represent the results of orbital integration unless e≥1 or i>π-H/a. Since the derived formulae are applicable for bodies not only in a protoplanetary disk but also in a circumplanetary disk, I discuss the possibility of the capture of satellites in a circumplanetary disk using the formulae.