Formation of planets around stars of various masses - I. Formulation and a star of one solar mass

Abstract

The processes of planet formation are investigated both in a gaseous nebula and after the gaseous nebula has been blown away. It is shown that a protoplanet of mass more than about 100 times the representative mass of the planetesimal rapidly captures the planetesimals whose orbital semimajor axes are near its own. Therefore the growth of the protoplanet is determined by the migration rate of planetesimals to the region where they can be captured. The growth and capture of planetesimals is investigated and the time of planet formation is determined as a function of distance from the central star. As an example, planet formation around a star of 1 M⊙ is investigated. The Earth is found to form at |$t\approx2\times{10}^{6}$| yr in the gaseous nebula. The protoplanets at Jovian and Saturnian orbits grow to 10 times the Earth mass at |$2\times {10}^{7}$| yr and |$5\times {10}^{7}$| yr respectively in the gaseous nebula. Therefore they can capture large amounts of gas and grow to giant planets as long as the gaseous nebula survives for |$5\times {10}^{7}$| yr in these regions. The formation time of Neptune in a gas-free state is found to be |$3\times {10}^{9}$| yr, which is shorter than the age of the Solar System.