### Abstract:

In this thesis we have investigated some aspects of the protoplanetary theory of planetary formation, namely, the structure of a protoplanet, sedimentation of heavy elements in a protoplanet, and the effect of mass loss on the orbit of a protoplanet. The thesis contains five different chapters. The first chapter deals with a brief outline of the current view of planetary formation while in the other chapters we have investigated the problems under consideration. In chapter 2, we have determined the structure of a protoplanet by numerical method in which the protoplanet is assumed to be a sphere of solar composition, which is in a steady state of quasi-static equilibrium. It is also assumed that the only source of energy in a protoplanet is gravitational. Regarding the heat transference of heat inside the protoplanet we have considered two cases of interest i) the convective case and ii) the conductive - radiative case.
In chapter 3, the distribution of thermodynamic variables in a protoplanet has been determined by polytropic method assuming that the protoplanet is a polytope of index n = .5, I, 3/2 and 3.
In the fourth chapter, we have investigated the segregation time of falling grains inside a protoplanet. We have calculated the time for two possible cases of interest, namely, i) the mass of the grain remains constant during falling, ii) the grain mass increases due to its adherence with other grains, and have found that a solid core having mass roughly equal to that of a terrestrial type planet can form at the center of a protoplanet in a reasonable short period of time on astronomical scale. In chapter 5, we have investigated the effect of mass loss on the orbital distance of a protoplanet in a two-body problem as well as in a three-body problem, and have shown that the planetary spacing observed today can satisfactorily be explained in terms of mass loss from a set of identical protoplanets.

### Description:

This Thesis is Submitted to the Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh for The Degree of Doctor of Philosophy (PhD)