Dust grain growth and settling time inside initial gaseous giant protoplanets in the mass range 0.3 to 5 Jovian masses, formed by gravitational instability, have been investigated. We have determined the distribution of thermodynamic and physical variables inside the protoplanets solving the structure equations assuming their gas blobs to be fully convective and with this distribution we have calculated growth and settling time of grains with different initial sizes (10 −2 cm ≤ r 0 ≤ 1 cm). The results of our calculations are found to be in good agreement with those obtained by different approaches.

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The structure of a protoplanet has been determined by numerical method in which the protoplanet is assumed to be a gaseous sphere of solar composition having Jovian mass, which is in a steady state of quasistatic equilibrium. It is also assumed that the only source of energy in a protoplanet is gravitational. Regarding the transference of heat inside the protoplanet, we have considered two cases of interest (i) the convective case and (ii) the conductive–radiative case. It is found that in both cases the system possesses unique solution.

Theoretical predictions of an accretion model of star formation in galactic clusters, published quite long ago, which is found to have some relevance with the current picture of star formation have been tested with observation of seven clusters of young and intermediate ages. It is found that the agreement between the theory and observation is very good.