Abstract
The present thesis is addressed to study two important subjects in the field of astrophysics(galactic structure). The first subject is dealing with the most important parameter in stellar astronomy which is the distance. The second subject is dealing with the space density distribution of stellar groups. In first part of the thesis, we developed A statistical method to determine the distance of stellar groups . The method depends on the assumption that, the members of the group scatter around a mean absolute magnitude in Gaussian distribution. The mean apparent magnitude of the members is expressed by frequency function to correct for observational incompleteness at the faint end. The problem reduces to the solution of a highly transcendental equation for a given magnitude parameter . For the computational developments of the problem, continued fraction by the Top –Down algorithm was developed and applied for the evaluation of the error function erf(z).The distance equation was solved by an iterative method of second order of convergence using homotopy continuation technique. This technique does not need any priori knowledge of the initial guess, a property which avoids the critical situations between divergent to very slow convergent solutions, that may exist in the applications of other iterative methods. The numerical applications of the method for the distances have shown that the accuracy of the computed distances of some stellar groups are very satisfactory, which prove the efficiency of the developed method. In second part of the thesis, we studied the space density for stellar groups. We used globular clusters as typical stellar groups. For this purpose, we established two new analytical solutions: the first solution depends on two parameters, while the second solution depends on four parameters. These parameters can be obtained from star counts.
