One of the important parameters that affects the performance of a solar collector is its tilt angle with the horizon. This is because the variation of tilt angle changes the amount of solar radiation reaching the collector surface. Meanwhile, is the rule of thumb, which says that solar collector should be orientated towards the Equator with a tilt equal to latitude, valid for high latitudes region? Thus, it is required to determine the optimum tilt for Equator facing collectors. In addition, the question may rise: how much adjustments of Equator facing solar collector tilt angle is reasonable to do during a year? A mathematical model was used for estimating the solar radiation on a tilted surface, and to determine the optimum tilt angle and orientation (surface azimuth angle) for the solar collector at any latitude. This model was applied for determining optimum tilt angle in the high latitudes zone in the Southern Hemisphere, on a daily basis, as well as for a specific period. The optimum angle was computed by searching for the values for which the radiation on the collector surface is a maximum for a particular day or a specific period. The results reveal that changing the tilt angle 12 times in a year (i.e. using the monthly optimum tilt angle) maintains approximately the total amount of solar radiation near the maximum value that is found by changing the tilt angle daily to its optimum value. This achieves a yearly gain in solar radiation up to 1.8 times of the case of a horizontal surface while the daily gain reaches 60 times approximately. Moreover, general formulas are proposed for predicting daily optimum tilt angle and optimum tilt angle over any number of days.