The geometry of the visible satellites is an important factor in achieving high quality results for GPS (Global Positioning System). A measure for the geometry is the Geometric Dilution of Precision (GDOP) factor. Small values of GDOP parameters indicate good arrangements in the geometry of the selected satellites and correspondingly small error in position. The values of GDOP itself is a composite measure that reflects the influence of satellite geometry on the combined accuracy of the estimate of user time and user position. In the paper he low Earth orbit satellite constellation satisfying the time requirements and having good GDOP over certain region is studied. The constellation can be used as the system which provides the positioning function.