The objective of this work is to present a new algebraic solution for the problem of remote determination of geographic coordinates of a target, using a new remote geopositioning system being developed in Brazil. It can be useful for double-check measurements obtained with other methods, for certain critical applications, being capable to perform independently from them. This system requires three-reference bases on the surface of the earth with synchronized clocks and a repeater in space. Calculations are derived from measurements of propagation time of clock signal transmitted by one base to all bases and target, via a transponder in space. The algorithm also provides the "instantaneous" determination of the repeater position in space and brings other applications in navigation and remote clock synchronization. The algorithm has been successfully tested through computational software.