Journal of the
Korean Mathematical Society JKMS

A feynman functional formulation is given for the Global Positioning System, GPS. Both the sequential and analytic Feynman functionals are presented for the classical, exterior, gravity problems which include rigid body rotations, special relativity and some general relativity corrections. A mathematically rigeorous approach is introduced whose solutions exist, are unique and which depend continuously on the initial data. This formulation is convergent and has the finite approximation property. It is emphasized that all of the problems studied are classical (not quantum) evolution systems.

Keywords: Feynman integrals, geodesy, celestial mechanics, weak fields in general relativity

MSC numbers: Preliminary 86A30, 83C25: Secondary 70F15, 81Q30, 47A55