  The circular orbits and elliptical orbits of moving objects in a
gravitational field are essential information in astronomy. There have been
many methods developed in the literature and textbooks to describe these
orbits. In this report, I propose to use the vis-viva equation to construct a
complex function to store the state of a moving object in elliptical orbits
such that one can calculate its near future numerically. This state function is
constructed by splitting its momentum into real and imaginary parts with one
perpendicular to the radius of the mass center and the other parallel. The
wavefunctions of electrons of hydrogen atoms in quantum mechanics inspire this
idea. The equations are derived for one-body problems. Two-body problems can be
constructed with subsets of one-body problems with the same center of mass, but
different effective mass pinned there, significantly different from existing
methods and providing the same results.
