Constructing Wavefunctions for One-Body and Two-Body Gravitational Orbits in Classical Mechanics

Constructing Wavefunctions for One-Body and Two-Body Gravitational Orbits in Classical Mechanics

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. This idea is inspired by the wavefunctions of electrons of hydrogen atoms in quantum mechanics. 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, which is significantly different from existing methods and provides the same results.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. This idea is inspired by the wavefunctions of electrons of hydrogen atoms in quantum mechanics. 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, which is significantly different from existing methods and provides the same results.