Abstract

An orbital simulation program is described that uses a geometrical approach to modeling gravitational and atomic orbits at the Planck scale. Orbiting objects A, B, C... are sub-divided into points, each point representing 1 unit of Planck mass, for example, a 1kg satellite would divide into 1kg/Planck mass = 45940509 points. Each point in object A then forms a rotating orbital pair with every point in objects B, C..., resulting in a universe-wide, n-body network of rotating point-to-point orbital pairs. Each orbital pair rotates 1 unit of Planck length per unit of Planck time at velocity c in hypersphere space co-ordinates, the results then summed and averaged giving the new co-ordinates, the program then repeats. When these rotations are mapped over time in a 3D space, objects A, B, C... appear to be orbiting each other. The basic simulation uses the fine structure constant alpha as an orbital constant to simulate gravitational orbit parameters. As each orbital comprises only 2 points, 1 at each orbital pole, information regarding the objects A, B, C... ; momentum, size, center of mass, barycenter etc ... is not required, instead only the start positions (co-ordinates) of each point are used as initial inputs. Each point, by having a mass of Planck mass, is itself a construct of multiple particles, and so we can also form particle to particle orbital pairs, transition energies for the H atom (an electron-proton orbital pair) are well documented and so can be used as reference. Atomic orbital pairs rotate slower than gravitational orbitals by a factor of alpha, 'gravity' therefore stronger than the 'electric force' when measured at the Planck scale.