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 corresponding 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 are then summed and averaged to give the new co-ordinates, the program then repeats. When these rotations are mapped over time on a 2-D plane (representing 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 (x, y, z) co-ordinates of each point are defined. Each point, by having a mass of Planck mass, is itself a construct of multiple particles, and so we can also form individual particle to particle orbital pairs. The simulation uses only geometry, no dimensioned constants (G, h, c ...) are required, although the results can be measured in Planck units for comparison. Points are physically linked together by a unit of momentum (a graviton), the rationale for this is described in a subsequent article on atomic orbitals.