# Abstract

An orbital simulation program is described that uses a geometrical approach to emulate gravitational and atomic orbits at the Planck scale. The gravitational orbital approach divides orbiting objects into multiples of Planck mass points to form an n-body complex of discrete point-to-point orbital pairs between the objects. Each orbital pair rotates 1 Planck length per unit of Planck time in a continuous loop such that when mapped over time gravitational orbits emerge. However 1 point may contain 10^{20} or more individual particles, and so to analyze individual particle-particle orbital pairing we can use atomic orbital transitions. For this, the gravitation simulation program is modified to map the orbital of an electron-proton pair (H-atom) by the addition of an alpha (fine structure constant) term. For transitions, the incoming photon is absorbed by (or ejected from) the orbital radius in discrete alpha steps (the orbital radius is assigned photon-like properties), the electron itself has a passive role in the transition process. An orbital radius variable delta; orbital radius = (2alpha + delta)*lambda(electron+proton), was selected to correlate with the Lyman series transition frequencies. A linear relationship was observed between delta and these frequencies with notably at delta = 0 (the classical Bohr model), the principal quantum number n = sqrt(2) and the transition energy = half ionization energy.