The Equation for Stable Planetary Orbits

Abstract: This is the first of 4 papers describing a new planet and star formation theory. A problem in Astronomy is that there is no current accepted theory explaining why planets form at particular positions, and an array of ideas including “resonant orbits”, exist, however these ideas do not support the majority of observed data. Bode’s Law[1], partly explains planet formation in our own Solar System, but does not explain observed exoplanets well. With current Core Accretion and Disc/gravitational Instability models[2], the problem is that in theory planetary systems could have just 1 large planet, soaking up all material in the accretion disc, or many smaller planets in random positions; there is not an accepted model which predicts where and how they will form. This paper, and its 3 successors, will address that. This first paper will show that for any accretion disc, planetary bodies will form on entirely predictable stable orbits, and the following equation (1) will describe the semi-major axes of those stable orbits around the centre via a power series of a constant B, which is defined by the parameters of the star at the centre. This paper derives the formula mathematically, and checks against observed data. This formula will apply to all accretion discs, (including Black holes, galaxies, when corrected for Relativistic effects). This paper will also show how we can identify Asteroid Belts and high propensity for life in Exoplanet systems, and allows us to predict new exo-planets and other phenomena – 4 predictions already observed, (see section 2.4). R2 = B x R1, and that R3 = B x R2 or R3 = B2 x R1, and more generally Rn = B(n-1) x R1 (1) [1] See section 2.1 [2] See section 2.3