Dynamics of Multi Planet Star Systems

Dynamics of multi Planet Star Systems the disturbing function R resonance is responible for energy and angular momentum betweenorbits. 2 body Celestial Mechanics Resonance is natures was of moving energy around, Tidal torque tranfers energy from spin to momentum. To model planetary systems resonance and gravitational tides must be added to derive equalibriums, Newtonian dynamics alone leave systems unstable. Newtonian Gravitational Law Gravity is the pull betewen two objects, force is determined by the size of the masses. Mass if the measure of matter in anobject. Gravity is inversly related to the square of the distance, if distance doubles than gravitational pull decreases by a factor of 4. Weight is the force pulling on an object. F = M * A (gravity * weight) F Mplanet r = -Mplanet (law of gravitation) Ar = GM/R^2 Ar = 4c^2 a/b^2(1/r^2) = GM = 4C^2 a/b^2 (bodies attract eachother) G = 9.8 m/sec^2 (gravity on earth) Dynamics of Multi Planet Systems Spin orbit synchronization, planets exert torque from stars and spin up. The more efficient the tidal effect, the efficient tidal allignment. Planets spin axis allignment is fast, stellar spin axis decays over time. Tides in stars are more efficient with convective zones, exploration for allignment and misalligned systems. Planets spin allignment is fast, stellar spin orbit decyas over time. Tidal efficiency efects allignment, stars with convective zones are more efficient. A harmonic angle is a linear combination of angles, it can circulate or vibrate. Resonance is scalar, all these terms are cancelling. mnn' is even smaller. If liberating angles are forced into neighboring harmonics chaos will result. Protoplanetary disks use convergant migration, energy transfer depends on efficiency. Resonance rate transfer of energy is greater than migration. Radial Velocity Changes along z axis in respect to time and barycentric orbit. Inclination difference between true orbit and projected orbit. a p e provide period and shape of orbit through r(t) and 0(t) w n i provide orientation of ellipse, semi major axis, period and eccentricity. Thermal Emission Flux Ratios Emmission spectra is from measurements of planets and stars. Flux Ratios