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

Universal Element

Since the beginning of time mankind has gazed upon the stars wondering if we are truly alone on this one sanctuary we call earth. The many unsolved problems of modern day physics may be closely related. If there is a key building block that has everything to do with light, space, mass, universal constants, gravitation, life and evolution what would it be? The many scientific breakthroughs of the last century present us with a new looking glass to analyze our universe and rethink everything we have learned so far. My best guess to solve all of the top unsolved problems in physics today is: The Universal Element Called Energy

Star and Sky

There exists some two fold element for everything that was came into existance, star and sky, night and day, love and hate the list is so long... each of these elements exists inside of us in some way, it is up to to look inside ourselves and find them. The best I can see is that there are pillars of hope for mankind; Truth Virtue Kindness Selflessness Forgivness Mercy Love