Least Action in Semi-Major Axis Orbital Analysis: A Statistical Comparison of Exoplanetary Systems and Solar System Data
Abstract
We present a chi-square analysis of the Least Action principle for semi-major axes of planets and their satellites. The Least Action dependent variable is a resonant node integer that varies from 1 to 10. The unknowns are three constants determined by the regression and chi-square analysis. The base resulting from the swarm models of the Least Action principle depends on the golden section of the Fibonacci series. This irrational number minimizes the Lagrangian action of our models. The Least Action principle adds a small, but statistically significant, expansion constant to this base. We compare the Least Action predictions with the observed semi-major axes for all eight planets and all major low inclination satellites of Jupiter, Saturn, and Uranus. A chi-square analysis of these data yields four very high population correlations between the observed and computed values of the semi-major axes.
Additionally, we compute assigned values for the specific scaling constants using the Lagrange planetary equations for the orbital elements, especially the semi-major axes. These equations describe dynamical changes in the semi-major axes, eccentricities and mean motions that may be expected to occur in the original accreting planetary disks. The computed statistical constants of the planetary node scaling factors enable us to predict semi-major axes that are within 0.01 AU of the observed values for more than eighty objects. The wide variety of objects so scaled include seven of the Sun's planets, the low inclination satellites of Jupiter, Saturn, and Uranus, and 33 planets in the 10 exoplanetary systems of dwarf stars, whose spectral types range from A to M. We also report on an accurate prediction of the semi-major axis of the first node of the exoplanet Gliese 581e to within 0.01 AU of recently observed values.- Publication:
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American Astronomical Society Meeting Abstracts #214
- Pub Date:
- December 2009
- Bibcode:
- 2009AAS...21460602F