Application of Semi-major Axis Length Analysis to the Determination of Temperature and Surface Composition of Solar System Objects in Various Stages of Solar Evolution
By Tejas Navaratna
From the very beginning of civilization, humans have pondered their future through innumerable myths and legends. Through the times of the ancient Greeks’ tales, with their stories of oracles prophesying the ruin of empires, and the Middle Ages, with seers like Nostradamus appearing to peek into the future, the idea of an ultimate destiny has become an obsession for many. Only nowadays do we have the scientific tools coupled with ultra-fast processing power necessary to make a well-substantiated picture of the distant future of the Solar System, which seems harbor large uncertainties for this planet. With the greatly increased radiation of an evolving Sun, our survival comes into question . . . Expansion of the Sun in the future will cause conditions to be vastly different from those today, leaving the Earth unsustainable. This study intends to establish which Solar System object will be most conducive to the survival of humans during five stages of solar evolution: (1) further along the main sequence at age 8.40 billion years (Ga), (2) during the red giant stage at 11.93 Ga (3) 6 million years (Ma) later prior to the helium flash (4) after the helium flash at age 12.17 Ga and (5) the beginning of core crystallization at age 12.23 Ga. The Evolve ZAMS code (Paxton, 2004) determines the mass and luminosity of the Sun at these stages. Semi-major axis lengths of each of the solar system objects (SSOs) are calculated based on mass loss (Schroder and Smith, 2008) and the principle of conservation of angular momentum. The potentially sustainable objects’ temperatures are solved for using blackbody equations, from which comparison of RMS gas speed with escape velocity determines the ability of a body to retain an atmosphere consisting of a specific gas. It is found that Earth and Mars are optimal SSOs in stage 1. In stages 2 and 3, Triton is most sustainable, but in stage 4, the Galilean moons and Titan appear to be more habitable. Stage 5 has Triton being the most optimal…