There ought to be an agreed-upon name for the science of studying predicted future geological and astronomical events. "Futurology" is too vague and lends itself mainly to exploring the human civilization within the few hundred years or so.
Anyway, here in no particular order is a batch of far-future studies on the fate of the Earth, Moon, Sun, and other stuff.
http://cdsads.u-strasbg.fr/abs/2015JGRD..120.5775W
The evolution of habitable climates under the brightening Sun
Wolf, E. T.; Toon, O. B.
06/2015
On water-dominated planets, warming from increased solar insolation is strongly amplified by the water vapor greenhouse feedback. As the Sun brightens due to stellar evolution, Earth will become uninhabitable due to rising temperatures. Here we use a modified version of the Community Earth System Model from the National Center for Atmospheric Research to study Earth under intense solar radiation. For small (≤10%) increases in the solar constant (S0), Earth warms nearly linearly with climate sensitivities of 1 K/(W m-2) and global mean surface temperatures below 310 K. However, an abrupt shift in climate is found as the solar constant is increased to +12.5% S0. Here climate sensitivity peaks at 6.5 K/(W m-2), while global mean surface temperatures rise above 330 K. This climatic transition is associated with a fundamental change to the radiative-convective state of the atmosphere. Hot, moist climates feature both strong solar absorption and inefficient radiative cooling in the low atmosphere, thus yielding net radiative heating of the near-surface layers. This heating forms an inversion that effectively shuts off convection in the boundary layer. Beyond the transition, Earth continues to warm but with climate sensitivities again near unity. Conditions conducive to significant water loss to space are not found until +19% S0. Earth remains stable against a thermal runaway up to at least +21% S0, but at that point, global mean surface temperatures exceed 360 K, and water loss to space becomes rapid. Water loss of the oceans from a moist greenhouse may preclude a thermal runaway.
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https://arxiv.org/abs/0801.4031
Distant future of the Sun and Earth revisited
Klaus-Peter Schröder, Robert C. Smith
(Submitted on 25 Jan 2008)
We revisit the distant future of the Sun and the solar system, based on stellar models computed with a thoroughly tested evolution code. For the solar giant stages, mass-loss by the cool (but not dust-driven) wind is considered in detail. Using the new and well-calibrated mass-loss formula of Schroder & Cuntz (2005, 2007), we find that the mass lost by the Sun as an RGB giant (0.332 M_Sun, 7.59 Gy from now) potentially gives planet Earth a significant orbital expansion, inversely proportional to the remaining solar mass. According to these solar evolution models, the closest encounter of planet Earth with the solar cool giant photosphere will occur during the tip-RGB phase. During this critical episode, for each time-step of the evolution model, we consider the loss of orbital angular momentum suffered by planet Earth from tidal interaction with the giant Sun, as well as dynamical drag in the lower chromosphere. We find that planet Earth will not be able to escape engulfment, despite the positive effect of solar mass-loss. In order to survive the solar tip-RGB phase, any hypothetical planet would require a present-day minimum orbital radius of about 1.15 AU. Furthermore, our solar evolution models with detailed mass-loss description predict that the resulting tip-AGB giant will not reach its tip-RGB size. The main reason is the more significant amount of mass lost already in the RGB phase of the Sun. Hence, the tip-AGB luminosity will come short of driving a final, dust-driven superwind, and there will be no regular solar planetary nebula (PN). But a last thermal pulse may produce a circumstellar (CS) shell similar to, but rather smaller than, that of the peculiar PN IC 2149 with an estimated total CS shell mass of just a few hundredths of a solar mass.
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http://cdsads.u-strasbg.fr/abs/2012MNRAS.421.2969V
The Solar system's post-main-sequence escape boundary
Veras, Dimitri; Wyatt, Mark C.
04/2012
The Sun will eventually lose about half of its current mass non-linearly over several phases of post-main-sequence evolution. This mass loss will cause any surviving orbiting body to increase its semimajor axis and perhaps vary its eccentricity. Here, we use a range of solar models spanning plausible evolutionary sequences and assume isotropic mass loss to assess the possibility of escape from the Solar system. We find that the critical semimajor axis in the Solar system within which an orbiting body is guaranteed to remain bound to the dying Sun due to perturbations from stellar mass loss alone is ≈103-104 au. The fate of objects near or beyond this critical semimajor axis, such as the Oort Cloud, outer scattered disc and specific bodies such as Sedna, will significantly depend on their locations along their orbits when the Sun turns off the main sequence. These results are applicable to any exoplanetary system containing a single star with a mass, metallicity and age which are approximately equal to the Sun's, and suggest that few extrasolar Oort Clouds could survive post-main-sequence evolution intact.
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https://arxiv.org/abs/1209.5996
Is the Solar System Stable?
Jacques Laskar
(Submitted on 26 Sep 2012)
Since the formulation of the problem by Newton, and during three centuries, astronomers and mathematicians have sought to demonstrate the stability of the Solar System. Thanks to the numerical experiments of the last two decades, we know now that the motion of the planets in the Solar System is chaotic, which prohibits any accurate prediction of their trajectories beyond a few tens of millions of years. The recent simulations even show that planetary collisions or ejections are possible on a period of less than 5 billion years, before the end of the life of the Sun.
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http://cdsads.u-strasbg.fr/abs/2009DDA....40.1303L
Large Scale Solar System Simulations
Laskar, Jacques
05/2009
As the motion of the planets in the Solar System is chaotic (Laskar, 1989, 1990, Sussman and Wisdom, 1992), a single trajectory of the planet evolutions over 5 Gyr can only be thought as a random sample of the Solar System possible evolution. In (Laskar, 1994), I demonstrated, using the secular equations, that Mercury can reach very high eccentricity, allowing for possible collisions with Venus. This was established by constructing by pieces an orbit leading to very high eccentricity for Mercury. The drawback of the method, is that the secular equations lose their validity close to collision, and there was no probability estimate. In (Laskar, 2008), the same experiment was conducted on 1001 orbits providing these probabilities. I also demonstrated that in a non relativist system, the unstability of Mercury is much larger than in the full GR model. In the same paper, I thus conducted some direct numerical integrations for 10 orbits, without averaging, without general relativity (GR), and indeed, 4 orbits out of 10 lead to very high increase of Mercury's eccentricity, allowing collisions with Venus. Soon after, (Batygin and Laughlin, 2008), presented similar results. Indeed, they had followed my previous paper (laskar, 1994), and could thus construct a solutions by pieces, leading to a collision of Mercury with Venus in less than 5 Gyr, but this was also done with a non GR model that is much more unstable than the full model. It was thus necessary to study the possibility of collisions with a full model, including GR over 5 Gyr. I will report here the results of the very extensive study that we made over 2501 solutions of the full Solar System over 5 Gyr, including GR and lunar contributions, with direct numerical integration, without averaging.