In about 5 billion years, when our Sun expands into a red giant making our planet uninhabitable, where will the new Goldilocks zone be? Could life form on a new planet in the Goldilocks zone? Environment suitable for human life?
[Physics] Where will the Goldilocks zone be when the Sun becomes a red giant
astrophysicssolar systemstarsstellar-physicssun
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There's a nice paper by Drs. Klaus-Peter Schroder and Robert Smith on the distant future of the Sun and Earth; it's available at the arXiv:
Table 1 in that preprint summarizes a number of parameters, but in simplified form the radii (in terms of the current value) at different times (given in billions of years) are:
Age Radius
ZAMS 0.00 0.89
present 4.58 1.00
MS:final 10.00 1.37
RGB:tip 12.17 256.
ZA-He 12.17 11.2
AGB:tip 12.30 149.
(hopefully that will render correctly.) For comparison, the current orbit of the Earth is 215 times the current solar radius. ZAMS is the zero-age Main Sequence, present is today, MS:final is the end of the Main Sequence, RGB:tip is the maximum size during the Red Giant branch, ZA-He is the start of core Helium burning and AGB:tip is maximum size during the asymptotic giant branch phase. After that the Sun will fade away as a white dwarf.
While there is 2.17 billion years between the end of the Main Sequence and the start of core Helium burning (which also marks the end of the Red Giant phase), for more than two billion years the Sun is less than ten times its current radius - it's only during the last 200 million years when the expansion towards the Earth's current orbit happens. This is plotted in Figure 1 of the preprint, which the radius of the Sun during the final three hundred million years.
So in the context of the Sun's overall lifetime, the expansion in the giant phase is extremely rapid. Of course, on our timescales it's a very long time...!
Stellar Life cycle: We know that sun and other stars generate heat and radiation through nuclear fusion. Generally, there are several stages that a star would've to cross through its life so called the Stellar Evolution.
Our Sun (1 solar mass) is a Mid-sized Main sequence (specifically G-Type or yellow-dwarf) star. Nuclear fusion takes place between protons to form helium at this stage (Reactions are provided here). It's surface temperature is about some 5000 °C and core temperature is about $10^7 K$. As more and more hydrogen fuel is consumed, the layers of hydrogen are decreased simultaneously while expanding the shells filled with helium. Finally, the core begins to contract still expanding the helium layers and by this time, the core would've reached $10^8 K$ which is strong enough for the fusion of helium to produce carbon and by this way, the Triple-alpha process begins. During the expansion of Sun, we'd arrive at a time (about 3 billion years) when the temperature in Earth could no longer hold water and all lives would've been terminated. Also, The inner planets Mercury, Venus and Earth would've been engulfed by the expanding sun.
Wiki has a good comparison for Red Giant... Future of Earth article is also good.
A White dwarf: Once the triple-alpha process in a red giant is complete, stars weighing less than 4 solar masses (like our sun) don't have enough energy to ignite the carbon fusion process and then explode into a Supernova. So, The star collapses to a white dwarf until it's halted by the pressure arising from electron degeneracy. The Hertzsprung-Russell Diagram is a plot of luminosity vs temperature which shows the decrease in luminosity of stars with decrease in their temperature. A teaspoon of a white dwarf would weigh 5 tons. A white dwarf with one solar mass would be about the size of the Earth.
It has been estimated that it takes about 5 billion years for Sun to become a Red Giant. But, now we have much larger situations to concern at present like protecting ourselves from PHA's (Potentially Hazardous Asteroids) than thinking about near future. One thing to keep in mind is that, More brainy guys are out there to think of building something like the AXIOM in Wall-E..! So, humans have chances of survival if those physicists build some crazy items to be placed in our future inventory list.
This paper explains the survival of a planet named V391 Pegasi b from a Red Giant (but only as a roasted one..!)
Edit: Then, You don't require any of the above facties... The answer is: "How long would you stay in a desert..?". At about 1 billion years - Sun would be 10% more luminous so that organisms start dying due to Moist greenhouse effects (Water starvation). At about 1.6 billion years, Sun's luminosity is at about 40% and hence all Life on Earth dies due to Runaway Greenhouse effect..!
Best Answer
The habitable zone is typically defined as the range of orbits where liquid water can persist on a planet. This is somewhat ill-defined, since climate modelling of planets with various properties (atmosphere density and composition, rotation, etc.) changes distances where water can persist. But to a first approximation the habitable zone scales as $R_{hz}=\sqrt{L/L_\odot}$ AU, with fuzzy boundaries somewhere around $0.7 R_{hz}$ and $1.4 R_{hz}$ (Venus and Mars might perhaps, had things gone differently, been habitable). Different sources will give you different limits.
Here I will use the stellar model in Schröder, K. P., & Connon Smith, R. (2008). Distant future of the Sun and Earth revisited. Monthly Notices of the Royal Astronomical Society, 386(1), 155-163.
As the sun evolves it will first become a sub-giant. The sun is estimated to reach its hottest surface temperature of 5820 K in 2.55 Gyr with a luminosity 1.26 times brighter than at present. At this point Mars (orbiting between 1.38 and 1.52 AU) might actually start looking habitable. This is still way after Earth's biosphere is expected to fail (in 1.6 Gyr, according to some estimates).
In about 5.42 Gyr the sun starts really going red giant. The luminosity shoots up from 1.84 times the current luminosity to 2730 times in 7.59 Gyr. Obvious bad news for Mars. But now the habitable zone sweeps out towards the Kuiper belt.
There are some complications here due to mass loss. The luminosity increases in a nonlinear way. As a red giant the sun will also lose significant amounts of mass, and this will make planets spiral outwards. (This is also why there is disagreement about whether the Earth will be absorbed by the sun or escape; this depends on a lot of factors with big model uncertainty.)
An earlier paper by Schroeder, Smith and Apps estimated the time different planets and moons would be in the life zone. Mars would according to them be in the habitable one in 11.6-11.7 Gyr. They suggest that Jupiter's moons would be there in 12.07-12.10 Gyr, Saturn (Titan) 12.139-12.147 Gyr, Uranus (Oberon) 12.162-12.164, and Neptune never really gets any habitable period. Note that the time intervals are really short, just a few million years in the outer system. Worse, the periods are temporally disjointed: the solar system will not be continuously habitable.
So, there is a bit of disagreement between the papers on the habitability periods of Mars, but it seems clear there will be a time in the future when Mars (if given enough volatiles) might be habitable. I would not expect much from the gas giant moons, although they would make a fascinating setting.