by wolram
 PF Gold P: 3,685 Did gravity effect the suns output? arXiv:1405.4369 [pdf, ps, other] Can a variable gravitational constant resolve the Faint Young Sun Paradox ? Varun Sahni, Yuri Shtanov Comments: 9 pages, 1 figure Subjects: Solar and Stellar Astrophysics (astro-ph.SR); Cosmology and Nongalactic Astrophysics (astro-ph.CO); Earth and Planetary Astrophysics (astro-ph.EP); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph) Solar models suggest that four billion years ago the young Sun was about $75\%$ fainter than it is today, rendering Earth's oceans frozen and lifeless. However, there is ample geophysical evidence that Earth had a liquid ocean teeming with life 4 Gyr ago. Since ${\cal L_\odot} \propto G^7M_\odot^5$, the Sun's luminosity ${\cal L_\odot}$ is exceedingly sensitive to small changes in the gravitational constant $G$. We show that a percent-level increase in $G$ in the past would have prevented Earth's oceans from freezing, resolving the faint young Sun paradox. Such small changes in $G$ are consistent with observational bounds on ${\Delta G}/G$. Since ${\cal L}_{\rm SNIa} \propto G^{-3/2}$, an increase in $G$ leads to fainter supernovae, creating tension between standard candle and standard ruler probes of dark energy. Precisely such a tension has recently been reported by the Planck team.
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"Temperature expected on Earth with present atmosphere"
This is pointless, it is known the atmospheric composition was not the same all the time. The composition is discussed in more detail below, but where is the point in a plot with something that is certainly wrong?

Also:
 Solar models suggest that four billion years ago the young Sun was ∼75% fainter than it is today, rendering Earth’s oceans frozen and lifeless.
[citation needed] - this should be an obvious point to cite a paper discussing this in detail, also taking into account the initial hot state of the earth, heating from compression / separation of heavier and lighter elements, radioactive decays and so on.
The first reference is a book "for Earth science undergraduates" (quote from amazon), the second reference is just about the sun and the third from 1972 and it offers a solution in its abstract: "Ammonia mixing ratios of the order of a few parts per million in the middle Precambrian atmosphere resolve this and other problems. Possible temperature evolutionary tracks for Earth and Mars are described."

The proposed change in G would need some non-linear time structure to be consistent with lunar ranging experiments.

I'm not convinced.
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 Quote by wolram Solar models suggest that four billion years ago the young Sun was about $75\%$ fainter than it is today, rendering Earth's oceans frozen and lifeless.
This is exactly why articles posted to the arxiv are not a good reference. This article makes a false assumption and proceeds to extrapolate massively based on that false assumption.

The faint young sun paradox is that the Sun shone with about 75% of the intensity it shines with now when the Earth was young. In other words, 25% fainter, not 75%.

 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,521 The faint sun paradox And in another 4 billion years, as the hydrogen in the sun's core is exhausted, the sun will shine brighter still (as it expands). This is not necessarily due to any change in the value of G, but a consequence of stellar evolution and aging.
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 Quote by D H This is exactly why articles posted to the arxiv are not a good reference. This article makes a false assumption and proceeds to extrapolate massively based on that false assumption. The faint young sun paradox is that the Sun shone with about 75% of the intensity it shines with now when the Earth was young. In other words, 25% fainter, not 75%.
To be fair, this is just a bad (or simply wrong) wording in the abstract and the introduction. The authors mean 75% of its current luminosity and work with this number throughout the paper.

@SteamKing: The authors suggest a change in G to make the young sun brighter than those 75%. This would give a luminosity evolution different from a model with a fixed G.

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