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I think that your question is not really answerable. But perhaps the reasons it's not answerable are themselves interesting. There are two parts to this answer: why do we think abiogenisis is likely? is Earth, today, hospitable for organisms which originate through abiogenesis, if it is likely? My answer to the first part is, I think, more well-founded ...

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Fossils are only in very rare cases dated directly, because they do not contain sufficient radioactive isotopes for dating. Most geological periods are first and foremost defined by biostratigraphy- fossil assemblages, typically. The Cambrian period starts with the Fortunian stage - this stage is defined by the appearance of a certain trace fossil in ...

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Jeffronicus's answer appears to be a good one re the influence of lunar tidal heating on the early Earth. To answer the other question that has emerged in comments, as to what proportion of total heating is from tidal effects now, we can turn to Munk & Wunsch 1998. They tell us that the lunar tidal power going into earth tides (as opposed to into the sea ...

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From this answer a modern day is 1,7ms longer than a century ago. The data is taken from wikipedia, but it is sourced to this book. Asuming the slowing down on earth's rotation has been constant since Cambrian, and that the sideral year duration has been constant too, it can be aproximated with a script: #Constants yearsSinceCambrian = 541000000 ...

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As a very rough approximation, one could start with equation (9) from Arbab (2009), https://arxiv.org/abs/physics/0304093 to get the effective number of days per year: $$T_{\text{eff.}} = T_0 \left(\frac{t_0-t}{t_0} \right)^{-2.6}$$ with $t$ the time difference between now and then $T_0 = 365.25$ the current number of days per year \$t_0=(13.799 \pm 0....

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The complications of calculating the moon's contributions to earth's heat budget are touched on in Emergence of a Habitable Planet (2007) by Zahnle, et.al. in Space Science Reviews, a paper trying to determine when in earth's history the planet's surface would become cool enough to support life. The portion of the paper that relates to tidal heating ...

3

Probably at the Hadean or at the beginning of the Archean, but there is no geological registry. The mechanism that can lead to inorganic limestone formation is weathering of magmatic carbonatite rocks. I found Siilinjärvi carbonatite complex in Fennoscandia is dated 2.6Ga (Tichomirowa et al, 2013), so Archean. It is the oldest one I found. Another ...

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Perhaps some of the oldest limestones are the banded Espanola Formation from 2.3 billion years ago. The Oxygenation of the environment happened 2.4 billion years ago. I'll find some references and chemistry info when my web connection works, here are some starter pages.

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