How much hotter or colder was the atmosphere because the Earth was spinning faster?
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1$\begingroup$ Why would the rotation be a factor and how could that be separated from any of the other factors that were different in the past? Or are you just asking what the historical records are of the Earth's (surface?) temperature? $\endgroup$– ProfRobCommented Aug 27 at 7:51
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$\begingroup$ @ProfRob. I was wondering if there is a general relationship between planetary spin and temperature. $\endgroup$– user57831Commented Aug 27 at 8:08
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$\begingroup$ Planetary rotation rate is a key parameter in determining atmospheric circulation and hence the spatial pattern of clouds. Since clouds can exert a dominant control on planetary radiation balance, rotation rate could be critical for determining mean planetary climate. arxiv.org/abs/1404.4992 $\endgroup$– snoCommented Aug 27 at 8:17
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$\begingroup$ @sno. Great reference. So slower rotation leads to denser clouds over a larger area that reflect more sunlight and give more surface cooling. And some slow rotating planets could be much closer to a sun than previously predicted and still be habitable. Venus may have rotated a lot faster when it had a runaway greenhouse. $\endgroup$– user57831Commented Aug 27 at 9:07
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$\begingroup$ @sno. So Earth may have been hotter because of faster spin a long time ago $\endgroup$– user57831Commented Aug 27 at 9:13
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The study Strong Dependence of the Inner Edge of the Habitable Zone on Planetary Rotation Rate by Yun Yang et. al. shows that planets previously believed to be too hot for life on their surface may be cool enough depending on their rotation rate. Slowly rotating planets have a weak Coriolis force and long daytime illumination, which promotes strong convection in the substellar region that produces a large area of optically thick clouds.
However, from their plots, one sees little heating for days shorter than 1d. For days longer than 4d there is substantial cooling.
Therefore, the temperature of the Earth was probably not significantly affected by the shorter days billions of years ago. One to two billion years ago the Earth's day was about 19h. Figure 1a of the Yang paper shows not quite $1^\circ$C less cooling compared to the 24h day.
