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Are there any known correlations between the changes in planetary surface temperatures in a solar system?

If so, do the farthest planets have smaller albeit correlated changes?

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It could be presumed due to changes in solar/stellar activity. –  Gerald Feb 25 at 1:27
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The activity of stars can change pretty much for some variable stars. Our sun is calm in comparison, but also has an 11- resp. 22-year activity cycle, with varying amplitude. Sometimes the sun produces flares or coronar mass ejections (CMEs), which may affect planets which happen to be located roughly in the same direction from the sun. Over long timescales of billions of years, solar activity and radiation changes. I'm not aware of systematic investigations of short-term surface temperature correlations between planets. But it doesn't look impossible to try it. –  Gerald Feb 25 at 20:07
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Eclipses would rarely lead to a synchronous temperature change for several planets, because constellations with several planets and the sun in exactly one row are very rare. –  Gerald Feb 25 at 20:11

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The simple answer to your question is yes. Taking a simplified equation from Carroll & Ostlie, An Introduction to Modern Astrophysics Second Edition, the temperature of a planet can be estimated as: $$ T_{p} = T_{\odot}(1-a)^{\frac{1}{4}}\sqrt{\frac{R_\odot}{2D}} $$ Where $T_p$ is the predicted temperature of a planet in a circular orbit of radius $D$ with an albedo of $a$ around a star with a temperature of $T_\odot$ and a radius of $R_\odot$. If the energy output of the star were to increase, raising $T_\odot$, then there would be a corresponding increase in the temperature of all planets orbiting said star.

In practice there are factors which can make this correlation difficult to measure. The albedo of a planet during the course of a day can vary greatly and the distance of a planet from the host star changes throughout the year. This equation also assumes that the planet is a perfect black body which most are not which can also change a planets temperature and obscure any changes caused by the host star.

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Uh, if I apply this formula to earth and it's distance, I get -24.6°C... is this approximation ok-ish and the difference due to the athmosphere? –  Alexander Janssen Apr 11 at 8:46
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The equation assumes that the planet is a blackbody radiator. Anything with an atmosphere is most definitely not a blackbody. I do not offhand know if there is one good equation that can be used to estimate the temperature taking into account atmospheric effects since these would depend greatly on the composition of the atmosphere –  moonboy13 Apr 11 at 14:45

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