Ratio of Planet Measured Temperature to Corrected Blackbody Temperature (Tsat /Te.correct) Graph, as a linear function of the Rotational Warming Factor = (β*N*cp)^1/16
Tsat /Te without Φ - Warming Factor
The Graph Ratio of Planet Measured Temperature to Corrected Blackbody Temperature (Tsat /Te.correct), as a linear function of the Rotational Warming Factor = (β*N*cp)^1/16
The Graph Ratio of Planet Measured Temperature to Corrected Blackbody Temperature (Tsat /Te.correct), as a linear function of the Rotational Warming Factor = (β*N*cp)^1/16.
In the first graph we have the Ratio of Planet Measured Temperature to Blackbody Temperature (Tsat /Te).
In this graph we use in (Tsat /Te) the planet blackbody temperatures - the planet effective temperatures Te. As we can see, there are two distinguished groups of planets.
The red dot planets and moons are the smooth surface planets. The green dot planets and moons are the rough surface planets.
We observe the group of red dot planets (the smooth surface planets Φ = 0,47) is stretched on the first graph almost in a perfect line.
So for the smooth surface planets there is a linear function of the Rotational Warming Factor = (β*N*cp)^1/16 present.
The linear relation has become so much obvious for the red dot planets because the group of smooth surface planets has a large diversion of the Rotational Warming Factor = (β*N*cp)^1/16 values.
The blue dot planets are gathered at upper end of graph, because their Rotational Warming Factor = (β*N*cp)^1/16 values are very much close between them.
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Tsat /Te.correct with Φ - Warming Factor
In the second graph we have the Ratio of Planet Measured Temperature to the Corrected Blackbody Temperature (Tsat /Te.correct)
In the second graph we have the Ratio of Planet Measured Temperature to the Corrected Blackbody Temperature (Tsat /Te.correct).
In this graph we use in (Tsat /Te.correct) the planet corrected blackbody temperatures - which are the planet effective temperatures Te.correct corrected by the use of the Φ -factor.
The Φ = 0,47 for smooth surface planets and moons, and the Φ = 1 for the rough surface planets and moons. As we can see, in the second graph, the red dot planets and the blue dot planets have stretched in a linear functional relation according to their Rotational Warming Factor = (β*N*cp)^1/16 values.
The bigger is the planet's or moon's the Rotational Warming Factor, the higher is the (Tsat /Te.correct) ratio. It is obviously a linearly related function.
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Tsat /Te.correct with Φ - Warming Factor
In the third graph we also have the Ratio of Planet Measured Temperature to the Corrected Blackbody Temperature (Tsat /Te.correct).
In the third graph all the planets are blue dots. In this graph all the planets are stretched in a linear relation to their Rotational Warming Factor = (β*N*cp)^1/16 values.
The biggest Rotational Warming Factor for Ceres puts it on the top of the line at the right end, and the smallest Rotational Warming Factor for Mercury puts it at the lowest left end.
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All planets and Moons without-atmosphere in solar system have higher than blackbody surface temperatures
Can rotational speed give a temperature higher than that expected for energy in equaling energy out in the case of the blackbody surface?
Yes, it can. And it always does.
Almost all planets and Moons without-atmosphere in solar system have higher than blackbody surface temperatures. We observe that in the Graph.
Only the very slow rotating Mercury has lower than blackbody surface temperature.
Our Moon has a slow enough rotational spin. And Moon's mean surface temperature is close (slightly lower) to Moon's blackbody temperature.
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We learned to correctly estimate the planet "energy in" left side in the Planet Radiative Energy Balance
Conclusion
The linear functional relation between the planets' Rotational Warming Factor = (β*N*cp)^1/16 values and the Ratio of measured to the theoretically calculated planet mean surface temperatures is very much expected functional relation.
It is expected, because we have already demonstrated that planet mean surface temperatures relate (everything else equals) as their (N*cp) products sixteenth root.
It is an observation and, therefore, it is a scientifically proven fact. The linear functional relation between the planets' Rotational Warming Factor = (β*N*cp)^1/16 values and the Ratio of measured to the theoretically calculated planet mean surface temperatures became possible only when we learned to correctly estimate the planet energy in left side in the Planet Radiative Energy Balance.
We learned to correctly estimate the "planet energy in" only when realizing smooth surface planets reflect a portion of the incident solar EM energy not only diffusely, but also specularly.
Thus the coupled physics term Φ(1 - a) was established.
With the use of the coupled physics term Φ(1 - a) it became possible to theoretically, very much close to the real planet surface's conditions, very much precise estimation of the planet energy in left side in the Planet Radiative Energy Balance equation.
The higher is the Rotational Warming Factor, the Warmer is the Planet
The higher is the Rotational Warming Factor, the Warmer is the Planet.
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We are capable now, with great confidence, to assert that the planet (without-atmosphere, or with a thin atmosphere) the theoretical calculated mean surface temperature is:
Tmean = (β*N*cp)^1/16 * Te.correct
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