# Planet's Without-Atmosphere Mean Surface Temperature New Equation: Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (K)

### Earth / Moon satellite measured mean surface temperatures 288 K and 220 K comparison

Let's demonstrate the Planet Surface Rotational Warming Phenomenon on the:

Earth's /Moon's example

Earth is on average warmer 68°C than Moon.

Earth and Moon are at the same distance from the sun. But Moon receives 28% more solar energy than Earth, because Moon's average surface Albedo is significantly lower (Moon’s Albedo a =0,11 vs Earth’s Albedo a =0,306). Yet Earth is on average warmer 68°C than Moon.

The average surface temperature difference of 68°C can be explained only by the Planet Surface Rotational Warming Phenomenon.

N = 1 rotation /per day, is Earth’s sidereal rotation spin

cp.earth = 1 cal/gr*oC, it is because Earth has a vast ocean. Generally speaking almost the whole Earth’s surface is wet.

Earth is on average warmer than Moon not only because of the Earth having 29,53 times faster rotational spin.

Earth also has a five (5) times higher average surface specific heat (for Earth cp.earth = 1 cal/gr*oC, it is because Earth has a vast ocean; and for Moon cp.moon = 0,19cal/gr*oC – its soil is a dry regolith).

Earth is warmer than Moon not because of Earth's very thin atmosphere trace greenhouse gasses content. Earth is warmer because its surface has 155,42 times higher the (N*cp) product than Moon’s surface.

Earth(N*cp) /Moon(N*cp) = (29,53/1)*(1/0,19) = 155,42

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If Moon had Earth's albedo (a=0,306), Moon's mean surface temperature would have been 210K.

As we know, Earth's mean surface temperature is 288K (15°C). Earth is warmer because its surface has 155,42 times higher the (N*cp) product than Moon’s surface. ...................................

Let's compare the Earth's and Moon's (for equal average Albedo) the mean surface temperatures:

Tmean.earth /Tmean.moon = 288K /210K = 1,3714

and the Earth's and Moon's (N*cp) products sixteenth root:

[ Earth(N*cp) /Moon(N*cp) ]^1/16 = (155,42)^1/16 = 1,3709

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The results (1,3714) and (1,3709) are almost identical!

It is a demonstration of the Planet Surface Rotational Warming Phenomenon:

Planets' mean surface temperatures relate (everything else equals) as their (N*cp) products' sixteenth root.