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

Let's work on Φ -factor hard. It is very important!

Φ - Planet surface Solar irradiation accepting factor.

Mathematician Pierre-Simon Laplace once said, "The more shocking an event is, the stronger evidence it needs."

The American cosmologist, Carl Sagan, famously restated it as follows: "Extraordinary claims require irrefutable evidence."

Let's work on Φ -factor hard. It is very important!

1. I did not calculated it. I took it from the table of Data:

https://en.wikipedia.org/wiki/Drag_coefficient

ttps://en.wikipedia.org/wiki/File:14ilf1l.svg

The number 0,47 for smooth surface in a parallel fluid flow is taken from the well measured and long ago known Drag Coefficient Data, where Cd =0,47 is for sphere.

It is the portion of incident on sphere energy which should be resisted by sphere to remain in balance.

2. I checked it on the planets without-atmosphere Mercury, Moon, Mars and also (for comparison reasons) on Earth. (Φ =0,47)

Then I continued with other without-atmosphere planets and moons.

Io

"With over 400 active volcanoes, Io is the most geologically active object in the Solar System."

https://en.wikipedia.org/wiki/Io_(moon)

https://en.wikipedia.org/wiki/File:Io_highest_resolution_true_color.jpg

(For Io Φ=1)

Europa

"Europa has the smoothest surface of any known solid object in the Solar System. The apparent youth and smoothness of the surface have led to the hypothesis that a water ocean exists beneath the surface, which could conceivably harbor extraterrestrial life."

https://en.wikipedia.org/wiki/Europa_(moon)

https://en.wikipedia.org/wiki/File:Europa-moon-with-margins.jpg 

(For Europa Φ=0,47)

Ganymede

"Its surface is composed of two main types of terrain. Dark regions, saturated with impact craters and dated to four billion years ago, cover about a third of it. Lighter regions, crosscut by extensive grooves and ridges and only slightly less ancient, cover the remainder. The cause of the light terrain's disrupted geology is not fully known, but was likely the result of tectonic activity due to tidal heating."

https://en.wikipedia.org/wiki/Ganymede_(moon)

https://en.wikipedia.org/wiki/File:Ganymede_-_Perijove_34_Composite.png

(For Ganymede Φ =0,47)

Calisto

"The surface of Callisto is the oldest and most heavily cratered in the Solar System.[16] Its surface is completely covered with impact craters."

https://en.wikipedia.org/wiki/Callisto_(moon)

https://en.wikipedia.org/wiki/File:Callisto.jpg

(For Calisto Φ =1

............................................

But has a coefficient from fluid dynamics a relevance to radiative physics?

There are universal laws describing for the matter interacting with energy flow.

I considered a parallel fluid flow as an analogue to the parallel solar rays...

It is the energy interaction with matter. The laws of reflection...

We can observe it in sports, football, basketball etc.

A bullet ricocheting from a target is also an analogue of reflection. The new trajectory is angular incidence on the target dependent direction.

Thus, we are fully convinsed - there is a very important relevance between the coefficient from fluid dynamics and the radiative physics the Φ - Planet surface Solar irradiation accepting factor.