# The Planet's Effective Temperature Complete Formula Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

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Full Moon 2010

Mars true color

### Mars and Moon satellite measured mean temperatures comparison: 210 K and 220 K

Mars and Moon satellite measured mean temperatures comparison:

210 K and 220 K

Let's see what we have here:

Planet or      Tsat.mean

moon            measured

Mercury           340 K

Earth                288 K

Moon               220 Κ

Mars                210 K

Let’s compare then:

Moon:

Tsat.moon = 220K

Moon’s albedo is amoon = 0,136

What is left to absorb is (1 – amoon) = (1- 0,136) = 0,864

Mars:

Tsat.mars = 210 K

Mars’ albedo is amars = 0,25

What is left to absorb is (1 – amars) = (1 – 0,25) = 0,75

Mars /Moon satellite measured temperatures comparison:

Tsat.mars /Tsat.moon = 210 K /220 K = 0,9545

Mars /Moon what is left to absorb (which relates in ¼ powers) comparison, or in other words the Mars /Moon albedo determined solar irradiation absorption ability:

( 0,75 /0,864 )¹∕ ⁴ = ( 0,8681 )¹∕ ⁴ = 0,9652

Conclusions:

1. Mars /Moon satellite measured temperatures comparison

( 0,9545 ) is almost identical with the

Mars /Moon albedo determined solar irradiation absorption ability

( 0,9652 )

2. If Mars and Moon had the same exactly albedo, their satellites measured temperatures would have been exactly the same.

3. Mars and Moon have two major differences which equate each other:

The first major difference is the distance from the sun both Mars and Moon have.

Moon is at R = 1 AU distance from the sun and the solar flux on the top is So = 1.362 W/m² ( it is called the Solar constant).

Mars is at 1,524 AU distance from the sun and the solar flux on the top is

S = So*(1/R²) = So*(1/1,524²) = So*1/2,32 .

(1/R²) = (1/1,524²) = 1/2,32

Mars has 2,32 times less solar irradiation intensity than Earth and Moon have.

Consequently the solar flux on the Mar’s top is 2,32 times weaker than that on the Moon.

The second major difference is the sidereal rotation period both Mars and Moon have.

Moon performs 1 rotation every 29,531 earth days.

Mars performs 1 rotation every ( 24,622hours / 24hours/day ) = 1,026 day.

Consequently Mars rotates 29,531 /1,026 = 28,783 times faster than Moon does.

So Mars is irradiated 2,32 times weaker, but Mars rotates 28,783 times faster.

And… for the same albedo, Mars and Moon have the same satellite measured mean temperatures.

Let’s take out the calculator now and make simple calculations:

The rotation difference's fourth root is

(28,783)¹∕ ⁴ = 2,3162

2,32 /(28,783)¹∕ ⁴ = 2,32 /2,3162 = 1,001625

It is only 0,1625% difference

When rounded the difference is 0,16 %

It is obvious now, the Mars’ 28,783 times faster rotation equates the Moon’s 2,32 times higher solar irradiation.

That is why the 28,783 times faster rotating Mars has almost the same average satellites measured temperature as the 2,32 times stronger solar irradiated Moon.

Thus we are coming here again to the same conclusion:

The Faster a Planet Rotates, the Higher is the Planet's Average Temperature.

And

It is the confirmation that the planet's rotations per day "N" should be considered in the fourth root in the Te planet complete formula:

Te.planet = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴.