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

Pluto (dwarf planet): Northern hemisphere of Pluto in true color[

Charon (Pluto's satellite): Charon in true color, imaged by New Horizons in 2015

### 12. Pluto’s (dwarf planet) Mean Surface Temperature calculation

Tmean.pluto

So = 1.362 W/m² (So is the Solar constant)

Pluto’s albedo: apluto = 0.49 to 0.66 (geometric) Let’s have apluto = 0.50

1/R² = 1/39,48² = 1/1.558 = 0,0006418

Pluto’s sidereal rotation period is 6,38723 days

Pluto does N = 1/6,38723 rotations/ per day

Pluto is a nitrogen ice crust surface planet, very cratered, and Pluto’s surface solar irradiation accepting factor Φpluto = 1.

Pluto's surface is composed of more than 98 percent nitrogen ice.

Pluto can be considered as a nitrogen ice crust surface planet,

Cp.nitrogen N2 = 0,24845 cal/gr*oC

β = 150 days*gr*oC/rotation*cal – it is the Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law constant

σ = 5,67*10⁻⁸ W/m²K⁴, a Stefan-Boltzmann constant

Surface temp.    min          mean               max

Kelvin                 33 K     44 K (−229 °C)    55 K

Pluto’s mean surface temperature equation Tmean.pluto is:

Tmean.pluto = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

Τmean.pluto = { 1*(1-0,50)*1.362 W/m² *0,0006418*[150 *(1/6,38723)* 0,24845]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =

Tmean.pluto = 41,59 K

Tsat.mean.pluto = 44 K (- 229 oC)

Notice:

Pluto has moderately eccentric orbit e = 0,2488 during which it ranges from 30 to 49 astronomical units or AU (4.4–7.4 billion km) from the Sun.

Pluto has orbital period of 247,94 years.

The New Horizons spacecraft performed a flyby of Pluto on July 14, 2015, becoming the first ever, and to date only, spacecraft to do so. During its brief flyby, New Horizons made detailed measurements and observations of Pluto and its moons.

The Pluto–Charon barycenter came to perihelion on September 5, 1989.

These makes us conclude that when the New Horizons on July 14, 2015 made its measurements of Puto's mean temperature Pluto was only 26 years away from the perihelion, so Pluto was still pretty much closer to the sun than its semi-major axis.

On July 14, 2015 the dwarf planet was approximately at 32.9 AU from the Sun.

And this partly explains the difference between the calculated and the measured Pluto's mean surface temperatures.