# The Planet Surface Rotational Warming Phenomenon

## The Planet Mean Surface Temperature Equation Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

Charon in enhanced color to bring out differences in surface composition.

Charon in true color, imaged by New Horizons

### Charon’s (Pluto’s moon) Mean Surface Temperature Calculation

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

Charon’s albedo: acharon = 0,2 to 0,5 at solar phase angle of 15°

let's have acharon = 0,2

1/R² = 1/39,48² = 1/1.558 = 0,0006418

Charon’s sidereal rotation period is 6,38723 days

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

Charon is an ice crust planet, very cratered, and Charon’s surface irradiation accepting factor Φcharon =1.

Charon’s surface is composed of water ice

Charon can be considered as a water ice crust surface planet,

cp.charon = 1 cal/gr*°C

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

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

Charon’s mean surface temperature equation Tmean.charon is:

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

Τmean.charon = { 1*(1-0,20)*1.362 W/m² *0,0006418*[150 *(1/6,38723)* 1]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ = 51,04 K

Tmean.charon = 51,04 K

Tsat.charon = 53 K (- 220 °C).

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 Charon's mean temperature Charon was only 26 years away from the perihelion, so Charon was still pretty much closer to the sun than its average distance.

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 Charon's's mean surface temperatures.