Mars, Phobos and Deimos Effective Temperatures comparison
Enhanced-color image of Phobos from the Mars Reconnaissance Orbiter with Stickney crater on the right
Mars, Phobos and Deimos Mean Surface Temperatures comparison
3. Mars’ Mean Surface Temperature Calculation:
Te.mars
(1/R²) = (1/1,524²) = 1/2,32 Mars has 2,32 times less solar irradiation intensity than Earth has
Mars’ albedo: amars = 0,25
N = 0,9747 rotations/per day, Planet Mars completes one rotation around its axis in 24 hours 37 min 22 s.
Mars is a rocky planet, Mars’ surface irradiation accepting factor: Φmars = 0,47
cp.mars = 0,18cal/gr oC, on Mars’ surface is prevalent the iron oxide
β = 150 days*gr*oC/rotation*cal – it is a Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law constant
σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant
Mars' Mean Surface Temperature Equation is:
Tmean.mars = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴
Planet Mars’ Mean Surface Temperature Tmean.mars is:
Tmean.mars = [ 0,47 (1-0,25) 1.362 W/m²*(1/2,32)*(150*0,9747*0,18)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =
= ( 2.066.635.547,46 )¹∕ ⁴ = 213,21 K
Tmean.mars = 213,21 K
The calculated Mars’ surface mean temperature Tmean.mars = 213,21 K is only by 1,53% higher than that measured by satellites
Tsat.mean.mars = 210 K !
Phobos’ ( Mars' moon ) Surface Mean Temperature Calculation:
Tmean.phobos
(1/R²) = (1/1,524²) = 1/2,32
Phobos has 2,32 times less solar irradiation intensity than Earth has
Phobos’ albedo: aphobos = 0,071
N = 24/7,7 rotations/per day, Phobos completes one rotation around its axis in about 7,7 hours
Phobos is a rocky planet, Phobos’ surface irradiation accepting factor: Φphobos = 0,47
cp.phobos = 0,19cal/gr oC, on Phobos’ surface is regolith
β = 150 days*gr*oC/rotation*cal – it is a Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law constant
σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant
Phobos' Mean Surface Temperature Equation is:
Tmean.phobos = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴
Phobos’ Surface Mean Temperature Tmean.phobos is:
Tmean.phobos = { 0,47 (1-0,071) 1.362 W/m²*(1/2,32)*[(150*(24/7,7)*0,19]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =
Tmean.phobos = 242,14 K
Tsat.mean.phobos ≈ 233 K !
Deimos’ ( Mars' moon ) Surface Mean Temperature Calculation:
Tmean.deimos
(1/R²) = (1/1,524²) = 1/2,32
Deimos has 2,32 times less solar irradiation intensity than Earth has
Deimos’ albedo: adeimos = 0,068
N = 24/30,3 rotations/per day, Deimos completes one rotation around its axis in about 30,3 hours
Deimos is a rocky moon, Deimos’ surface irradiation accepting factor: Φdeimos = 0,47
cp.deimos = 0,19cal/gr oC, on Deimos’ surface is regolith
β = 150 days*gr*oC/rotation*cal – it is a Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law constant
σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant
Deimos' Surface Mean Temperature Equation is:
Tmean.deimos = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴
Deimos’ Surface Mean Temperature Tmean.deimos is:
Tmean.deimos = { 0,47 (1-0,068) 1.362 W/m²*(1/2,32)*[150*(24/30,3)*0,19]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =
Tmean.deimos = 222,98 K
Tsat.mean.deimos ≈ 233 K !
As you can see none of my calculations are the same as the satellites measured. Both Phobos and Deimos have the same approximate Tsat.mean ≈ 233 K
Also I realize this:
Tmean.phobos = 242,14 K
Tmean.deimos = 222,98 K
Tsat.mean.phobos ≈ 233 K
Tsat.mean.deimos ≈ 233 K !
Also it is obvious that two different celestial bodies on the same R = 1,5 AU distance from the sun and with Phobos rotating 4 times faster than Deimos there should be a substantial difference in temperatures.
Let’s compare the calculations
Tm.mars : Tm.deimos : Tm.phobos
213,21 K : 222,98 K : 242,14 K
0,9747 rotation/day : 24/30.3 rotation/day : 24/7,7 rotation/day
amars = 0,25 : adeimos = 0,068 : aphobos = 0,071
Mars and Deimos have close rates of rotation but Mars has higher albedo
Phobos and Deimos have close albedo but Phobos has a higher rate of rotation.
The Phobos and Deimos Surface Mean Temperatures were calculated with the Planet Surface Mean Temperature Equation:
Tmean.planet = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴
Tmean.phobos = 242,14 K
Tmean.deimos = 222,98 K
On the other hand the satellite measured
Tsat.mean.phobos ≈ 233 K
Tsat.mean.deimos ≈ 233 K
were actually calculated with the Effective Temperature Incomplete Equation:
Te.incompl = [ (1-a) So (1/R²) /4σ ]¹∕ ⁴
Lets do the calculation for Phobos
Te.phobos.incompl = [ (1-0,071) 1.362 W/m²*(1/2,32) /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =
Te.phobos.incompl ≈ 233 K
Lets do the calculation for Deimos
Te.deimos.incompl = [ (1-0,068) 1.362 W/m²*(1/2,32) /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =
Te.deimos.incompl ≈ 233 K
Thus we conclude now that the Phobos and Deimos Effective Temperatures calculated with the Planet Effective Temperature Complete Formula are the correct Phobos' and Deimos' effective temperatures
Tmean.planet = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴
Tmean.phobos = 242,14 K ( which is the faster rotating ) and
Tmean.deimos = 222,98 K.
An enhanced-color image of Deimos (MRO, 21 February 2009). Image: NASA/JPL-Caltech/University of Arizona
.
https://www.cristos-vournas.com
The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean:
Tmin↑→ T↑mean ← T↓max
.