Mars, Phobos and Deimos Mean Surface 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:
An enhanced-color image of Deimos (MRO, 21 February 2009). Image: NASA/JPL-Caltech/University of Arizona
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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
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 Equation Te (not corrected):
Te = [ (1-a) So (1/R²) /4σ ]¹∕ ⁴
Lets do the calculation for Phobos
Te.phobos = [ (1-0,071) 1.362 W/m²*(1/2,32) /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =
Te.phobos ≈ 233 K
Lets do the calculation for Deimos
Te.deimos = [ (1-0,068) 1.362 W/m²*(1/2,32) /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =
Te.deimos ≈ 233 K
Thus we conclude now that for the Phobos and Deimos the mean surface temperatures calculated with the Planet Mean Surface Temperature Equation are the correct Phobos' and Deimos' mean surface 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 one) and
Tmean.deimos = 222,98 K.
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The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean:
Tmin↑→ T↑mean ← T↓max
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