Spacecraft External Temperatures |
References:
Elements of Space Technology for
Aerospace Engineers by Rudolph X. Meyer
The Geostationary
Satellite by Peter Berlin
Spacecraft Systems Engineering by Peter
W Fortescue, John Stark and Graham Swinerd
Spacecraft
Thermal Modelling and Testing by Isidoro Martinez
Thermal
Systems Design PDF – UMD ENAE 483/788D – Principles of
Space Systems Design (1.5 MB PDF)
An Excel 2010 file with the equations from this page already entered is available HERE.
T = [ E / (4 • σ) ]^{1/4}
Where:
T: Temperature of Black-Body in Kelvin.
E: Irradiance in Watts/m2 from a solar source
σ: Stefan-Boltzmann’s constant, which is: 5.67 x 10^{-8} W/m^{2} K^{4}
EXAMPLE: What is the Black-Body Temperature of a sphere at 0.23 AU from the sun, where E is 25,822 W/m2? [25,822 / (4 • 5.67 x 10^{-8})]^{1/4} = 580.88 K |
NOTE: This is a good way to “eyeball” the effects of different coatings on the thermal control of your spacecraft with a relatively simple equation.
T = [ (α • E) / (4 • ε • σ) ]^{1/4}
or as
T = [ (α / ε) • (E / 4 • σ) ]^{1/4}
Where:
T: Equilibrium temperature of sphere in Kelvin.
α: Absorptivity
ε: Emissivity.
E: Irradiance in Watts/m2 from a solar source
σ: Stefan-Boltzmann’s constant, which is: 5.67 x 10^{-8} W/m^{2} K^{4}
T = [ (E • α • A_{S} + P_{INT}) / ( ε• σ • A_{RAD}) ]^{1/4}
where
E: Irradiance in Watts/m2 from a solar source
α: Absorptivity
ε: Emissivity.
P_{INT}: Internal heat/power generation.
A_{RAD}: Radiative area in square meters. (Surface area of your ship basically)
A_{S}: Absorption area in square meters. (The area of the side that faces the sun).
σ: Stefan-Boltzmann’s constant, which is: 5.67 x 10^{-8} W/m^{2} K^{4}
EXAMPLE: The AERCam/SPRINT Satellite, a 30 cm sphere with 200 W of internal power, an absorptivity of 0.2 and an emissivity of 0.8 is launched into free space around earth. We do not consider reflected albedo or any effects that raise it's temperature, just internal power and solar irradance. What is its equilibrium temperature? [ (1366 • 0.2 • 0.0707 + 200) / ( 0.8 • 5.67 x 10^{-8} •0.2827) ]^{1/4} = 361.6K |
T = [ P_{INT} / ( ε• σ • A_{RAD}) ]^{1/4}
where
ε: Emissivity.
P_{INT}: Internal heat/power generation.
A_{RAD}: Radiative area in square meters. (Surface area of your ship basically)
σ: Stefan-Boltzmann’s constant, which is: 5.67 x 10^{-8} W/m^{2} K^{4}
EXAMPLE: The AERCam/SPRINT Satellite, a 30 cm sphere with 200 W of internal power, an absorptivity of 0.2 and an emissivity of 0.8 is launched into the darkness between the stars. What is its equilibrium temperature? [ 200 / (0.8• 5.67 x 10^{-8} • 0.2827) ]^{1/4} = 353.4K |
Emissivity/Absorptivity
Properties of Selected Materials |
|||
Material |
Condition |
Solar Absorptivity |
Infrared Emissivity |
White Enamel Paint |
Over Aluminum Substrate |
0.250 |
0.853 |
White Epoxy Paint |
Over Aluminum Substrate |
0.248 |
0.924 |
Black Paint |
Over Aluminum Substrate |
0.975 |
0.874 |
Aluminum Paint |
As Received |
0.250 |
0.250 |
Graphite Epoxy |
As Received |
0.950 |
0.750 |
Fiberglass |
As Received |
0.900 |
0.900 |
Aluminum (6061-T6) |
Polished Metal |
0.031 |
0.039 |
Stainless Steel (AM350) |
Polished Metal |
0.357 |
0.095 |
Titanium (6AL-4V) |
Polished Metal |
0.448 |
0.129 |
Teflon, Silvered |
As Received |
0.080 |
0.660 |
Teflon, Aluminized |
As Received |
0.163 |
0.800 |
Optical Solar Reflector |
As Received |
0.077 |
0.790 |
Q = m • c_{p} • (ΔT/Δt)
Where:
Q: Input/Output of energy in joules.
m: Mass of the material in kilograms.
c_{p}: Specific heat capacity of the material in J • kg^{-1}K^{-1}
ΔT: Temperature increase (or decrease) in Kelvin.
Δt: Duration of input/output energies in seconds.