# Typical external temperature profile for a LEO satellite

I bumped into a question regarding LEO orbit. Is an external temperature profile available in literature as a first approximation for thermal analysis? I bumped into articles mentioning that the external environment is changing its temperature between -125 and + 60 degree Celsius. I know it really depends on the orbit altitude but I was wondering if general values can be read from literature. Thanks in advance.

• Altitude is not the main driver, because the near-vacuum of space is an excellent insulator. If your spacecraft is experiencing significant heating from friction, you are in re-entry, not orbit. In orbit, there is no conduction or convection, so all heat transfer is by radiation. That means being lit by the Sun or shadowed by the Earth makes a huge difference, and changes rather suddenly. Often, the main thermal concern is the waste heat generated by your onboard equipment as it operates; in many satellites, the core problem is how to keep them cool, rather than warm. Commented Nov 22, 2023 at 17:06
• Thanks @RyanC. By now I'm not really confident on a more detailed thermal analysis since no equipment is defined. I was studying possible effect of external temperature variation for a space tank. Commented Nov 22, 2023 at 22:06
• The temperature of a spacecraft 1) can vary greatly from one point to another on its surface, and 2) is really specific to the shape, attitude, eclipses during orbit, visible emissivity, and thermal emissivity of each surface, as well as the generation of heat internally (electronics, propulsion, etc) needing to get out. I would propose that there is absolutely no such thing as a typical temperature. I mean, if someone asked you "What is the typical surface temperature of Earth?" what number would you say is the right answer?
– uhoh
Commented Nov 22, 2023 at 23:52
• I agree with you @uhoh. I'm assuming it would be a great semplification for the problem. By now, I'm not able to do a complete thermal analysis since I'm not sure of where this component will be inserted. I will try to stick to some approximations knowing that this computation can be furtherly adjusted in the future. Commented Nov 23, 2023 at 13:46
• May be you misunderstood the articles, "the external environment is changing its temperature between -125 and + 60 degree Celsius". In LEO there is a very good vacuum, not as good as in MEO, but it is difficult to evacuate a chamber on Earth to the same vacuum as in LEO. In a high quality vacuum, an environment temperature is not defined, the temperature range given may be valid for a satellite. There are too few atoms in the vacuum to measure a temperature as done in a gas under a pressure.
– Uwe
Commented Nov 23, 2023 at 16:10

...By now, I'm not able to do a complete thermal analysis since I'm not sure of where this component will be inserted. I will try to stick to some approximations knowing that this computation can be furtherly adjusted in the future.

OK, then why not take the "spherical cow" approach and use the Planetary equilibrium temperature approximation?

$$P_{absorbed} = I_0 \ \epsilon_{vis} \ \pi \ r^2$$

$$P_{radiated} = \sigma \ \epsilon_{therm} \ T^4 \ 4 \ \pi \ r^2$$

where the epsilons are emissivities at visible and thermal wavelengths, $$\sigma$$ is s the Stefan-Boltzmann constant about 5.67E-08 W/m2/K-4 and $$I_0$$ is the solar constant of about 1360 W/m2

Then the the equilibrium temperature of your spherical cow spacecraft will be obtained by setting $$P_{absorbed} = P_{radiated}$$

$$I_0 \ \epsilon_{vis} = 4 \sigma \ \epsilon_{therm} \ T^4$$

or

$$T = \left( I_0 \ \frac{\epsilon_{vis}}{4 \ \sigma \ \epsilon_{therm}} \right)^{1/4}$$

So if you want a relatively cool surface on your LOX tank, choose a surface treatment with low visible emissivity and high thermal emissivity, so it absorbs relatively little radiation but effectively re-radiates what it gets.

For example, if you choose one of those exotic materials with low $$\epsilon_{vis}$$, like say 0.3 (fairly close to white) reflecting most incident sunlight, and $$\epsilon_{therm}$$ is high, like 0.9 (almost black, an effective radiator) your average thermal temperature (assuming you're rotating rotisserie style

will be a surprisingly cold 211 Kelvin or -62°C due to that unusual paint with very different emissivities in thermal and visible wavelengths!

Now, for longer and more detailed answers, see:

• I've never seen that emissivity notation before, but I like it. too many people think that something that's visibly black must be black through the whole spectrum Commented Nov 23, 2023 at 21:23
• @ErinAnne ya, in careful calculations there's spectral emissivity $\epsilon(\lambda)$. Then $I_0$ becomes an integral over the solar radiation spectrum and the $T^4$ becomes an integral over the Planck distribution. But for most materials the two effective emissivities (each is actually averaged over the relevant spectral band) gets you very close.
– uhoh
Commented Nov 23, 2023 at 22:28
• Thanks again @uhoh, very detailed analysis. I will have a look on it for further study on the topic of thermal management. Commented Nov 25, 2023 at 21:07

The dominant external factor is radiation balance. The radiation environment is not in equilibrium at at single temperature. The Sun is very hot, the Earth is cool, and deep space is very cold. So, the temperature depends on what the particular part of the spacecraft faces.

On HETE-2, a small (100 kg) scientific satellite, the GPS receiver on the sunlit side could be operating at 80C, while the CCD detectors on the dark side operated at about -40C.

• Thanks, much appreciated Commented Nov 25, 2023 at 21:06