If the surface of the moon is 100°C, what temperature would it be four feet off the surface, given the vacuum on the moon?
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27$\begingroup$ Temperature of what? $\endgroup$– Organic MarbleCommented Feb 26 at 18:57
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7$\begingroup$ The temperature of a vacuum is undefined. It's a little like asking how big a box you need to hold six pounds of vacuum. $\endgroup$– Darth PseudonymCommented Feb 27 at 18:15
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2$\begingroup$ @DarthPseudonym The temperature of vacuum is the temperature that a thermometer in the vacuum measures if the radiation field is at equilibrium. In an out of equilibrium situation, different thermometers will measure different temperatures, vacuum or not. $\endgroup$– John DotyCommented Feb 27 at 18:19
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$\begingroup$ Hey, there would be a few atoms there, they have a temperature. Might not be easy to measure $\endgroup$– NachtCommented Feb 28 at 23:01
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$\begingroup$ To (slightly mis)quote a former US president, "It depends on what the definition of 'it' is." $\endgroup$– uhohCommented Mar 1 at 3:03
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4 Answers
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We are used to talking about the temperature at a given location, but that's because we are used to living in a sea of air. The reality is that locations don't have temperatures, substances do. When we talk about the temperature 4 feet off the ground on the earth, we mean the temperature of the air at that location. Its molecules are bouncing around at certain velocities, and that gives it a temperature.
People talk about the temperature "of space" or "in space", but that's not really a well-defined concept. Depending on context, it might mean different things. People sometimes say that the temperature of "space" is 2.7K, because that's the black-body temperature of the cosmic microwave background. A rock between the galaxies would eventually reach that temperature as it radiated its heat away to space and received meager heat from the CMB.
Another way you could specify the temperature at a point in space is to look at the average kinetic energy of the very sparse atoms that will still be present. But that's not useful if you are thinking about how hostile the environment is. For instance, the temperature of the solar wind near the orbit of the earth can be more than a million degrees C, but it is so diffuse it does not meaningfully heat up spacecraft passing through it.
This is why the answer depends on the material and amount of sun. Even on earth, the current temperature doesn't tell the whole story. A cast iron pan will get hotter in the sun than a piece of paper. But in space, without a bath of air to even out the heat, there's just no single, simple answer.
Probably the most meaningful and informative answer, if you really want a number, is to look at examples of how hot things get under similar conditions. For instance, you could drop the "four feet above the surface" part of the question and look at the answer to this question (which you may have already read) about the surface temperature of the moon. The incoming heat from the sun will be the same, and the moon's surface four feet away will shield you from deep space about as well as if you were touching the moon. Those temperatures ranged between about -80°F and 150°F. For comparison, however, the sun-facing parts of the LM should be similar to the sun-facing side of the ISS, which would apparently get as high as 250°F without thermal controls. (In degrees C, that's about -60°, 65°, and 120°, respectively.) So there's a very significant temperature range depending on the material, but it's in the range you should expect at a habitable distance from the sun. See also this question, which is almost a duplicate except that it specifies "shade". It comes to a specific answer, but again, it has to specify a lot of variables.
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$\begingroup$ Well, is it really not possible to answer what a thermometer would measure at that time and location? Surely the soon would heat it up too. $\endgroup$ Commented Feb 28 at 13:06
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8$\begingroup$ @TomášZato Yes, but that would tell you the temperature...of the thermometer. As the answer states, it's not meaningful to talk about the temperature of a vacuum. $\endgroup$ Commented Feb 28 at 13:09
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16$\begingroup$ The temperature that a thermometer would measure would depend on the color of the thermometer. $\endgroup$ Commented Feb 28 at 13:47
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4$\begingroup$ @TomášZato On Earth, we don't expect a thermometer directly exposed to the Sun to accurately measure the ambient air temperature. Meteorologists use a Stevenson screen so that the thermometer can reach an equilibrium temperature. We'd need to do something similar on the Moon. $\endgroup$– PM 2RingCommented Feb 28 at 23:57
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2$\begingroup$ The problem is that "its surroundings" do not have a temperature in any meaningful sense. The idea of an ambient temperature depends on an environment where conduction and convection are the main forms of heat transfer. Then, whatever the emissive and reflective spectra of the thermometer are, it will still reach equilibrium with its environment and give a consistent reading. But a radiative environment is different. The equilibrium temperature will depend on how the spectrum of incoming radiation interacts with the spectrum that the thermometer absorbs and emits. $\endgroup$ Commented Feb 29 at 14:13
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Depends on emissivity, absorptivity, shape, orientation, illumination, etc. of your thermometer.
At such a location, there's nothing of any thermal significance except the radiation field. The radiation field is wildly out of equilibrium, with 6000K Sun, 370K Moon, 3K cosmos, and maybe the Earth, too. You can't define a simple temperature.
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$\begingroup$ Depending on the size of the object, there are things of thermal significance four meters above the surface of the Moon that you did not mention, which are the interplanetary medium and the Moon's very, very thin atmosphere. These too are way out of equilibrium. $\endgroup$ Commented Feb 29 at 15:36
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1$\begingroup$ @DavidHammen Both are too thin to matter. We don't even include the thicker exosphere in LEO in spacecraft thermal balance calculations. $\endgroup$ Commented Feb 29 at 15:38
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$\begingroup$ They're not too thin to matter if your "thermometer" is the size of an atom. Even the very, very thin intergalactic medium has a "temperature", and it is not 3 kelvins. It is instead in the tens of millions of kelvins, if not higher. That very, very thin intergalactic medium can support sound waves, but only at extremely low frequencies. Astronomers have even detected those extremely low frequency sound waves propagating through that very sparse medium. $\endgroup$ Commented Feb 29 at 17:05
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1$\begingroup$ @DavidHammen Well, sure, for a tiny enough thermometer with negligible capability to interact electromagnetically. As for the intergalactic medium, I helped show its emission is thermal almost half a century ago articles.adsabs.harvard.edu/pdf/1976ApJ...205L..65S. $\endgroup$ Commented Feb 29 at 17:18
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In the most commonly understood definition of temperature, there is no temperature 1.2 metre above the lunar surface. Typically, temperature is a statistical property of bulk matter that describes how fast the molecules are moving on average. When there are no molecules, or not enough molecules to have bulk matter, there is no temperature. This applies above the lunar surface.
One can also define the temperature of electromagnetic radiation (see John Dotys answer), or of a plasma. Plasma physicists even speak of parallel and perpendicular temperature (I think they shouldn't — temperature is a scalar quantity), which near the Moon would depend on what the solar wind is doing and would vary whether the Moon is inside or outside the Earth magnetosphere.
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$\begingroup$ There's no air temperature 4 feet above the moon's surface, but if you put a ball on a 4-foot stand, the ball would certainly have a temperature... $\endgroup$ Commented Feb 27 at 18:10
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1$\begingroup$ It is perfectly sensible to talk of different temperatures for different degrees of freedom when you can isolate them and they separately are near thermal equilibrium. $\endgroup$ Commented Feb 27 at 18:23
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$\begingroup$ @JohnDoty I believe you. And yet I get a hiccough whenever I hear "parallel temperature" and "perpendicular temperature", or similarly for pressure. I'm sure those are sensible quantities, but I think they should be called something else. $\endgroup$– gerritCommented Feb 27 at 21:18
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$\begingroup$ @gerrit "Thermodynamics doesn't work in plasmas." -- Bruno Coppi $\endgroup$ Commented Feb 27 at 21:20
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The temperature of an object above the surface is mainly influenced by the sunlight shining on that object, and the object's albedo (ie how much sunlight it reflects). A rock 4ft above the surface would be at 100ºC just like the surface.
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1$\begingroup$ Not disagreeing with the overall concept of your answer, but if factoring in being in contact with the surface it seems like the temperature of the object would be (slightly) affected. Hovering at 4 ft the object can only reflect and radiate away the sunlight hitting it. However on the surface it can conduct some of the heat away into the now shaded regolith or rock that is underneath it. Or in some cases receive conducted heat from some of the surface material, which could be more than the small amount of radiated and reflected heat that it receives from the surface while hovering above it $\endgroup$ Commented Feb 27 at 14:30