# Temperature of object in space due to background radiation

I recently had a discussion where we did not come to a conclusion because of several seemingly equivalently good arguments that contradicted each other. Maybe someone can help here.

Suppose we have an object (a satellite, or maybe just a rock) in deep space. We assume that the only relevant interaction is with the cosmic background radiation that can be described as a black body radiation of roughly $T_b\approx 3K$. No heating up from stars, no friction due to stellar gas molecules, just the background radiation.

The question is: Would the object eventually have a temperature of the background radiation, i.e. $T\rightarrow T_b$?

On the one hand, it seems that the background radiation is kind of a (near-infinite) thermal bath, and any object in a thermal bath will eventually have the temperature of the bath.

On the other hand, the assumption that the background radiation can be viewed as a bath in equilibrium seems questionable. If I understood it correctly, the homogeneity of the radiation stems from a situation shortly after the Big Bang where the universe was very uniform, which is not the case anymore, so I am not sure if the typical rules of a thermal bath apply.

What would happen with the temperature of such an object?

• – user178231
Dec 14, 2017 at 13:18
• @Countto10 Okay, but this only partly answers it because the question remains why the cosmic background radiation can be seen as a thermal bath. As far as I understood it, it was a thermal bath in equilibrium shortly after the Big Bang, but then inflation happened and expanded the universe faster than light, so the equilibrium condition has been lost. Or is this incorrect? Dec 14, 2017 at 13:39
• -1 Not clear. Are you asking about reaching thermal equilibrium with local space, or reaching thermal equilibrium with the distant CMB? Thermal bath means that there is exchange of thermal energy. Is such an exchange taking place in your hypothetical scenario? Dec 14, 2017 at 13:54
• The background radiation is being redshifted and dispersed, but at least at present it is a good approximation of a heat bath. Mostly because the time to get close to equilibrium for the object is far shorter than the time constant for the CMB cooling (about a Hubble time). In the future, for supercold objects and CMB this may no longer be true. Dec 14, 2017 at 14:19
• @sammygerbil Is there a difference between these two cases? The local space is pervaded with the CMB as well, so I currently fail to see the difference. I would expect that an exchange of thermal energy happens with the CMB, which is also present in the local space. Dec 14, 2017 at 14:38