<p>This is not a simple question to answer. Outside the influence of the earth's magnetic field then "space" is actually filled with the solar wind, which has a high nominal temperature but low energy density - in other words the particles in the solar wind are moving very fast but there are not that many of them.</p>

<p>If you mean what temperature a black body in constant sunlight would reach then probably not that dis-similar from the temperature of the Earth, but you are not measuring the temperature of space then, but rather the intensity of solar radiation.</p>

CC BY-SA 3.0
2015-10-21T13:26:54.320Z
2015-10-21T13:26:54.320Z
adrianmcmenamin
<p>Assume you have a spherical blackbody.</p>

<p>The solar flux at the radius of the Earth is given to a good approximation by $L/4\pi d^2$, where $d = 1$ au. This is $f=1367.5$ W/m$^2$ (though note the distance between the Earth and the Sun has an <em>average</em> of 1 au).</p>

<p>If it is a <em>blackbody</em> sphere it absorbs all radiation incident upon it. Assuming this is <em>just</em> the radiation from the Sun (starlight being negligible), then an easy bit of integration in spherical polar coordinates tells us that the body absorbs $\pi r^2 f$ W, where $r$ is its radius.</p>

<p>If it is then able to reach thermal equilibrium and it entire surface is at the same temperature, then it will re-radiate all this absorbed power. Hence
$$\pi r^2 f = 4 \pi r^2 \sigma T^4,$$
where $T$ is the "blackbody equilibrium temperature". Hence
$$ T = \left( \frac{f}{4\sigma}\right)^{1/4} = 278.6\ K$$</p>

CC BY-SA 3.0
2015-10-21T14:26:09.840Z
2015-10-21T14:26:09.840Z
ProfRob
<p>What is the equilibrium temperature that a black body will reach at the Earth's distance from Sun?</p>

CC BY-SA 3.0
2015-08-02T22:21:19.447Z
Black body temperature depends on color and reflective properties.   Also, a rotating object or non rotating?   Permanently facing the sun it would be fairly hotish, but a rotating object like the earth, the average black body temp of the Earth is somewhere around -18 degrees (our atmosphere traps about 27 degrees and the internal heat from the earth adds the other 5, bringing the average temp up to about 15 on the surface.   Google black body temperature of earth or moon.   https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law#Temperature_of_the_Earth
userLTK
CC BY-SA 3.0
2015-08-02T22:55:34.500Z
"Black body temperature depends on color and reflective properties." - already said, a black body, so why asking for color?
Anixx
CC BY-SA 3.0
2015-08-02T23:32:14.853Z
@Anixx: Because any physical (non-ideal) black-body will have a finite reflectance that plays a decisive role in how much energy it finally recieves and can absorb.
AtmosphericPrisonEscape
CC BY-SA 3.0
2015-08-02T23:38:50.153Z
I've seen the term used both ways.   https://docs.kde.org/trunk5/en/kdeedu/kstars/ai-blackbody.html   Didn't mean to not answer the question.
userLTK
CC BY-SA 3.0
2015-08-03T00:58:49.053Z
@userLTK tour first link says it is 6 C, not -18 C.
Anixx
CC BY-SA 3.0
2015-08-03T04:04:18.367Z
It says both numbers.
userLTK
CC BY-SA 3.0
2015-08-03T08:21:12.667Z
@userLTK regarding my question it says 6 C. Also -18 is senseless because a body cannot reflect as white body but emit like black body.
Anixx
CC BY-SA 3.0
2015-08-08T11:11:28.617Z
I'm not sure what the point of this is.   It might not have been what you were asking but it's not "senseless".   It wouldn't be in the article if it was "senseless".    Also, are you talking about something permanently facing the sun, or on a rotating sphere?
userLTK
CC BY-SA 3.0
2015-08-17T21:07:45.390Z
I think the term "black body" is clear enough to a physicist.
adrianmcmenamin
CC BY-SA 3.0
2015-10-21T14:17:14.420Z
@AtmosphericPrisonEscape No. A black body has zero reflectivity and absorbs all light incident upon it. You are confusing this (and the OP) with a grey body.
ProfRob
<solar-system><temperature><radiation><habitable-zone><radiative-transfer>
What is space temperature around Earth?
Anixx
# What is space temperature around Earth?

(Asked by: username_0 on 2015-08-02)

What is the equilibrium temperature that a black body will reach at the Earth's distance from Sun?

**Tags:** solar-system, temperature, radiation, habitable-zone, radiative-transfer
> **Comments:**
> **username_1**: Black body temperature depends on color and reflective properties.   Also, a rotating object or non rotating?   Permanently facing the sun it would be fairly hotish, but a rotating object like the earth, the average black body temp of the Earth is somewhere around -18 degrees (our atmosphere traps about 27 degrees and the internal heat from the earth adds the other 5, bringing the average temp up to about 15 on the surface.   Google black body temperature of earth or moon.   https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law#Temperature_of_the_Earth  
> **username_0**: "Black body temperature depends on color and reflective properties." - already said, a black body, so why asking for color?  
> **username_2**: @Anixx: Because any physical (non-ideal) black-body will have a finite reflectance that plays a decisive role in how much energy it finally recieves and can absorb.  
> **username_1**: I've seen the term used both ways.   https://docs.kde.org/trunk5/en/kdeedu/kstars/ai-blackbody.html   Didn't mean to not answer the question.  
> **username_0**: @userLTK tour first link says it is 6 C, not -18 C.  
> **username_1**: It says both numbers.  
> **username_0**: @userLTK regarding my question it says 6 C. Also -18 is senseless because a body cannot reflect as white body but emit like black body.  
> **username_1**: I'm not sure what the point of this is.   It might not have been what you were asking but it's not "senseless".   It wouldn't be in the article if it was "senseless".    Also, are you talking about something permanently facing the sun, or on a rotating sphere?  
> **username_3**: I think the term "black body" is clear enough to a physicist.  
> **username_4**: @AtmosphericPrisonEscape No. A black body has zero reflectivity and absorbs all light incident upon it. You are confusing this (and the OP) with a grey body.  

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## 2 answers

### Answer by username_4 on 2015-10-21. Score: 4 | Accepted answer

Assume you have a spherical blackbody.

The solar flux at the radius of the Earth is given to a good approximation by $L/4\pi d^2$, where $d = 1$ au. This is $f=1367.5$ W/m$^2$ (though note the distance between the Earth and the Sun has an *average* of 1 au).

If it is a *blackbody* sphere it absorbs all radiation incident upon it. Assuming this is *just* the radiation from the Sun (starlight being negligible), then an easy bit of integration in spherical polar coordinates tells us that the body absorbs $\pi r^2 f$ W, where $r$ is its radius.

If it is then able to reach thermal equilibrium and it entire surface is at the same temperature, then it will re-radiate all this absorbed power. Hence
$$\pi r^2 f = 4 \pi r^2 \sigma T^4,$$
where $T$ is the "blackbody equilibrium temperature". Hence
$$ T = \left( \frac{f}{4\sigma}\right)^{1/4} = 278.6\ K$$


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### Answer by username_3 on 2015-10-21. Score: 0

This is not a simple question to answer. Outside the influence of the earth's magnetic field then "space" is actually filled with the solar wind, which has a high nominal temperature but low energy density - in other words the particles in the solar wind are moving very fast but there are not that many of them.

If you mean what temperature a black body in constant sunlight would reach then probably not that dis-similar from the temperature of the Earth, but you are not measuring the temperature of space then, but rather the intensity of solar radiation.


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