Why is the Sun so bright, but you can feel it far away?

Question

First of all, the Sun's surface temperature is only about 6000 K. Years ago I was working at at a melt work with furnace temperatures 0f about 2-3000 K; of course you could not be near a furnace without protection, when it was open, but you could still stay some 20-30 metres away from it. Likewise, a light bulb has no long reach, till it fades away. But how about the Sun? Why can experience it at 150 000 000 km away?

Besides, I wonder why space is not heated up, because the heat radiating from all the stars and galaxies is so enormous, and actually the matter density in space is so low. How, actually, can heat be absorbed in space? What temperature is measured in space - is it just the wavelengths of radiations, from which temperature is calculated?

Answer 1

The answer to your first question has to do with luminosity. It's a measure of power, the energy given off by an object in a certain amount of time, which you can think of as brightness. The more luminous the object, the brighter it appears.

We can treat the Sun as an idealized object called a black body, which emits thermal radiation according to something called the Stefan-Boltzmann law. Assuming the Sun is spherical, with a radius $R$ and temperature $T$, then its luminosity $L$ is $$L=4\pi\sigma R^2T^4$$ where $\sigma$ is the Stefan-Boltzmann constant. The important thing here is that $L\propto R^2$. If the Sun was the size of one of your furnaces, it would not be very bright; if the furnace was spherical and could be treated as a black body, the two would have the same luminosity.

The Sun, however, has a radius on the order of about $7\times10^8$ meters. I don't know how big the furnace is, but I'm assuming it can't be larger than ten meters, to an order of magnitude. First, that's a size difference of about $10^7$. Second, we square the radius when determining luminosity, meaning that there's a difference of a factor of $10^{14}$. To make this a bit more meaningful, the Sun is then essentially one hundred million million times more luminous than the furnace, even though the temperatures are the same.

I feel like your second question may be a duplicate of What is the temperature of outerspace? (see also the questions linked therein), and Run like hell has already tried to address it. barrycarter's comment, though, is spot-on. The flux from the source, $F$, drops off via the inverse-square law - that is, at a distance $r$ from the source, $$F\propto\frac{1}{r^2}$$ Remember how we just established the power (pun intended) of squaring a large quantity? Interstellar distances are enormous; the nearest star system, Alpha Centauri, is roughly $10^{16}$ meters away, or ten thousand million million meters. Now square that distance. That's a tiny factor - even when multiplied by the luminosity of all three stars, which combined is still on the same order of magnitude as the Sun.

Answer 2

Your question is far more complex than you think. You need matter to have temperature, cause temperature is nothing else than the measure of the mean energy of a group of particles (this definition is quite accurate for our purposes here). So you need particles and something that can give them energy to heat the matter up. The photons from the stars heat the matter and you measure a temperature.

So what's the temperature in space? It depends, it depends where you are and what's there. In a galaxy for example you have some matter between stars, it's called the interstellar medium (ISM), it's mainly gas, but there is a very important (for astronomers) fraction of (usually cold) dust. So what are the temperature of this medium? We can divide it in categories:

• Hot ionized medium: composed of ionized particles. Its temperature ranges from one million kelvin to 10 millions kelvin. You can find it in the bulge of our galaxy

• Warm ionized medium: temperatures around 10000 kelvins. You can find it in the spiral arms, around the hottest stars (O, B type: the blue ones).

• Warm neutral medium: Its temperature ranges from 1000 to 10000 kelvins. It's diffused in the disk of our galaxy and it extends way farther than the zone where the stars in the galaxy are.

• Cold neutral medium: Its temperature ranges from 10 to 100 kelvins, it's mainly composed of molecules of hydrogen and it's very important for the star formations, so you can find it in the spiral arms.

Then you have the dust which get heated up by stars radiation and its temperature can vary depending on its composition, location and dimensions of grains.

What temperature is measured in space? -Is it just wavelengths of radiations, from which temperature is calculated?

Basically yes, we measure the radiation that arrive to us, and we know the processes that can make this radiation possible and from this knowledge we can calculate the temperature those particle had to have in order to emit like that.

Answer 3

There are two parts to the answer and neither has anything to do (directly) with how far away the Sun is.

The first part is to consider the temperature of the Sun vs the temperature of your furnace. The amount of radiation power emitted per unit area is proportional to $T^4$ (the fourth power of temperature) and it really doesn't depend on anything else. If the Sun is twice the (absolute) temperatures of your furnace then it is emitting 16 times as much power per unit area. That power is carried to the Earth by light (photons), which travel through the vacuuum of space without any problem.

However, other than that factor of 16, there is no reason why a blast furnace shouldn't "feel" as hot as being exposed to the Sun if it subtends a 16$\times$larger solid angle. This is defined as apparent surface area divided by distance squared and is basically what fraction of your field of view the object occupies.

For example, if you stand 20m away from a blast furnace and the "opening" (i.e. whatever allows your to view the interior) is 17cm across then it will look about as big as the Sun appears in the sky. In these circumstances you would receive only 1/16 of the radiative power that you would being outside under a noon-day Sun. On the other hand, if the opening were 4 times wider then you would receive the same amount of energy as you do from the Sun - so yes, you could be 20m away from a blast furnace opening of about $< 1$m, without any special protection. However, if it were say 2m across, or you were to move to only 10m away, you would be getting >4 times as much radiation. And that would feel decidedly hot.