If the sun is so hot, why is space so cold?

Apparently, this is a question people ask, and they don’t like it when you make fun of them.

On Nov. 8 Bill Nye, America’s iconic “Science Guy”, was torn to shreds on Reddit while holding an online discussion to promote his TV show on Netflix.

The show, modestly titled Bill Nye Saves the World, has been panned as shallow and out-of-touch, and so when Nye posted on Reddit, “I’m Bill Nye and I’m on a quest to end anti-scientific thinking. AMA Ask Me Anything”, the sound of knives being sharpened was deafening.

Some of the greatest scorn concerned his flippant response to the question: “If the Sun is hot, why is space cold?” Nye’s full answer:

“There is a fantastic amount of space in space. I mean it’s not all that cold, is it? It’s 3 Kelvins. Toasty.”

So for all those angry Redditors-and everyone else who has ever wondered-here goes. (I will not try to imitate Nye’s signature style.)

If the sun is hot, why is space cold?

First, you need to know that the question doesn’t exactly make sense-not as phrased. Space is not “cold”, because space is not anything; it doesn’t have a temperature.

Temperature, technically, is a measure of how fast atoms and molecules are moving. So things in space, such as planets and stars and dust clouds and spaceships and astronauts, have temperature, because they are all made out of atoms and molecules. Space itself doesn’t, because it isn’t.

OK. But even “empty” space contains atoms, albeit not many. Deep space, far from stars and planets, is filled with a very thin gas, about one atom per spoonful (10 cubic centimeters) of space. By contrast, a spoonful of air here on Earth contains 1020 molecules, or more than 100 billion billion.

That very thin gas does have a temperature: around “3 Kelvins”, as Bill Nye said (though real scientists don’t pluralize or capitalize kelvin). That means 3°C (5°F) above absolute zero. Absolute zero is the coldest possible temperature there is-the point at which molecules and atoms have stopped moving altogether.

So, to be properly pedantic about it, the question should really be:

Why is the gas in space cold?

Flippancy aside, Nye was right: It’s because space is big. If you were floating in space halfway between our sun and the next nearest star, Proxima Centauri, you’d be about 2.1 light years away from either one. (This density of stars is about average in a galaxy.) How much heat do you get from a star 2.1 light years away? Not much! Let’s do a little math.

The heat output of the sun is 3.8 × 1026 watts. That’s as much as 3.8 × 1023 (or 380 billion trillion) one-kilowatt electric heaters, of the kind you might use in your bedroom.

So yes, the sun is hot. But if you’re 2.1 light years from it, all that heat has spread out through a sphere 2.1 light years, or 2 × 1016 meters, in radius before it reaches you. The surface area of that sphere (4πr2, if you remember your math) is 5 × 1033 square meters. The surface area of your body-at least the side of it facing the sun-is about 1 square meter.

So you’re getting one fifth of one 1033-th of the sun’s heat. That’s 0.000000076 watts, or roughly 13 billionths of the heat of a single 1-kilowatt heater, feebly toasting you out there in space.

Put another way, it would be like trying to use just one of those heaters to warm a giant cubic room about 2,360 meters along each side. Or, if it were a regular room with a 3-meter (10-foot) ceiling, it would be a square more than 66 km (41 miles) along each side. And remember, this isn’t a room on Earth surrounded by air at a nice comfortable temperature, but a room in deep space with no other sources of heat for several light years. With a single lousy electric heater in the middle of it.

So yeah, that’s why it’s cold.

OK, but why is space also cold near the sun?

Aha! This was really the question all along, wasn’t it. And, well, it’s a fair one.

If you’re not light years from the sun but a mere 150 million km (92 million miles) away-which is how far we are from it here on Earth-then the sun’s heat is considerably more concentrated: 1,368 watts per square meter. In other words, if you float outside the earth’s atmosphere in direct sunlight, you have a whole electric heater, plus some more, focusing all its heat straight on to your body. To see how that feels, try turning on your bedroom heater and sitting right up against it. (It’s OK, I’ll wait.)

So yes, if you’re in direct sunlight near the sun, you will not be cold. Which is why we have spacesuits: Apart from protecting you from vacuum, they protect you from being cooked. Objects in direct sunlight in Earth orbit get heated to around 120°C (248°F).

And yet, there’s a paradox: You also need spacesuits to protect you from being frozen. Even in Earth orbit, space can be very cold. How come?

Well, down here on Earth, if you go out of the sunlight into the shade, the reason you don’t suddenly freeze is that a lot of warmth is still stored in the air around you. You’re in a sort of heat bath, though you can’t see it. In space, though, if you clamber around your space station to get out of the sunlight, there’s no air and no heat bath.

Your own body heat will start to escape-though not all at once, because in another paradox, space is actually a pretty good insulator. Down on Earth, if you’re in a fierce wind or a cold sea, you can lose heat quite fast because the air and water pick it up from your body and carry it away. In space there’s nothing to carry heat away, so you can lose it by radiation but not by conduction. (That’s why vacuum flasks keep drinks hot or cold for hours.) Nonetheless, without a heated spacesuit to protect you, you will eventually freeze-except that the lack of oxygen will kill you long before that.

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