How/why is space between the sun and the earth so cold, when we can feel heat coming from the sun?
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There’s a lot to unpack there.
Space isn’t really either cold or hot. It’s … nothing much. It’s mostly vacuum, so there’s not really a single temperature there. (That’s why thermoses have vacuum between the inside part and the outside part — so heat won’t conduct out to cool off Daddy’s coffee, or in to warm up your milk).
Space can feel cold, because you radiate heat all the time. When you stick toast in the toaster and push down the knob, the wires in the toaster get hot. They radiate reddish light, which is why they look red. But they also radiate infrared — a kind of light that’s too red to see. The light and the infrared carry heat energy. They carry enough heat energy to toast your toast! You are warm, so you always radiate a lot of energy outward as infrared light, too. Right now, you’re surrounded by a warm room that is radiating infrared light back in to you, which balances out the light you’re radiating out. That keeps you comfortable. In deep space, nothing radiates back at you very strongly, so you can cool off quite quickly unless you have special clothing on to prevent that. (Silvery things, like a suit made out of tinfoil, work great for that, because they don’t glow very well in infrared.)
Space can also feel hot if you’re near the Earth. That’s because the Sun radiates a lot of sunlight onto you, and the sunlight can warm you up. That’s part of why the Earth is warm so we can live here. The outermost part of the Earth (the upper layers of the atmosphere) settles down to about 0 degrees Centigrade. We feel warmer than that because of the “greenhouse effect”. Our air lets in sunlight, which heats up the Earth, but air also blocks in infrared light, which keeps the ground from cooling off very well. So the outer part of the Earth’s atmosphere settles down to about 0 degrees Centigrade, but the ground is quite a bit warmer than that, on average.
Space near the Earth is also full of very, very thin gas that is very, very, very hot. In interplanetary space, there are about 50 atoms in each teaspoon. Near you, right now, there about 500,000,000,000,000,000,000 molecules of air in each teaspoon. So space is pretty close to empty. But the atoms that *are* there act like a gas, and that gas is at about 100,000 degrees. Astronauts don’t get burned by it, because there’s just not very much of it — so it doesn’t hold very much heat. Sort of like how you can stick your hand inside a 350 degree oven for a few seconds and feel fine, but if you put your hand in 120 degree water it will feel scalding hot instantly. The hot water dumps a lot more heat into your hand than the much hotter air in the oven does.
So there are at least three different temperatures in space, all at once: -270 degrees centigrade, which is the temperature of the “room” around you if you block out the Sun and Earth; about 0 degrees centigrade, which is the temperature a basketball would reach if it were floating around in space near the Earth, from sunlight landing on it; and about 100,000 degrees centigrade, which is the temperature of the material in outer space.
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