Astronomers know that the Universe is for the most part terribly empty. If there were much gas between the planets and the stars, then we could tell because then light would get absorbed and scattered by the gas that the light travelled through on its way to us, just as if there were a kind of fog in the Universe.
If the atmosphere of the Earth extended very far into space, then the Moon would feel noticeable friction from that atmosphere while the Moon travelled around the Earth through the atmosphere. The friction would take energy away from the motion of the Moon, which would make the Moon get closer and closer to the Earth, and eventually fall down to Earth. If the atmosphere of the Earth extended to today's orbit of the Moon with a density similar to the density of air near the ground today, then the Moon would be able to complete only a few orbits before it would fall down to Earth. In a similar way, artifical satellites (such as communication satellites and weather satellites) would not be able to stay in orbit for very long. Space around the Earth must therefore be very empty already, compared to the atmosphere near the ground.
That the air gets thinner (and the air pressure less) when you go to higher altitudes has been known for centuries. You can measure this with a barometer, and simple altimeters are really barometers that estimate the altitude from the air pressure. Close to the surface of the Earth, the pressure of the air is on average about 1000 millibar = 1000 hPa (hectopascal), and the pressure drops by about 1 hPa for each 8 m (about 25 ft) that you gain in altitude. At 5.5 km altitude the pressure has dropped to half of its value at sea level, at 10.3 km to a quarter, at 16.2 km to a tenth, at 31.2 km to a hundredth, at 48 km to a thousandth, and so on. The density of the air drops about as fast with height as the pressure.
Based on physics, it is also to be expected that the density of the air would decrease as you go higher, because the gravity of the Earth causes the atmosphere to be reasonably stable only when the denser layers are lower down and the less dense layers higher up.
The greatest part of the Universe contains fewer than 10 protons and neutrons per cubic meter. Compare this to the atmosphere of the Earth near sea level, which contains about 700 000 000 000 000 000 000 000 000 protons and neutrons per cubic meter, and it will be clear that most of the Universe is very empty indeed.
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