I've heard that gases like hydrogen and helium leak out of the earth's gravity a little by little. but where are they going? where do they end up after leaving earth's pull? would the sun pull them towards itself? or they just wander in space until they find another space object with some mass?
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$\begingroup$ Related: physics.stackexchange.com/q/78586/123208 $\endgroup$– PM 2RingMay 11, 2020 at 14:16
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It takes a long time for hydrogen and helium to work their way to the outer reaches of Earth's atmosphere, millions of years. The outer layers of the atmosphere are the thermosphere and the exosphere. These layers are very tenuous, but the gas in them is still considered to be gravitationally bound to the Earth. The thermosphere begins about 80 km above sea level, the base of the exosphere ranges from about 500 to 1,000 km above sea level depending on solar activity. (The altitude of the ISS is 408 km).
When gases leave the exosphere they get swept up by the solar wind, a stream of charged particles released from the upper atmosphere of the Sun which blows through the solar system. This wind is very thin - in Earth terms it's a hard vacuum, but it is moving quickly.
The solar wind is observed to exist in two fundamental states, termed the slow solar wind and the fast solar wind. Near Earth, the slow solar wind has a speed of 300 - 500 km/s, and a temperature around 100,000 K, the fast solar wind has a typical speed of 750 km/s and a temperature around 800,000 K.
So our lost hydrogen and helium (and other gases) eventually get blown by the solar wind to the outer limits of the solar system, unless they happen to bump into a planet, moon, or asteroid in the mean time.
For more details on the exact mechanisms by which various gases escape Earth's atmosphere, please see Wikipedia's article on atmospheric escape.
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$\begingroup$ thanks for the explanation! That cleared up how the gases are escaping in the first place. although I do wonder now where is this solar wind going? are the velocities which you've mentioned enough to send the gases out of our suns gravitation? $\endgroup$ May 11, 2020 at 15:07
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$\begingroup$ and what is the hard vacuum that you speaketh of? isn't vacuum empty? or is it made up of particles that we don't know yet? $\endgroup$ May 11, 2020 at 15:11
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$\begingroup$ cool! just out of curiosity do they escape the solar gravitation due to the radiation from a super nova? $\endgroup$ May 11, 2020 at 15:18
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2$\begingroup$ Might be worth pointing out that the velocities you mention (hundreds of km/s) are way beyond the solar escape velocity of about 42 km/s. So those particles are headed for interstellar space... $\endgroup$ May 11, 2020 at 16:02
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2$\begingroup$ @gerrit - There is a termination shock and heliopause (i.e., two electromagnetic boundaries) that greatly alter the dynamics of charged particles. The solar wind reaches a roughly constant speed usually before even getting to Mercury. Newly ionized particles, called pick-up ions, are accelerated up to the solar wind speed extremely fast (e.g., something like ~95 km $s^{-2}$ for protons near Earth). $\endgroup$ Jan 27, 2022 at 13:33