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I am wondering what kinds of materials that are released by Earth into space due to natural processes.

If possible, what are their approximate rates in kg per day or year?

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Hydrogen and Helium, mainly, at rates of 3000g and 50g per second, respectively. The process is called "Jeans Escape", and is due to the atoms being light enough to gain a significant velocity from radiation. The effect is really small - 3Kg of Hydrogen and 50g of Helium per second is tiny compared to the mass of the atmosphere. Also notice how big a disparity between H and He - He is just 4 times more massive, but is lost at a rate 60 times slower. Most other molecules are too massive to be lost this way.

If you are asking about the future, though, things get interesting. The escape of mass of the atmosphere is due to the sun. When the sun gets significantly brighter, then you will lose many more things. Like water and other massive particles. You can read more about Jeans escape here.

There is one other process that may also happen, but we have no hard evidence for it at this time. A large impact can throw material off of Earth and send it into space. This is how we think the moon formed, so in terms of how much mass - a lot! However, this requires a huge impact, which we haven't had for a while, so there is no "mass per year" number that makes sense. It is thought that maybe Apollo astronauts found one such meteorite.

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    $\begingroup$ +1 slightly related (and currently unanswered): Where does molecular hydrogen in the atmosphere come from? $\endgroup$
    – uhoh
    Commented May 15, 2019 at 11:23
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    $\begingroup$ I don't agree with the description of Jeans escape being due to "velocity from radiation" - it's simply that light enough particles in the high-energy tail of the Maxwell-Boltzmann distribution have velocities larger than the escape velocity. There are radiation-induced losses from the solar wind, but this is suppressed on earth by the magnetic field $\endgroup$
    – llama
    Commented May 15, 2019 at 17:33
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    $\begingroup$ @llama while the layers of atoms that make up the top layers of the atmosphere are mostly transparent to visible light, they can be heated by UV and X-rays and probably protons from the Sun, e.g. ionizing radiation. When this happens the high energy tail of the Maxwell-Boltzmann distribution moves out to higher energy and therefore higher velocity. You are both right. This is why the profile of pressure versus altitude is so different during high solar activity versus low activity, and why satellites loose altitude much faster when the Sun is active. $\endgroup$
    – uhoh
    Commented May 15, 2019 at 17:50
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    $\begingroup$ @llama See Which LEO satellite lost over 30 km of altitude in the geomagnetic storm of 13-14 March 1989? though it really wasn't anywhere near 30 km. Also see the answer(s) to What are the causes of these episodes of faster than average altitude loss by the ISS? (spoiler alert: it correlates with increased atmospheric pressure at high altitude (400 km!) due to solar activity). $\endgroup$
    – uhoh
    Commented May 15, 2019 at 17:56

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