Re: How much mass is the earth gaining/losing each year?

Wow... this is a loaded question (and equation), but I think you're on the right track.

In my opinion, though, the major contributor to Earth gaining mass is space debris, including space junk. On the timescale of a year, mass of the solar wind is negligible, as is neutrino mass (most of them pass right through Earth anyway). "Recently" (though, how recent, I don't know), about 10^8 kg of meteoritic material has been falling onto Earth (Morbidelli et al. 1994), and George Flynn at SUNY-Plattsburgh in a presentation to our research group reports that today, "tons" may be falling each year.

The major factor contributing to Earth losing mass is loss of gases, especially hydrogen (H). Remember that particles need to escape Earth's gravitational field by reaching escape velocity ~ 11 km/sec ~ in order to arrive in space. This can be written as

GMm/r = (1/2)mv^2

so v(esc) = SQRT(2GM/r)

where G is the graviational constant, M is the mass of Earth, and r is the radius of Earth (Hartmann, 1999).

Atmospheric escape is highly dependent on this escape velocity, so the heavier elements will not be able to leave. Light emitted by humans and nature is massless and does not contribute to mass loss. Neither does thermal radiation. (Even if you want to worry about E=mc^2 and think in terms of energy, there's no net loss from light - the earth is in equilibrium, meaning that it loses as much heat/light energy as it gains from the sun.) Particles in fire will probably fall back to Earth, and particles emitted by volcanoes probably do not have the velocity to escape Earth. Therefore, they return, too. Space shuttles and their cargo eventually return to Earth, so the loss and gain from them cancel each other out.

Therefore, change in Earth mass = space debris - H escape, using my best assumptions, and I would guess that H loss is much much less than mass gained from space debris, since Earth retains most of its atmosphere (Hartmann, 1999).

Morbidelli et al. 1994, Astronomy and Astrophysics, vol. 282, p. 955-979.
Hartmann, W. K. Moons and Planets, 4th edition. Wadsworth Publ. 1999