If the hydrogen gas escaped and left the atmosphere, would it affect the orbit around the sun, possibly causing the Earth to cool too much?
• I can't think offhand of any mechanism by which it would escape in some preferred direction. I'd expect to be pretty much evenly spread in all directions, so any effects on the orbit of what remains caused by the hydrogen leaving in any particular direction would be cancelled out by the effects of hydrogen leaving in the opposite direction.
• We are talking about 5.6 x 10^12 tons of hydrogen. The mass of the Earth is 5.972 x 10^21 tons. The mass of the hydrogen is about 1 billionth the mass of Earth. That's about the ratio of the mass of a grain of rice to the mass of the International Space Station.
Tossing that small of mass away, even if it was all in one direction, is not going to do anything significant to your orbit unless you tossed it away with very very very high velocity. A naive calculation just using Newtonian mechanics suggests it would have to be much faster than the speed of light to carry enough momentum away to matter. I'll leave it to others to figure out what fraction of the speed of light it would have to be going to have equivalent momentum.
I think the sun’s heat would give it a slight preference to escape from the sunny side of earth.
But does this hydrogen escapee like a rocket gas. Or it is just a restructure or a bit move of CoG.
One also note if it not too fast escape as earth rotate the overall effect depend upon the uniformity of the “escape” as the net effect can be zero or more depends upon its location on earth. Mostly as it is not align with the tangent of travel, it will affect.
How much as point out relates also the mass. But even the minor variations make the polar star changes. It will have affect.
> For a hydrogen atom to escape from the exobase, it must first travel upward through the atmosphere from the troposphere. Near ground level, hydrogen in the form of H2O, H2, and CH4 travels upward in the homosphere through turbulent mixing, which dominates up to the homopause. At about 17 km altitude, the cold tropopause (known as the "cold trap") freezes out most of the H2O vapor that travels through it, preventing the upward mixing of some hydrogen. In the upper homosphere, hydrogen bearing molecules are split by ultraviolet photons leaving only H and H2 behind. The H and H2 diffuse upward through the heterosphere to the exobase where they escape the atmosphere by Jeans thermal escape and/or a number of suprathermal mechanisms.
No free/unbound hydrogen from the surface is going to escape directly that way. It will bind with oxygen or the like long beforehand and become water.
But yes, a small portion of those molecules may later be broken down and may escape the planet that way. But statistically, very few of them are likely to do so.
So, maybe technically correct?