What effect does Earth losing a part of its mass have, is there an impact on the Earth's orbit around the Sun?

Question

This is a random question that popped into my mind. I'm not a physicist or astronomist, however, I am genuinely curious. Also, this is not intended as a science fiction question, but an actual science question.

I had doubts about where this question should be posted - the Astronomy or the Physics SE page, in the end, I decided to post it here.

Sub-questions that I have, all being closely related to the one in the title:

1. Do the liftoffs of spaceships have any impact on Earth's orbit? As negligible as they might be?
2. Every bit of mass lost (sent into space) decreases the gravity of our planet, as tiny as the change might be. Is that correct?
3. Could the loss of Earth's mass over time (Hypothetically - centuries in the future, with tens of thousands of spaceships having left Earth.) change the orbit of Earth or produce any side-effects?

Answer 1

According to this answer to Is Earth getting heavier or lighter?:

tl;dr: The Earth receives 40,000 tons of dust from space every year, but looses 95,000 tons of Hydrogen and 1,600 tons of Helium every year as well. After all additional effects are balanced, the Earth looses about 50,000 tons a year.

According to this answer to Does launching a device into orbit change earth's orbit?

As long as "what happens in GEO stays in GEO" and there's no mass lost to deep space, the Shuttle and the Earth will mostly orbit around their common center of mass.

When the Shuttle is moving (relative to Earth) in the prograde direction (Earth's motion around the Sun), the Earth will be moving slightly slower than it normally would, but a half-orbit later when the Shuttle is moving retrograde, the Earth will be moving slightly faster than it normally would.

When the Shuttle returns, to 1st order (and maybe 2nd order as well) the Earth will be in the same place it would be if the Shuttle had never taken off.

It's quite a bit like the Earth and Moon orbiting around their common barycenter, and it being pretty much the EM barycenter that moves in a nice elliptical orbit around the Sun, except that as @RussellBorogove points out very effectively, it's a quite a bit smaller effect than that.

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So as long as the launched mass stays in orbit around the Earth, the Earth's orbit is essentially unaffected. If the spacecraft goes off into deep space, then there will be an extremely tiny change in the Earth's velocity (rather than due to its mass change) by conservation of momentum.

If the Earth loses mass by natural process isotropically, the orbit will be essentially unaffected. Of course the Earth and Sun orbit around their common center of mass, so if the Earth gets lighter it will have an extremely tiny second-order effect on the orbit, but that's nothing compared to the effect that the outer planets have on the Sun.

Answer 2

The thing that is unaffected by liftoffs is the center of mass of all the material that goes into the rockets and the Earth. Since it is likely the rockets will launch in all directions, if their mass was ever anything to account for (quite unlikely), it would still not affect the orbit of the Earth. Also, the (tiny) reduction in Earth mass would also have little impact, because the Earth mass does not affect its own orbit, and the Earth has very little effect on the orbit of anything else other than the Moon. So there could be a tiny affect on the Moon's orbit, which in turn could affect Earth tides, but we are talking completely unmeasurably small here. Also, launching rockets in the direction of Earth's spin might ultimately produce a (minutely small) reduction in the Earth's spin, but again, hardly measurable even if you launched a million rockets.

Answer 3

Yes, the blast off of a rocket from Earth obeys Newton's 3rd Law: for every action there is an equal but opposite reaction. Think of it in terms of a man firing a gun. The bullet goes one way, the man's shoulder, absorbing the recoil, goes the other way, though only a very short distance because the man is heavier than the bullet. The same principle applies to the rocket fired into space: the rocket goes one way, the Earth goes the other. That is the theory, but because the mass of the Earth is trillions of times greater than that of the rocket, the movement of the Earth in the opposite direction to the rocket is so tiny as to be undetectable and unmeasurable.

Now for the decrease in Earth's mass. Again you must bear in mind that the Earth has trillions of times more mass than a large rocket, so not only is the mass loss trivial, but most of the objects sent into space eventually come back down to Earth. Also. there is a constant rain of space debris into Earth's atmosphere: space dust, meteors, meteorites and occasionally asteroids, so the Earth gains more mass than it loses.

Could loss or gain of mass eventually change the Earth's orbit? No, not to any measurable extent. Just as the mass of the Earth far exceeds any mass that leaves us, it also far exceeds the amount which arrives, so it doesn't have any detectable effect on our orbit.