Excuse my ignorance but a funny thought popped up in my head. If we start bringing material from asteroids the total mass of Earth will increase over time. How much material can we bring on Earth safely without affecting the Moon and our planet's course around the Sun?
I feel this question belongs to /r/theydidthemath/
For what it's worth, estimated combined mass of all currently cataloged asteroids in our system (currently just over 1 million) is less than our moon's.
Edit: just found my notes. Awhile back I tried to reason out how fast we'd get in orbital trouble if we started ejecting all of our garbage into the sun, just an academic exercise. Rough estimate by an established astronomer [1] was that we're safe in the 0.95 AU - 1.69 AU range, so our orbit could vary from -7.25 mil km to +54.7 mil. km and we'd stay within the habitable zone. After that I plugged known values into an orbital simulator [2] and eyeballed how much mass loss that'd have to be and how long it would take.
5,973,600,000,000,000,000,000,000 (kg) mass of the earth
597,360,000,000,000,000,000 (kg) we're in slight trouble at 0.0001 loss
50,000,000 (kg) per year normal loss to space
126,642,989,704 (kg) garbage landfilled per year
242,944,073,372 (kg) handled total per year
World est: 2,010,000,000,000 (kg) per year (300 mil years!)
Another astronomer on mass: "If the force of gravity was halved, [Earth's] speed would be exactly the escape speed. In fact, any body orbiting in a circular orbit would become unbound if the force of gravity was reduced by a factor of two"
The mass of the earth is irrelevant for its orbit around the sun, so there's no effect there. That's why comets, asteroids, motes of dust, and planet can all maintain orbits (see https://faculty.virginia.edu/skrutskie/ASTR1210/notes/orbeq...., for example).
Meteorites fall on Earth all the time so I wouldn't be worried about that. Also we've removed lots of mass from Earth with all the stuff we've put up in space.
