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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

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/

deleted 6y ago
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hiccuphippo 6y ago
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.
iamgopal 6y ago
Daily we receive about 72000 kg.
- csunbird 6y ago
  We also probably lose somewhere near that from atmosphere.
spenczar5 6y ago
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.html https://faculty.virginia.edu/skrutskie/ASTR1210/notes/orbeq...., for example). It matters for the moon in theory, but not in practice. The moon needs to move at 1,001m/s to stay in orbit (formula: https://www.wolframalpha.com/input/?i=+sqrt%28G+*%28mass+of+the+earth%29%2F+distance+to+the+moon%29+ https://www.wolframalpha.com/input/?i=+sqrt%28G+*%28mass+of+...). If we added the mass of the entire asteroid belt to the earth's mass... it would still be the same within a rounding error; the orbital velocity changes by a tiny amount (https://www.wolframalpha.com/input/?i=+sqrt%28%28gravitational+constant%29+*%28%28mass+of+the+earth%29+%2B+total+mass+of+asteroid+belt%29%2F+distance+to+the+moon%29+ https://www.wolframalpha.com/input/?i=+sqrt%28%28gravitation...).
pp19dd 6y ago
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. Doubling mass of our moon wouldn't change the orbit: https://public.nrao.edu/ask/what-would-happen-to-the-orbit-of-the-moon-if-it-were-twice-as-massive/ https://public.nrao.edu/ask/what-would-happen-to-the-orbit-o... 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" [1] http://curious.astro.cornell.edu/our-solar-system/39-our-solar-system/the-earth/other-catastrophes/58-how-big-a-change-in-the-earth-s-orbit-would-be-required-to-destroy-all-life-intermediate http://curious.astro.cornell.edu/our-solar-system/39-our-sol... [2] http://orbitsimulator.com/gsim.html http://orbitsimulator.com/gsim.html

deleted 6y ago

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hiccuphippo 6y ago

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.

iamgopal 6y ago

Daily we receive about 72000 kg.

csunbird 6y ago
We also probably lose somewhere near that from atmosphere.

spenczar5 6y ago

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.html https://faculty.virginia.edu/skrutskie/ASTR1210/notes/orbeq...., for example). It matters for the moon in theory, but not in practice. The moon needs to move at 1,001m/s to stay in orbit (formula: https://www.wolframalpha.com/input/?i=+sqrt%28G+*%28mass+of+the+earth%29%2F+distance+to+the+moon%29+ https://www.wolframalpha.com/input/?i=+sqrt%28G+*%28mass+of+...). If we added the mass of the entire asteroid belt to the earth's mass... it would still be the same within a rounding error; the orbital velocity changes by a tiny amount (https://www.wolframalpha.com/input/?i=+sqrt%28%28gravitational+constant%29+*%28%28mass+of+the+earth%29+%2B+total+mass+of+asteroid+belt%29%2F+distance+to+the+moon%29+ https://www.wolframalpha.com/input/?i=+sqrt%28%28gravitation...).

pp19dd 6y ago

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. Doubling mass of our moon wouldn't change the orbit: https://public.nrao.edu/ask/what-would-happen-to-the-orbit-of-the-moon-if-it-were-twice-as-massive/ https://public.nrao.edu/ask/what-would-happen-to-the-orbit-o... 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" [1] http://curious.astro.cornell.edu/our-solar-system/39-our-solar-system/the-earth/other-catastrophes/58-how-big-a-change-in-the-earth-s-orbit-would-be-required-to-destroy-all-life-intermediate http://curious.astro.cornell.edu/our-solar-system/39-our-sol... [2] http://orbitsimulator.com/gsim.html http://orbitsimulator.com/gsim.html