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When the Earth passes by Mars they exert a slight gravitational pull on each other, but the force is so small that their orbits are not significantly disturbed.

However, if we imagined that the orbits of the Earth and Mars were coplanar and much closer to one another, then there would presumably be some critical distance at which they would move together and collide.

What is that critical distance? In other words, if we shrunk the radius of the orbit of Mars, how much would it have to shrink before a collision would occur by the natural force of gravity between the two bodies?

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    $\begingroup$ Why do you think they would collide? Direct collisions are very improbable without friction. If anything, they would exchange angular momentum and fly off on different paths. $\endgroup$ – AtmosphericPrisonEscape Feb 11 at 12:12
  • $\begingroup$ @AtmosphericPrisonEscape Because gravity causes objects to move towards each other. $\endgroup$ – Tyler Durden Feb 11 at 12:15
  • $\begingroup$ Why do you think do we not fall into the sun? It also exerts gravity onto Earth. How are satellites able to orbit Earth, instead of falling onto it? $\endgroup$ – AtmosphericPrisonEscape Feb 11 at 12:16
  • $\begingroup$ I shrunk the orbit of Mars in a simulator some millions kms, and Mercury, Venus, Mars and the Earth got tossed from the solar system $\endgroup$ – Pablo Feb 11 at 21:18
  • $\begingroup$ When you shrunk the orbit of Mars what I think it happens is this. Earth and Mars arent in the same position in their orbits, first Mars orbit is pulled down when Earth gets closer and it ends orbiting closer to the sun than Earth, later when Earth passes again (now Earth is further away to the sun) it's pulled out so it ends orbiting further away, this cycle happens many times until Earth changes its orbits enough as for Mars being tossed away of the solar system $\endgroup$ – Pablo Feb 11 at 21:45
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It's more likely that perturbations by another planet might induce a collision.

In other systems with bodies in almost the same orbit, what happens is like a game of orbital catch-up: one overtakes the other, then they swap places, so in your (rather vague) scenario, that might well be the outcome instead of an outright collision.

Some of the Saturn ring moonlets interchange positions, for example.

The solar system is stable over a timeline of millions of years (as far as we know), but there have been instabilities in the past, and due to "butterfly effects" instabilities could occur in the future. (See also https://plus.maths.org/content/rocks-suggest-theres-chaos-solar-system)

Have a play with a simulator such as orbitsimulator.com !

http://orbitsimulator.com/gravitySimulatorCloud/simulations/1433364162018_Solar%20System.html

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