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As we know the predominant theory where does the moon come from is that a Mars size planet hit the earth and took a chunk out of it which eventually materialized into moon.

My question is that if a Mars size object were to hit Earth, wouldn't it knock it off the orbit all together? What kind of collision is required to knock a planet of its orbit. By 'knock off' I mean it would alter the orbit of Earth and possibly speed so that it will not have stable orbit anymore so it will either (gradually) leave solar system or (gradually) collapse into sun.

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The hypothetical collision has been mathematically modeled, and the results of those models are consistent with what see.

The impacting body (referred to as "Theia") would have hit at a low velocity and relatively shallow angle. It would certainly have affected the Earth's orbit, but not enough to knock it out of the Solar System or into the Sun.

Knocking Earth out of the Solar System would require speeding it up by about 40% (escape velocity is sqrt(2) times circular orbital velocity), which means doubling its kinetic energy. This would require a high-velocity impact by a body whose mass is comparable to Earth's -- which would probably be enough to disrupt the planet altogether, creating a new dense asteroid belt. Theia is believed to have been about the size of Mars, which has only about 10% of Earth's mass.

Ignoring gravitational influences from other bodies, any solar orbit is stable, as long as the velocity is greater than zero (so it doesn't fall into the Sun) and less than solar escape velocity.

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+1 for "any solar orbit is stable...." Laypeople, as demonstrated by OP, seem to sometimes think there are special orbits and if you knock something out of the rut, something radical happens. – ThePopMachine Jul 30 '12 at 22:25
@ThePopMachine: In the original Star Trek, the ship's orbit around a planet was often portrayed as unstable, requiring power to maintain it. That may actually be part of the reason for the misconception. – Keith Thompson Jul 30 '12 at 22:39
If the Enterprise's orbit was low enough it would indeed be unstable due to atmospheric drag. The orbit of the International Space Station is unstable for exactly this reason, and it needs occasional nudges to keep it orbiting at a constant distance. – John Rennie Jul 31 '12 at 5:40
@zadane: Only if they're low enough to experience significant atmospheric drag. Manned satellites (the shuttle, ISS, Skylab, Mir, etc.) tend to be launched into as low an orbit as practical, because it's cheaper, and because you need minimal fuel to re-enter and go home; that's worth the expense of an occasional re-boost. GPS satellites orbit at about 20,000 kilometers, and geosynchronous communications satellites are about about 36,000 kilometers; they experience no significant drag, and their orbits are much more stable. – Keith Thompson Aug 1 '12 at 2:41
@zadane: No, that's not how it works. Drag doesn't just slow the satellite's motion by x; it slows it continuously over time. Gravitational force pulls a satellite towards the body it's orbiting, and for a stable elliptical or circular orbit it just curves the satellite's path. Drag always acts opposite to the direction of motion, slowing the satellite down and changing its orbit. – Keith Thompson Jan 16 '13 at 15:57

There are no simple orbits that gradually spiral in or out. In the two body system orbits are either closed ellipses or open (hyperbolic) with the (barely open) parabolic orbit as the dividing case.

The decay of the orbits of artificial satellites is due to interaction with the Earth atmosphere.

There is an interesting questions here: how do we come to have a near circular orbit in this epoch given that such an event would likely have left the Earth/Moon system with a substantial eccentricity in the immediate aftermath?

Perhaps one of our astronomers can provide some insight.

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Do gravitational interactions with other planets tend to circularize orbits over time? – Keith Thompson Jul 30 '12 at 22:04
@KeithThompson Don't know in general. They can hold certain types of resonances together. – dmckee Jul 30 '12 at 22:05
It's possible, but unlikely, that Earth's orbit was eccentric before the collision and nearly circular after. – Keith Thompson Jul 31 '12 at 2:08
@KeithThompson I imagine circularizing is possible but not easy with that mechanism, given how far apart things are in our SS. dmckee: A bunch of colleagues and I just had fun working this out, and we found that even the worst case scenario (Mars-sized object hitting Earth w/ enough energy to liberate a lunar mass, at just the right angle to maximize change in eccentricity, assuming minimal transfer of L into spin of Earth) does not induce terribly much eccentricity. – Chris White Jan 30 '13 at 0:28

What kind of collision is required to knock a planet of its orbit.

It actually wouldn't require a collision. If a sufficiently massive object passed very close to Earth, the gravitational interaction (no collision) might eject Earth out of the solar system.

Here's an article about a conjecture that a 5th gas giant was ejected from our solar system.

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