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## L1 Stability

If something was magically placed at the Earth-Sun L1, how long would it take for it to move a few thousand kilometers (from the perspective of the Earth, as Jens pointed out)? Would it be on the order of years, thousands of years, or millions of years?
Last edited by larrew; 2012-Feb-09 at 12:07 AM. Reason: Clarification

2. When you say "move a few thousand kilometers," from whose perspective do you mean? From the perspective of the earth?

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Yes, from the perspective of the Earth.

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I'll guess one month = 1000 kilometers drift from Earth-Sun L1, after which it would likely move away faster. Perhaps 2200 kilometers at the end of the second month. It would depend somewhat on where Earth is in it's orbit around the Sun at the beginning of the month, as in near perigee or near apogee. Station keeping thrust is trivial if you correct before the error is 1000 kilometers. Jupiter and Venus also produce a bit of drift. Over part of each year the drift would be in approximately the opposite direction. L1 moves farther from Earth when Earth is farther from the Sun, approximately: Then moves closer to Earth as the Earth-Sun distance decreases. Please correct, refute or embellish. Neil
Last edited by neilzero; 2012-Feb-09 at 01:05 AM.

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Thanks for replying neilzero! I was actually talking about the Earth-Sun L1 point, which means no drift due to the Sun (which I assume was by far the biggest factor). Jupiter is still a problem though

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I just tried this in Gravity Simulator. I set up a 3-body simulation: Earth at 1 AU around the Sun, and in a perfectly circular orbit, and a test particle placed directly on L1 with a velocity that gave it a period identical to Earth's. Theoritically, it should remain there forever, as there is nothing to perburb it away. But since the computer uses double precision variables and a non-zero time step, it got numerically perturbed. It took 13.5 months to drift 1000 km.

I tried it again. This time I added Jupiter at 5.2 AU. This time it only took about 8 months to drift 1000 km.

The Earth's eccentricity and the contribution by the Moon will be much more perturbing than Jupiter. I didn't try these because I didn't want to spend the time to re-compute the position and velocity of L1 under these circumstances. But at least you have something to go by. It will drift by 1000 km in a matter of months or sooner. I'll go with neilzero's guess.

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Thanks everyone! I'm guessing you're probably roughly right.

I guess I vastly underestimated the effects of the gravity of other bodies, because I was guessing around a couple decades.

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I'd think the biggest perturber would be the eccentricity of Earth's
orbit causing the Earth to speed up and slow down relative to your
object. Second would probably be Venus's gravity when it comes
around the near side of the Sun.

-- Jeff, in Minneapolis

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