Put it in one of the LaGrange points?

I assume you mean 'Earth orbit'.

In any case, Lagrange orbits are very stable.http://en.wikipedia.org/wiki/Lagrange_orbit

L4 and L5 are the most stable and L1 the least (as best I remember).

Some things to point out: (1) Close passing asteroids can mess with even stable orbits (if close enough) (2) Within a Lagrange point there might be multiple masses, each of which is doing a complicated little circular dance; so if you have more than one satellite you might have collisions over that long a period (3) Over a millennia dust abrasion and micrometeors are going to be major issues (4) All Lagrange points are outside the Earth's magnetosphere (aka, the 'Van Allen Belt'), meaning they get the full brunt of solar storms and other extant radiation.

You mentioned it during FOOTPRINTS slushing :)

Brain, brain, what is brain...

zombie food?

I was beaten to the Lagrange points.

But there is another very stable orbital position... Sitting on the Moon's surface.

Sorry, I was unclear. I am thinking of a fictional planet with no major moons, otherwise Earthlike in mass, orbit, etc.

(And I swear I saw an article about an artificial satellite in a million-year+ orbit...)

Thanks! And yes, this can be a dysfunctional orbit -- the artefact is abandoned, but still orbiting. So I'll just leave it as "high orbit".

And I give you...

The checkered panels showed plentiful signs of both the original damage that had slain all occupants, and the millennium of micrometeroids that had since peppered the station. Still, it was in rather good shape.

As the very, very old joke went, it was not remarkable that the dog spoke well, it was remarkable that the dog spoke at all.

Well-done on the -ite/-oid call, too. ;)

I actually had to look that up to make sure I got it right...

I take the credit for being smart enough to know I needed to look it up, and knowing what to look *for*... :D

wot he said.

Also, I don't think it's sufficiently clear from the above that Earth's LaGrange points are not orbits around Earth; they are points relating to Earth's orbit around the sun.

You want to make sure a device stays where you put it for milennia, orbiting Earth? I second jtdiii's suggestion: stick it on the surface of the Moon.

Otherwise, I'd go for something like geostationary orbit. It depends what your aim is.

agree, but I'm not sure if any of the other commenters were. LaGrange points refer to the relationship of two bodies, not one. So it depends on what orbit we're talking about. I haven't gone into it in this much detail, but I imagine the Earth-Moon LaGrange points would be less stable than the Earth-Sun ones.

The question remains if in the long term E-L L4 or L5 would be more stable than geostationary orbit.

I think it also depends on how tightly you define 'stable' for the sake of writing fiction. It could mean something very different if all you want is for the device not to crash back to Earth or wander off somewhere else, or if you want to be able to pinpoint it milennia later.