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.
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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.
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