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Questions regarding the mechanics or attributes of objects falling 'around' other objects, thereby orbiting them.

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How could a satellite follow Earth around the Sun while staying outside of Earth's orbit?

I'm wondering if its possible for a satellite to follow Earth around the Sun while staying outside of its orbit. … I read something about objects in L4 or L5 zone taking about a year to orbit earth. I assume that might produce a similar result for what I'm looking for, and maybe its simpler? …
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