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Ignore how it got there in the first place. Assuming that this satellite has any instruments we have already built or we can proveably build (meaning it is physically possible to build and put into space with known science). The only limitations is that it can be no bigger than the ISS. Fuelling is not a factor.
Round one: normal communications at light speed.
Round onepointfive: arbitrarily high bandwidth (applies to the next two rounds).
Round two: communication between earth and the satellite is negligible but finite.
Round three: instantaneous communications with satellite and perfect knowledge that both antennas are precisely one lightyear apart at all times.
Bonus round: please give this spaceceaft a cool name.
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