What experiment could you do to determine whether the other planet is spinning, or your planet is revolving around it while facing it?
check whether you are experiencing a centrifugal force.
Regarding your answer, standard physics seems to indicate that you can tell the difference, unless the laws of physics change to violate newton's laws when there are fewer than 3 bodies. Mach proposed this (I think) but people seem to doubt him.
The universe adheres to General Relativity, not Newton's laws. What does GR say about the effect of spinning and revolving bodies?
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