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I imagine it looks a bit like how the Earth looks from the surface of the moon - undulating around a fixed point in the sky. In fact you can see for yourself if you install Celestia. Go to a point on Pluto from which Charon is visible, track Pluto's orbit (Y), enable Options->Show Grids->Grid: Horizontal, accelerate time (L) and you should see Charon bobbing up and down about 20° along the ecliptic.