Identify the motion of earth that causes these stars to appear to move in a circular path.

The rotation of the Earth on its axis makes it look like everything
in the sky is moving in a circular path.

-- The Earth is rotating.

-- We are rotating along with it.

-- In order to keep looking at the same object in the sky, you must
constantly change the direction in which you're looking.

-- You can't feel the Earth rotating, so as you keep changing
the direction of your eyes to follow the object, your brain interprets
that to indicate that the object itself is moving in a circular path
across the sky.