Imagine a satellite is orbiting the moon. how would the satellite behave if the moon were to suddenly disappear?

When a satelite is orbiting a moon, what makes the trajectory to become circular is the centripetal (gravitational attraction) force between the moon and the satelite (between the two masses). At each point of the trajectory the speed of the satelite is tangent to the trajectory while the centripetal force (and the centripetal acceleration) is perpendicular to the speed (towards the center of the circle).

When the moon disappears this centripetal acceleration disappears so that the speed remains constant. The answer is that when the moon disappears the satelite will continue to move in a line (tangent to the circular trajectory, at that moment) with constant speed.