## Epicycle Arising from Coriolis Force |

Non-rotating (inertial) Frame (Left: A) and Rotating Frame (Right: B) In a frame B that rotates with constant angular velocity relative to an inertial frame A, the accelerations (forces) that appear in frame B are given by:
In our case, frame B rotates with the galaxy: so
The animation shows two views of a system in which there is a centripetal force (in this example, the force is harmonic, i.e. The right hand image is the same motion but seen in a frame rotating at the mean orbital frequency (so the periphery now looks stationary). From this frame, the particle seems to execute a retrograde circular epicycle. Notice the acceleration is always perpendicular to the velocity in this rotating frame. This particular animation (from the wikipedia) matches a well-known illustration of the Coriolis effect: a concave paraboloid bowl gives the harmonic centripetal force, and a dry-ice-puck moves without friction across the surface, in an "orbit". One can spin the bowl at just the right rate so that the puck can remain stationary (moving in a circle in the inertial frame). Perturbing this sends the puck in a non-circular "orbit". A camera rotating with the bowl now sees just the epicycle. |