Model of Ocean Tides This animation shows tidal forces and displacements of 4 lakes due to tidal forces. This is a rather extreme example of a tidal model because the eccentricity of the orbits is large so that the net tidal forces are very much larger at closest approach (perigee) than at farthrest distance (apogee). Also, in order to show the orbits as well as the planet and moon, the ratio of planet radius to the moon orbit's a parameter is reasonably large. The tidal forces at the rim of the planet are obtained by computing the gravity force on an arbitrary particle at angle phi and then subtracting off the force on the same mass particle located at the center of the planet sphere. Similar forces at radii less than the rim are also computed and these force magnitudes are plotted with a color plot where red is the largest force and blue is the smallest force. To see the tide force effects on motion of water, I show 4 lakes located near the rim and at longitudes, 0, 90, 180 and 270 degrees. Assuming that the bottoms of the lakes have a parabolic shape, then the displacement of the lake shorelines due to the tide forces will be approximately proportinal to the forces at theur centers. This displacement is a lot larger at closest approach (perigee) than at apogee and that displacement is shown and should be easy to see. Click Here for Force Equations
wE rP mRatio a eps Single Step Show Net Force Vectors Net Force Magnitude Color Plot