Description

This simulation illustrates the fall of an object on a rotating Earth. Two views are shown. The view on the left shows a frame that is co-rotating with the Earth (so the Earth itself appears to stay still). The view on the right shows an inertial frame in which the Earth is seen to rotate counterclockwise. The dropped object appears as a red ball. A green plumb line runs from the object's location downward. The plane of the object's inertial motion (the plane formed by the line from the object's initial position to the Earth's center, and the object's initial velocity vector in the inertial frame) is shown in magenta. The user can adjust the simulation speed, the height from which the object is dropped, the latitude from which the object is dropped, and the rotation rate of Earth.

Options allow the user to use "true down" (i.e. toward Earth's center) rather than "effective down" (i.e. the direction of the effective gravitational field which incorporates the centrifugal force). In addition, the user can choose whether or not to show the Earth and the inertial plane, whether or not to make those things transparent, and whether or not to show the trace of the object's motion or the plumb line. Note that it is best to avoid making both Earth and the inertial plane transparent, as the intersection of the two surfaces will not be clearly shown.

The user can select whether or not the object should be allowed to pass through the Earth's interior (if not then the simulation pauses when the object hits Earth's surface). In addition, the user can select from various models for the gravitational force in the interior: treating the Earth as a uniform density sphere, treating the Earth as a point mass using a central force whose magnitude is always equal to the object's weight at Earth's surface. Finally, the user can choose whether or not to include resistive forces in the Earth's interior, with options for linear or quadratic resistance (with adjustable resistance coefficient).

Plots of longitude and latitude versus time are shown at the bottom. The longitude is measured eastward from the launch point. These plots are most useful when the simulation is set to pause when the object hits the Earth's surface. The plots can then be used to estimate how far to the east or south form its launch point the object will fall.