Falling Body On Rotating Earth (3D)


General Description

This simulations illustrates the trajectory of an object dropped from rest (relative to the rotating Earth) from a point near Earth's surface. The user can set the initial height of the object above (or below) the Earth's surface, as well as the rotational speed of Earth. The motion of the object can be viewed from an inertial reference frame, or from a frame that rotates with the Earth. The simulation can be made to stop when the object hits Earth's surface, or it can allow the object to move through the Earth.

A variety of models can be used to determine the forces on the object once it passes into the Earth. The gravitational forces can be modeled by treating the Earth as a uniform solid sphere, by treating the Earth as a point mass, or by treating the Earth as the source of a constant magnitude attractive force pointing toward Earth's center (with magnitude equal to Earth's surface gravity). There are also options to include a resistive force proportional to the object's speed, proportional to the square of its speed, or no resistive force. The user can adjust the coefficient of proportionality for the resistive force (linear or quadratic).

In this 3D version of the simulation the object can be dropped from any latitude. The simulation can define "up" either as directly away from Earth's center, or as the direction of a plumb line (which includes the centrifugal effect of the rotating Earth). The simulation can also display plots of the object's longitude and latitude as functions of time.

This simulations illustrates the Eastward deflection of a falling body on the rotating Earth (now attributed to the Coriolis effect in a non-inertial reference frame). It also shows that although the object's motion is confined to a single plane in the inertial frame, it is NOT confined to a single plane in the rotating frame. The simulation also serves to illustrate certain aspects of a historical debate between Robert Hooke and Isaac Newton over the path of a body falling through the Earth.


Rotating Frame

This frame shows the motion of the object in a reference frame that rotates with Earth. This frame also includes all of the controls for the simulation.

Inertial Frame

This frame shows the motion of the object in an inertial reference frame.

Latitude Frame

This frame displays a plot of the object's latitude (in degrees) as a function of time (in seconds).

Longitude Frame

This frame displays a plot of the object's longitude (in degrees) as a function of time (in seconds).

Controls (in Inertial Frame)


Todd K. Timberlake (ttimberlake@berry.edu)