Book: # 5

Using computer generated animation this demonstration shows the behavior of two bodies attracted to each other by a force varying inversely as the square of the separation of the bodies (e.g., gravitational force field).  The initial velocities in each case are chosen so that the center of mass of the system remains at rest. 

NOTE:  The conventions used in the film are all shown in the figure:  the size of the circle shows the mass (2:1 ratio), the direction of force is along the arrow and the magnitude of the force is proportional to the length of the arrow, the center of mass of the two-body system is marked by a cross, and a line traces the path of each body.

In the first scene the initial velocity is zero and the bodies pull each other together.  As the bodies move  toward each other the force (arrows) increase as 1/R*R; just before they collide the forces get so large that the arrows representing them extend off the screen.  In the following three scenes the initial velocities of the bodies are chosen so that the two bodies would orbit about each other forever in closed elliptical or circular paths;  the kinetic energy is less that the absolute value of the potential energy - the bodies remain captured in periodic orbits.  The initial velocities in the last scene are so large the bodies fly apart along hyperbolic paths;  the kinetic energy is greater that the absolute value of the potential energy - the bodies have velocities greater that that necessary to escape from the force field between them.