Orbital Motion in the Two-Body Problem

This is an animation of two bodies moving under the action of mutual inverse-square gravitational attraction. The blue dot represents the primary, the more massive of the two bodies. The red dot is the less massive of the two bodies (the secondary).  The white dot is the center of mass of the two-body system which moves along a straight line at uniform speed.  The blue and red curves are the orbits of the two bodies as seen by an observer in an inertial frame moving with the center of mass. Notice that each of these two curves is an ellipse with its focus at the center of mass. The black curve depicts the orbit of the secondary as seen from the primary. An observer located on the primary will see the black curve as stationary. Notice that the black curve is an ellipse with its focus at the primary, as Kepler's Law of Orbits predicts. Notice also how both the bodies speed up as they approach each other and slow down as they recede from each other. This is a consequence of Kepler's Law of Areas.

Ground Trace of an Earth Satellite

The ground trace of a satellite is the curve traced on the surface of the rotating earth by a point directly underneath the satellite. The animation on the right shows the satellite (shown by a pink diamond) tracing out the red ground trace on a Mercator map of the earth. The black curve shown in the animation is the curve that is obtained by simultaneously projecting all points of the satellite orbit on the surface of the earth. This orbital projection appears to move against the map because of earth's rotation. The satellite traces out the red ground as it traverses the black orbital projection which itself moves relative to the earth. The ground trace thus results from the combined orbital motion of the satellite and the rotational motion of the earth, and helps to visualize the motion of the satellite as seen from the earth. The ground trace directly shows locations that the satellite is going to pass over. On the other hand, at any instant the moving orbital projection shows locations on the earth's surface that currently happen to lie in the plane of the satellite's orbit, but not necessarliy directly below the satellite. The best time for launching a second spacecraft into the same orbit is when the orbital projection passes through the launch site.

                                                        The animations appearing on this page were created with help from Debashish Bagg.