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.