 Theory of the N-Body Problem
June 9, 1996
11
FIGURE 5. shows the x and y positions of the comet with the sun located at (0,0).
As the comet moves around the sun, the force of gravity is always pulling the comet
toward the sun. The momentum of the comet keeps it moving in a direction that is slightly
away from the sun. When the comet is closest to the sun, it will be moving the quickest
and it will have the most force exerted on in.
While showing both the x and the y locations of the comet in one plot lets the orbit
of the comet be seen clearly, it is also possible to show just the x or y component of the
position as a function of time, as in FIGURE 6. and FIGURE 7. These plots let us see how
quickly each component of the position is changing, as both the x and y component do not
change at the same rate. As you can see, both graphs are very vaguely sinusoidal. Had the
comet's orbit been a perfect circle, these graphs would have been perfect cosine and sine
functions. The comet never gets within 10 units of the sun and yet the position functions
already show some large changes in a short amount of time. Most comets are even more
elliptical, which would cause the graphs to become even more distorted.
t
t
= equal time periods
FIGURE 5. An X-Y plot of a two body system
Sun