Theory of the N-Body Problem
June 9, 1996
15
If, instead of just two bodies, we had plotted the case of four bodies, all of these
functions would have become much more complex. A few things would have remained
constant though: there would have been large time periods where the functions would
have been very smooth and slowly changing, and there would have been short periods of
times where large fluctuations would occur. While these sharp peaks represent a small
amount of time, they represent a fairly large distance in the x-y plane. Take the time period
from around 3900 to 4800 as an example. While it takes around 6000 time units for the
comet to orbit the sun, this small 900 unit time period accounts for a surprisingly large
proportion of the ellipse. (See FIGURE 12.)
While the spikes in the graphs look very sharp, under closer inspection (See
FIGURE 13.) we see that the functions are still very smooth. Later on, it will be shown
these functions will always be smooth, when looked at close enough. There can never be
any jumps or sharp bends in the functions.
FIGURE 12. Path of the comet during the spikes
t=3900
t=4800
Previous page    Home    Table of Contents    Next page
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
This document is best viewed as n-body.pdf because the translation to html was buggy.