Theory of the N-Body Problem
June 9, 1996
13
As mentioned in the start of this section, the velocity of the comet at any given
point of time will be the slope of the position curve. (That is, the velocity is the derivative
of the position). The places where the position function is not changing (i.e. the tangent to
the curve is a flat line) are the places that velocity function will cross the
t
axis. The places
where the position function is changing the quickest is where the velocity function is the
largest. Looking at FIGURE 8. and FIGURE 9. we can see that this is the case. Note that
the velocity curves are even sharper than the position curves. Had the comet's orbit been a
circle, the velocity functions would have been the sine and cosine functions.
FIGURE 8. The X component of the velocity as a function of time
FIGURE 9. The Y component of the velocity as a function of time
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