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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