"Bald Eagle" <cre### [at] netscapenet> wrote:

>
> [from Feynman's lectures, calculating all the positions of all the planets in the
Solar System]...
> "We need nine columns for the motions of Jupiter, nine for the motions of
> Saturn, and so on." [snip]
>
> http://www.feynmanlectures.caltech.edu/I_09.html
>

Here's something interesting to consider: In that particular part of the
lecture, Feynman is basically discussing the "n-body problem." The method
Feynman uses to get the results of all the interacting planetary positions is a
numerical *summation*, of the values in his list(s) of figures. As such, the
result is an approximation (which can be made more and more precise, but is
still an approximation.) In his previous simpler example-- the motion of a
spring-- he also uses a list of found values, but then notes that there is an
actual *equation* x=cos(t) that describes the situation exactly.

As far as I know, there is no exact solution or *equation* for solving the
"n-body problem", except for special cases where one or more of the variables is
simplified.

I think this is the reason why interplanetary spacecraft need 'course
corrections' every now and then, to arrive at their destinations. There are just
too many interacting variables to consider.

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