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Originally Posted by Robert Tulip
1. How close is the position of the barycentre to an arithmetic sum of each individual planetary influence?
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Fairly close, but since gravity isn't a linear function, there will be differences between simultaneous computation of all the planets and the summation of individual computations.
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2. How close an approximation of the barycentre plot will be obtained by calculating the pull of each individual planet on the position of the sun and graphing the combined result?
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Sounds like the first question, except it's obtained graphically, rather than arithmetically - same answer, but with the induced graphic error (by hand? or by computer?)
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3. Is combined planetary gravity significant in addition to individual planetary effects?
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Sounds similar, but this isn't really a question, as there's no qualification of "significant," as in significant as compared to what? Again, combined calculations will differ slightly from the summation of individual effects.