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This question springs from a comment against my question posted on the Space SE My questions may seem inane, or obvious to most of you real physics people too ...

Any number of sources put the peg the Sun at approximately 99.8% of the total Solar System mass.

If one were to consider any interaction of the Sun with a body exhibiting gravity perhaps several orders of magnitude higher, could the Solar System be assumed to be concentrated in the Sun?

In other words, how much would planetary movement in orbit around Sol be relevant to any interaction of Sol, and another body where the other body is (potentially) several orders more massive than Sol?

p.s. The context for the other body being more massive is available in the original question on Space SE (in case it is relevant/required for an answer here)

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    $\begingroup$ If I'm understanding the space.SE discussion correctly, this is about whether the system consisting of Sagittarius A* and our sun has Lagrange points at various places in the galaxy. In that case, the issue isn't the fact that our solar system is a compound object, it's that there are billions of other stars in the galaxy. $\endgroup$ – Ben Crowell Sep 10 '13 at 19:40
  • $\begingroup$ The general answer to the title question is "To zeroth order, yes. How sensitive are you to corrections?". But that just expresses the tendency of physicists to see everything as a perturbitive expansion. $\endgroup$ – dmckee Sep 10 '13 at 21:59
  • $\begingroup$ @BenCrowell: The other billions of stars didn't even occur to me .... Yet the Galactic Hole may be construed to form the hub for the spiral arms - potentially exerting influence as far out as we are. But that may just be me unwilling to give up my idea (+: /me contemplates genuflection $\endgroup$ – Everyone Sep 11 '13 at 2:41
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You are talking of the concept of center of mass, which is widely used in astronomical and general kinematics problems.

In physics, the center of mass, of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero. The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are often simplified when formulated with respect to the center of mass.

How good an approximation this is in case of the solar system depends on the distance between the solar system and the nearest heavy stellar mass. Consider that the force goes as

gravitation

once the distance is large enough the internal structure is irrelevant .It is only relevant for close encounters .

The center of mass of the solar system is not in the center of the sun, by the way; this also is irrelevant for very large distances.

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  • $\begingroup$ Grand! Fits the question parameters incredibly well! Out of curiosity, where is the centre of mass in the Solar System? $\endgroup$ – Everyone Sep 10 '13 at 18:52
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    $\begingroup$ @Everyone -- for a graph of the movement of the solar system center-of-mass, see: timingsolution.com/TS/Study/cm $\endgroup$ – Johannes Sep 10 '13 at 19:53
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    $\begingroup$ Think of a ball half filled with liquid. If you throw it in the air, its center of mass will follow the expected parabola, the ball itself will be wobbling and turning about its center of mass. From a distance of kilometers only the parabolic path is relevant in defining the trajectory of the ball the wobbliness cannot be "seen" . $\endgroup$ – anna v Sep 11 '13 at 3:28

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