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What are the orbital parameters of the Sun such as orbit velocity etc in it's orbit around the Solar System's center of mass? Consider the Sun pointlike or alternatively when talkin about the Sun's movement I mean it's center of mass.

Do not tell me that the Sun is stationary because the planets' masses can be neglected. I do no want such oversimplifications.

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  • $\begingroup$ Welcome to astronomy SE. Your question currently sounds like a "do my homework for me" kind of question, which is off-topic here. Please edit your question to include detailed explanations of your attempts to answer your own questions, and describe specifically the concepts that confuse you. Otherwise, this question will likely be closed as off topic. $\endgroup$ May 24 at 14:14
  • $\begingroup$ Do I really have to explain what orbital parameters are? This is a question in celestial mechanics and it's got nothing to do with formal education. $\endgroup$
    – Pete
    May 24 at 14:18
  • $\begingroup$ No, it's more about the concepts. For example see the question that your question is a duplicate of. $\endgroup$ May 24 at 20:02
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    $\begingroup$ @DaddyKropotkin Then have a look at I can't find this site's “homework policy” or find out how “suspected homework question askers” should be treated in meta. "There is NO prohibition against homework questions here at Astronomy. StephenG's comment that he was voting to close for suspicion of homework was ill-advised and had no basis in site policy." Stack exchange works by applying the same basic tenants to all questions and all users evenly and equally. We work hard to avoid "this sounds like" thinking whenever possible. $\endgroup$
    – uhoh
    May 24 at 21:47
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    $\begingroup$ @uhoh Sorry, homework is an open discussion here, I'm still used to Physics SE. astronomy.meta.stackexchange.com/questions/87/homework-policy $\endgroup$ May 24 at 22:49
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Since the Solar system is a multi-body system (with $N>2$ bodies of significant mass), the orbits of its constituents are not exact Keplerian orbits.

To lowest order, each planet orbits the Sun (or rather the centre of mass of all interior planets) on a Keplerian orbit, but the interactions with the planets as well as the fact that the centre of mass of the interior is not fixed lead to deviations of the true orbit from this simplification. These deviations can be treated either numerically or via perturbation theory, but are non-trivial functions of time.

The same holds for the Sun: to lowest order one can neglect all planets but Jupiter (which is more then twice as massive as all the remaining planets combined), when the Sun follows an elliptic orbit with semi-major axis of about 0.005AU (smaller than that of Jupiter by their mass ratio). This is of the same order as the radius of the Sun, i.e. the barycentre of the Solar system hardly leaves the Sun. However, as above, the pull by all other planets lead to a deviation from this simple model. Again, these deviations are non-trivial.

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