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I know that a 'sun day' is the time that a sun spot takes to orbit one time across the suns surface (25-30 days dependent on location I think) and what is actually defined as a 'sun year' is how long it takes for our solar system to orbit the galaxy.

But I would like to know how long it takes for the centre of the sun to return to its starting point, hence the caption marks marks around 'sun year'

Am I correct to think that the sun translates a very little bit because of the planets rotating around it?
Is it even measurable?

edit: by sun year i mean my definition of sun year, not the standart definition

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  • $\begingroup$ Wait, you have two questions here. One about the time for the sun to orbit the center of the galaxy (is that not googleable?). Second about the effect of planets, right? $\endgroup$ – Bernhard Oct 11 '15 at 14:01
  • $\begingroup$ no, i know that it takes ~ 250 mil. years for the sun to orbit around the galaxy, i only want to know how long it takes for the center of mass of the sun at a given time to move and return back to that spot relative to that spot. $\endgroup$ – this.foo Oct 11 '15 at 14:06
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    $\begingroup$ Then I do not get at all what you are asking. You already answered your question "How long is a sun year?" with this comment? $\endgroup$ – Bernhard Oct 11 '15 at 14:15
  • $\begingroup$ @Bernhard if you ignore the rotation around the galaxy, and only focus on the solar system, how long does it take for the tiny translations of the sun caused by planets to revert the sun to its original position. (for instance, we measure the exact location of the com of the sun at a given point in time, and wait for the com of the sun to return back there, ignoring translation around the galaxy) $\endgroup$ – this.foo Oct 11 '15 at 14:27
  • $\begingroup$ The problem with this question is that it assumes there's a way to measure an absolute position. We can't measure the "exact location" of a "spot relative to that [same] spot." We can only measure relative locations, and taking any reasonable reference point (I.e. one of the Sun's own planets) gives us an answer of "one [reference planet] year." $\endgroup$ – Asher Oct 11 '15 at 14:39
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The Sun will never return to the 'same spot' (e.g. relative to the Solar System centre of mass) because the orbital periods of Solar System bodies are not all rational multiples of each other. By far the largest influence on the Sun's position is caused by Jupiter (can check this by computing the force exerted by each planet). So to a decent approximation, the period of the Sun's year as you've defined it is 1 jovian year.

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  • $\begingroup$ "[A]re not all rational multiples of each other" strikes me as missing the point. (Are you indeed suggesting that some of those divisions yield irrational numbers? That would be nitpicking to the extreme.) Of course, there is some (possibly big-ish) number of years that will (roughly, but close enough) fit multiples of all bodies' orbital periods (assuming they have stable orbital periods, which they do not - in the long run). $\endgroup$ – Řídící Oct 11 '15 at 16:46
  • $\begingroup$ @GlenTheUdderboat They are irrational - as you say, the periods aren't quite constant, and the irrationals outnumber the rationals by infinity-to-one, so the period ratios are necessarily irrational 100% of the time. It's not so much nitpicky as true, but as you point out doesn't matter that much because the orbits aren't long-term stable. $\endgroup$ – Kyle Oman Oct 11 '15 at 20:38
  • $\begingroup$ Thanks for that probabilistic argument. It is slightly handwavy towards the first conclusion in the answer, but you are convincing. +1 $\endgroup$ – Řídící Oct 12 '15 at 5:31

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