The first is due to the center of the Milky Way and the second is due to the Solar System, these are obvious orbits. That doesn't mean we KNOW THE SUN'S PRECISE MOTIONS EXACTLY, which seems to be the foolish assumption you are trying to provide support for.
I don't need to prove anything ol chap. You are the one that needs to show evidence that what you claim is fact.
What I have said, is accepted mainstream opinion
...so other stars provide support for stars orbiting stars? Ok....Thanks for appreciating that is a reality.

As I have pointed out, that situation is observationally verified. We see the Centauri system for example....well at least those instruments you seem not to have much faith in, sees the individual stars in that system, which cannot be discertained by normal eyesight.
We call that instrument a telescope.
Our Sun has no such companion.
You even went so far as to show evidence of a system that orbits ON THE SAME ORDER OF MAGNITUDE. But let's ignore the significance of that, since we ignore everything else.
You mean ignore the Sun's imaginary companion???

The same Imaginary companion that instruments such as telescopes have not seen?..But which you say must exist to reinforce your shattered ego and support your nonsesne hypothesis?
"unsupported dribble"--simply because you don't understand the support doesn't mean it is unsupported. Perhaps you should consider this "often heard hypothesis" of "some hidden companion" finds EVIDENCE in the solar cycles. Or continue to assume you, and the scientific community as a whole, knows everything.
It is unsupported because we have nothing to indicate it could exist.
You may need to put it down to an unseen companion, much as your unseen God, I prefer to put it down to more mundane reasons.....like Jupiter/Saturn gravitational Interactions, like the uneven rotations the Sun experiences, based on whether one is at the equator or poles, the cooler Sunspot regions, the twisted magnetic field lines, the incredible Fusion machinery involved in the Sun itself.
Plenty of explanatory reasons to explain the solar flares, all rather natural mundane Occam's razor type of reasons, and all far more likely than some nonsensical unevidenced, unseen, Imaginary companion that you see the need to propose.
I bet you truly BELIEVE the Big Bang, don't you?
Yep, sure I do.
I align with what the overwhelming evidence tells us, and what has been accepted by mainstream as by far the most likely.
Even our hypocritical Catholic Church has seen the need to recognise the BB, as well as Evolution, due to the staggering amounts of evidence that supports it.
That our observation power is limitless in an infinite universe, that our knowledge is supreme. So many fallible steps made, your whole belief hinges on each assumption, that is so unfortunate. Do you KNOW what assumptions you believe without thought?
No, our observations are not limited...they are contained to t+10-43 seconds after the BB, up to the present, and entails around 96 billion L/years diameter, or the parameters of the observable Universe.
I accept assumptions based on logic, and good sample sizes, such as Isotropy and homegenity.
I do not accept some imaginary deity that made everything from nothing.
In fact mainstream science in many respects are moving towards a position where they maybe able to illustrate quite reasonably, that any such deity is redundant and unneccessary.
http://preposterousuniverse.com/writings/dtung/
Whether you accept legitimate scientific reasoning and evidence, or whether you accept some mythical deity invoked by ancient man to explain the wonders of the Universe is your business.
But I will [and others will] continue to refute your bullshit driven by your fanatical belief in whatever mythical deity you chose to believe in.