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Thread: Sidereal, anomalistic and draconic periods of Sun in Milky Way

  1. #31
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    Quote Originally Posted by chornedsnorkack View Post
    Thanks! So within the margin of error the local standard of rest is corotating - Perseus Arm is always 2000 pc outwards and Sagittarius Arm always 1000 pc inwards.
    How far from Sun, in radial direction, are Sunīs periapse and apoapse?
    I think that the Sun's motion through the galaxy appears to be pretty close to circular, with an eccentricity well below 0.1, so that would mean a variation of just a few hundred parsecs or so. However, the orbit is very much non-Keplerian (heck, it bobs up and down through the galactic plane a few times per orbit), and there's quite a bit of opportunity for perturbation during the course of an orbit. So its orbit is not well defined or consistent the same way the orbits of the planets are.
    Conserve energy. Commute with the Hamiltonian.

  2. #32
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    Quote Originally Posted by Grey View Post
    I think that the Sun's motion through the galaxy appears to be pretty close to circular, with an eccentricity well below 0.1, so that would mean a variation of just a few hundred parsecs or so. However, the orbit is very much non-Keplerian (heck, it bobs up and down through the galactic plane a few times per orbit), and there's quite a bit of opportunity for perturbation during the course of an orbit. So its orbit is not well defined or consistent the same way the orbits of the planets are.
    Opportunity for perturbation, but in the absence of such perturbation, is Sun permanently stuck in interarm space? Not reaching an arm by eccentricity (maximum a few hundred parsecs, nearest arm at a thousand parsecs) and not reaching an arm by drift (because corotating)?

  3. #33
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    Quote Originally Posted by chornedsnorkack View Post
    Opportunity for perturbation, but in the absence of such perturbation, is Sun permanently stuck in interarm space? Not reaching an arm by eccentricity (maximum a few hundred parsecs, nearest arm at a thousand parsecs) and not reaching an arm by drift (because corotating)?
    I think that when you say "in the absence of such perturbation" you're missing the whole point of the orbit being highly non-Keplerian. Unlike the planets, orbiting a dominant central mass, where each orbit is almost the same as the last, the Sun's orbit is probably a bit different each time, and is almost certainly not a neat ellipse. Not having any perturbations would be the unusual case. So it probably does wander in and out of the arms over galactic-scale time, even though on average it more or less keeps pace with them.
    Conserve energy. Commute with the Hamiltonian.

  4. #34
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    Quote Originally Posted by Grey View Post
    I think that when you say "in the absence of such perturbation" you're missing the whole point of the orbit being highly non-Keplerian. Unlike the planets, orbiting a dominant central mass, where each orbit is almost the same as the last, the Sun's orbit is probably a bit different each time, and is almost certainly not a neat ellipse. Not having any perturbations would be the unusual case.
    To begin with, like planets or Moon, Sun undergoes apsidal precession, meaning the orbit is rosette-shaped - apside line is not the same each apside.
    This is direct consequence of the mass distribution not being at the centre but extending to Sunīs orbit.
    But the apside line changing with each orbit does not mean apside distance changes!

    What are the perturbations of Sunīs orbit caused by a statistically smooth and axisymmetric distribution of dark matter particles, or of stars?

    And what would be perturbations caused by mass of spiral arms?

  5. #35
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    Quote Originally Posted by Grey View Post
    I think that the Sun's motion through the galaxy appears to be pretty close to circular, with an eccentricity well below 0.1, so that would mean a variation of just a few hundred parsecs or so.
    I found data presented at Wikipedia:
    https://en.wikipedia.org/wiki/Sun#Orbit_and_location
    Those are pretty rare: plenty of sources talk only about circular orbit.
    X direction seems to be te radial direction, so the "width in the X direction", quoted as 691 pc, is the alleged distance between Sunīs periapse and apoapse. Correct?

  6. #36
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    Quote Originally Posted by chornedsnorkack View Post
    I found data presented at Wikipedia:
    https://en.wikipedia.org/wiki/Sun#Orbit_and_location
    Those are pretty rare: plenty of sources talk only about circular orbit.
    X direction seems to be te radial direction, so the "width in the X direction", quoted as 691 pc, is the alleged distance between Sunīs periapse and apoapse. Correct?
    That's pretty cool. But X, Y, and Z look to be rectangular galactic coordinates, rather than polar coordinates. So, that means that the distance from a circular orbit could vary by as much as the 1035 parsecs of the Y coordinate, depending on how the ellipse is aligned when it reaches that. Also note that it mentions that the duration of the "epicycle" is 166 million years, significantly shorter than the time to orbit, so the two won't stay synchronized. And I'd be willing to bet that although this is the current motion of the Sun, it might change significantly over the course of one or more full orbits, given the non-uniform mass distribution of the Galaxy.
    Conserve energy. Commute with the Hamiltonian.

  7. #37
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    From my old Encyclopedia of the Solar System, 2nd Edition (2007):
    The Sun and the solar system are located approximately 8.5 kpc from the galactic center, and 10-20 pc above the central plane of the galactic disk. The circular orbit velocity at the Sun's distance from the galactic center is 220 km/sec, and the Sun and the solar system are moving at approximately 17 to 22 km/sec relative to the LSR. The Sun's velocity vector is currently directed toward a point in the constellation of Hercules, approximately at right ascension 18h 0m and declination +30°, known as the solar apex. Because of this motion relative to the LSR, the solar system's galactic orbit is not circular. The Sun and planets move in a quasi-elliptical orbit between about 8.4 and 9.7 kpc from the galactic center, with a period of revolution of about 240 million years. The solar system is currently close to and moving inward toward "perigalacticon," the point in the orbit closest to the galactic center. In addition, the solar system moves perpendicular to the galactic plane in a harmonic fashion, with a period of 52 to 74 million years and an amplitude of ~49 to 93 pc out of the galactic plane. (The uncertainties in the estimates of the period and amplitude of the motion are caused by the uncertainty in the amount of dark matter in the galactic disk.) The Sun and planets passed through the galactic plane about 2-3 million years ago, moving "northward."
    Grant Hutchison

  8. #38
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    Leading to two pretty different estimates of eccentricity: for the radial distance between perigalacticon and apogalacticon, Wikipedia offers 691 pc, and provides derivation, while Encyclopedia of Solar System offers 1300 pc, without details. What is closer to state of art?

  9. #39
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    Quote Originally Posted by chornedsnorkack View Post
    Leading to two pretty different estimates of eccentricity: for the radial distance between perigalacticon and apogalacticon, Wikipedia offers 691 pc, and provides derivation, while Encyclopedia of Solar System offers 1300 pc, without details. What is closer to state of art?
    I think we are up against the uncertainties in determining the mass distribution in the galaxy. I would have to flip a coin or roll the dice on this one.

  10. #40
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    Quote Originally Posted by chornedsnorkack View Post
    Leading to two pretty different estimates of eccentricity: for the radial distance between perigalacticon and apogalacticon, Wikipedia offers 691 pc, and provides derivation, while Encyclopedia of Solar System offers 1300 pc, without details. What is closer to state of art?
    Wikipedia quotes a secondary source: a paper from 2006, which in turn provides references for its epicycle equation dating from 1959 and 1982.

    Grant Hutchison

  11. #41
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    Some teaching about the epicycles:
    http://www.astro.rug.nl/~ahelmi/gala...class_VI-b.pdf

  12. #42
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    Quote Originally Posted by chornedsnorkack View Post
    Good find. I have forgotten too much math to check it with certainty but it looks good. Let's remind novices who may be reading this that the epicyclic term is not indicative of local orbital motion around some sort of massive object. What we have here is a useful mathematical modeling technique for generating a good approximation of the actual eccentric motion we would see if we could somehow observe the star for hundreds of millions of years.

  13. #43
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    So, the Wikipedia numbers suggest the radial width of epicycle as 690 pc and current location at -205 pc.
    Do I read it right to understand that Sun is now 140 pc from perigalacticon (radially)?

  14. #44
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    Quote Originally Posted by chornedsnorkack View Post
    So, the Wikipedia numbers suggest the radial width of epicycle as 690 pc and current location at -205 pc.
    Do I read it right to understand that Sun is now 140 pc from perigalacticon (radially)?
    Again, that X coordinate isn't always radial. The equations there were using rectangular coordinates.
    Conserve energy. Commute with the Hamiltonian.

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