apodman wrote:So then I looked back at the picture to try to apply the principle to the actual geometry. I couldn't see it, so I thought of projecting the positions (and therefore angles to the A-B line) back in time. Wondering what direction they each came from
... not to mention where the actually are. The picture seems to give no clear hints on whether the galaxy to the right is in front of or behind the one to the left, nor whether we're seeing it from the top or from below.
apodman wrote:Eddies move parallel to their own plane of rotation. Same for wheels and little plastic flying saucers. So I'm predisposed to view galaxies the same way - moving in their own plane of rotation. But is this true? Is a spiral galaxy's plane of rotation related to its line of travel at all?
I don't see how it could be. Excepting tidal encounters, the disc will keep its orientation, while the galaxy's center-of-mass moves in curved orbits within its local group of galaxies. And galaxy clusters do not appear to have any preferred planar structure.
As a smaller-scale analogy, consider Uranus. Due to its extreme axial tilt, it is currently traveling through the solar system in a direction nearly parallel to its axis of rotation. But when Voyager 2 visited in 1986, it was more like rolling along the ecliptic.
apodman wrote:Or have I done it again? In a relativistic universe, is it even valid to ask a question about "line of travel" in terms of fixed coordinates? In any case can my question be posed in terms of one galaxy's local motion with respect to the other?
Measuring thing with respect to the common center-of-mass sounds potentially meaningful. If the galaxies are part of a gravitationally bound group, its center-of-mass would be an even better choice.
In case we're measuring from the center of mass for just the two interacting galaxies, we have a two-body problem, and the galactic centers will stay in the plane traced out by the A-B line and their initial mutual velocity. But their orbits in that plane will be curved, so unless the disc just happens to be aligned with the twobody plane, the angle between velocity and rotation axis will be varying, and most rapidly during the closest encounter.
[quote="apodman"]So then I looked back at the picture to try to apply the principle to the actual geometry. I couldn't see it, so I thought of projecting the positions (and therefore angles to the A-B line) back in time. Wondering what direction they each came from[/quote]
... not to mention where the actually are. The picture seems to give no clear hints on whether the galaxy to the right is in front of or behind the one to the left, nor whether we're seeing it from the top or from below.
[quote="apodman"]Eddies move parallel to their own plane of rotation. Same for wheels and little plastic flying saucers. So I'm predisposed to view galaxies the same way - moving in their own plane of rotation. But is this true? Is a spiral galaxy's plane of rotation related to its line of travel at all?[/quote]
I don't see how it could be. Excepting tidal encounters, the disc will keep its orientation, while the galaxy's center-of-mass moves in curved orbits within its local group of galaxies. And galaxy clusters do not appear to have any preferred planar structure.
As a smaller-scale analogy, consider Uranus. Due to its extreme axial tilt, it is currently traveling through the solar system in a direction nearly parallel to its axis of rotation. But when Voyager 2 visited in 1986, it was more like rolling along the ecliptic.
[quote="apodman"]Or have I done it again? In a relativistic universe, is it even valid to ask a question about "line of travel" in terms of fixed coordinates? In any case can my question be posed in terms of one galaxy's local motion with respect to the other?[/quote]
Measuring thing with respect to the common center-of-mass sounds potentially meaningful. If the galaxies are part of a gravitationally bound group, its center-of-mass would be an even better choice.
In case we're measuring from the center of mass for just the two interacting galaxies, we have a two-body problem, and the galactic centers will stay in the plane traced out by the A-B line and their initial mutual velocity. But their orbits in that plane will be curved, so unless the disc just happens to be aligned with the twobody plane, the angle between velocity and rotation axis will be varying, and most rapidly during the closest encounter.