"Joseph Lazio" wrote...
in message ...

"P" == Painius writes:
. . .
P The farther away an object is, the more *time* we must wait to be
P able to sense how far to the left or right the object has moved.

P We now know that both of the other large galaxies in our Local
P Group have a radial velocity that is in our general direction, that
P is, they both show a blue shift. This could mean many things, but
P i think it means that all three galaxies, Andromeda, Triangulum and
P our own Milky Way are gravitationally bound to a common center of
P gravity. All three are "falling toward" each other as they revolve
P around... something. (What this "something" is can be anybody's
P guess. Since scientists are finding huge masses of dark matter in
P the center of other galaxy clusters, it may follow that our Local
P Group revolves around a huge clump of this dark matter?)

Yes and no. It is probably the case that the three major galaxies are
gravitational bound together. This does not mean that there is
something "at" the common center of mass. Remember that saying one
object "orbits" another is an approximation. The Moon does not orbit
the Earth. The Earth and Moon orbit a common center of mass, which is
somewhere inside the Earth but not inside the center of the Earth.
Jupiter and the Sun orbit a common center of mass that happens to be
just outside the Sun's surface. The Milky Way, Andromeda, and
Triangulum galaxies orbit a common center of mass.

Yes, thanks Joseph... Earth and Moon are a relatively simple
two-body problem with one body a bit larger than the other.
The galaxies on the other hand represent an interesting three-
(or perhaps even four-)body problem that is, as might be
expected, far more complicated.

If you go here...

http://www.arachnoid.com/gravitation/

....there is a Java orbital analysis program that can be used
to see what happens when three bodies orbit around just a
common center of mass with no actual mass in the center.

I've tried various positionings of the bodies in an effort to
approximate the relative positions of the three galaxies.
And it seems that even if the three bodies begin in a stable
orbit around the common center, the orbit quickly becomes
unstable and deteriorates. Eventually one object gets
thrown into a flattened elliptical orbit and ends up colliding
and merging with one of the other objects. And this turns
the system into a two-body problem with the merged body
larger than the other body.

It seems to me that there must be a large mass for the three
bodies to orbit in order for them to maintain fairly stable
orbits. In addition, the center mass can be expected to be
a good deal more massive than the galaxies that orbit it.

I could be wrong, but it appears to me that there may very
well be an unimaginably huge mass of dark matter out there
somewhere between our Milky Way and the two other big
galaxies in the LG. And all three galaxies maintain fairly
stable orbits around it.

One thing that hurts the feasibility of my idea is the evidence
that Andromeda and Triangulum have already experienced
a bit of a glancing collision. This may mean that you're right
after all.

P So my question is this... Is there a formula to compute how long we
P must wait before we can gather fairly accurate measurements of
P transverse velocity? In other words...

Sure. The amount of time you have to wait is

t = (D/v)*theta

where v is the velocity of the object, D is its distance, and theta is
the size of the angle that it needs to move for you to determine that
it has moved. For instance, suppose you could observe water masers in
the Andromeda galaxy using VLBI techniques. You might hope to obtain
a resolution of about 0.3 milliarcseconds, so that you could determine
they had moved after they shifted about 1 mas (= 5 nanoradians = 5E-9
radians). Suppose that the Andromeda galaxy has a transverse velocity
of 200 km/s, and it is 750 kpc distant (= 2.3E19 km). Then t =
561777408 seconds ~ 17 years.
--
Lt. Lazio, HTML police | e-mail:
No means no, stop rape. | http://patriot.net/%7Ejlazio/
sci.astro FAQ at http://sciastro.astronomy.net/sci.astro.html

How did you come by your Andromeda Galaxy transverse
velocity supposition? Educated guess? or have we been
watching it long enough to have measured it?

happy days and...
starry starry nights!

--
A smidgeon of fear and a sprinkle of strife
And a whole lotta love till your cold...
Most everyone here wants to live a long life,
Ah! but nobody wants to get old.

Paine Ellsworth