How do they calculate how fast celestial objects are moving?

[Glenstr]

The Andromeda galaxy is hurtling towards us at 250,000 mph, in relation to what?

Speed here on Earth is generally measured in relation to the surface, assuming it to be stationary. In space, nothing is stationary, nothing is upside down etc. If you're traveling in space and you meet another traveler going the opposite direction, and after you meet you recede from each other at a speed of let's say 5kmh. You have no idea really if you're both going 2.5kmh, you're stationary and he's traveling at 5kmh, or your floating along at 50 kmh and he's going 55 kmh..

So back to my example Andromeda - is the 250,000 mph in relation to the Milky Way? Since our galaxy is also hurtling through space, are we traveling in the same direction and Andromeda is just catching up, or are the two galaxies actually moving towards each other? If all celestial objects are getting further away from each other would I be correct in assuming Andromeda is "catching up"?

If everything in space is moving, there is no real reference point, and if Andromeda is moving towards us at this speed, I'm assuming that speed is calculated with the assumption our galaxy is standing still (even thought it isn't) much like how we calculate speed here with the assumption the surface is standing still..

 

[Bandersnatch]

Velocities of celestial objects are measured using doppler shift - the known characteristic spectra of light get either blue or red shifted depending on the velocity. Closing in means blueshift, recession=redshift.
This is necessarily measuring ONLY the helio-radial velocity. I.e., the velocity with respect to the Solar System in the direction towards(or away from) it.
More precisely, it measures the velocity w/r to Earth, but the yearly variation due to orbital movement is usually deducted from the result and described w/r to the Sun, as the latter takes so long to move in its orbit that for most intents and purposes it can be considered stationary within the galactic context. Unlike Earth, which can add/deduct 30km/s over the span of one year's observations, so it'd make little sense to use it as a reference frame.

Go to the Andromeda Galaxy wiki page, and you'll see the velocity shown there(300 km/s) is measured w/r to the Sun.

If you want to find out the closing velocity w/r to the galactic centre, you have to add the velocity vector from the redshift measurement to the galaxtic orbital velocity vector(i.e., our Sun's velocity as it orbits the galactic centre).


As for 'catching up' I'm not sure what you mean.
Both galaxies are moving towards their common centre of mass. From its reference frame Milky Way, as the less massive of the two, is moving faster, at a larger fraction of the total closing speed.

 

[paisiello2]

All velocities observed are relative. So the 250,000mph (110km/s) is the relative velocity between the two galaxies.

Now the sun orbits the center of the milky way galaxy at 250km/s and the Andromeda galaxy just happens to lie close to the plane of this orbit. So I think this explains why the directly measured velocity is 300km/s:
http://ned.ipac.caltech.edu/cgi-bin...ker=30000.0&list_limit=5&img_stamp=YES#ObjNo1

Both the Andromeda and Milky Way galaxies are in turn both moving toward the constellation Hydra with a speed of 550 km/s with respect to photons of the cosmic background radiation.

 

[Glenstr]

By "catching up" I just meant are both galaxies traveling in the same relative direction, but Andromeda is just going 110 km/s faster than us. If the universe is expanding, I would assume that all celestial objects are on an outward trajectory.

 

[Bandersnatch]

From the wording of your comment I'm deducing you're thinking of the expansion as having some definable centre, from which all galaxies are receeding outward?

It is not so. There is no centre to the universal expansion, or - equivalently - the centre of the expansion is anywhere you're standing.


Also, remember that the 110km/s is the closing velocity - velocity w/r to the MW. From the point of view of aliens in the Andromeda galaxy, it's MW that's closing in at 110km/s.

 

[Glenstr]

Ok, so from the perspective of an alien in say, M81, would it be the MW closing in on Andromeda?

 

[Bandersnatch]

After performing proper observations and calculations(he can only measure doppler shift in the direction radial to his apparatuses), the alien would see that Andromeda is moving towards MW at 110 km/s, OR that MW is moving towards Andromeda at 110km/s. OR that the two are moving towards each other with speeds that added together net 110km/s.
OR that they're both moving in some other direction, but one of them does so with extra 110km/s.

Arguably choosing their centre of mass is useful for understanding the dynamics of the system(why they are closing - mutual gravitational attraction). Still, these are all equivalent statements. It all depends on where you want to locate your reference frame.
The important bit is that they're closing at 110km/s. This last fact is frame-independent.

Edit: sorry, I wrote m81 where I should write Andromeda!

 

[Glenstr]

I've had a chance to do a bit more reading, and according to this article, if I read it right, the alien from the M81 galaxy should see us overtaking Andromeda, as shown in this image.

 

[Bandersnatch]

Nice find!

Here's the paper the article is talking about:
http://arxiv.org/abs/1403.3667

I'm afraid you're not reading it right.

The black arrow is the velocity of the Local Group(MW, Andromeda, and a bunch of nearby dwarf galaxies) with respect to the centre of the "Council", as the article dubs the galaxies surrounding and influenced by the LG.

Relative to Council galaxies and pairs, the velocity of the Local
Group along the plane of the Sheet is 11+/-12km/s away from
the Council centre toward -56° +/-70° with respect to the displayed
x direction of rotated Sheet coordinates. The vector is displayed as
a thick black arrow in the top panel of Figure 3.

The velocities of individual galaxies are not depicted. In that reference frame, both MW and Andromeda would be moving towards their mutual centre of mass.


(by the way, in my previous post I wrote M81 where I should write Andromeda. It's now corrected. Sorry if that confused you.)