Measuring the Movement of the Stars

[ScientificMind]

I was wondering, since the Earth is constantly moving around the sun, the sun is moving around the milky way, and the milky way is moving through space (and for all I know the milky way might also be rotating around our local group, cluster, super cluster, etc.), how do we know how fast anything is moving? For example, it seems like if two objects are moving away from one another at say 2 m/s, from the point of view of either one it would look like it was standing still while the other was moving away at 4 m/s.

 

[russ_watters]

Yes, by definition, speed is measured between any two objects and either can self-label as the one which is "standing still" (unless there is acceleration). You may be struggling under the misconception that there is a universal rest frame against which a "true" speed can be measured.

 

[ScientificMind]

Yes, by definition, speed is measured between any two objects and either can self-label as the one which is "standing still" (unless there is acceleration). You may be struggling under the misconception that there is a universal rest frame against which a "true" speed can be measured.

I suppose that I didn't think of it that way, thank you. Though that raises another question for me, what do we do instead to measure the motion of celestial bodies? That is, do we measure them using the Earth as "standing still," do we simply measure them in a general sense of motion without bothering to give them exact speeds, or is it something completely different?

 

[Bandersnatch]

I suppose that I didn't think of it that way, thank you. Though that raises another question for me, what do we do instead to measure the motion of celestial bodies? That is, do we measure them using the Earth as "standing still," do we simply measure them in a general sense of motion without bothering to give them exact speeds, or is it something completely different?

There's always a reference frame specified or implied when talking about velocities in astronomy. All observations are by necessity conducted from the reference frame of Earth, so you'll always get a speed w/r to Earth as the basis.
When the daily and yearly motions of our planet are deducted from it, we get motion w/r to the so called "local standard of rest" (LSR), that is w/r to the Sun and its closest neighbourhood. This is a good reference frame to describe motion of nearby stars.
You can then deduct the rotation of Milky Way to get the galactic reference frame. This one is useful for describing interactions with other galaxies.
You can talk about the reference frame of the centre of mass of the Local Group of galaxies if you deduct the relative motion of MW with respect to it.
You can also talk about the frame of reference of the cosmic microwave background radiation (CMBR) if you deduct all the other contributions. This frame of reference is used by most cosmological models to describe the global behaviour of the universe.

So, let's say you measure the divergence from homogenity of the CMBR - you look at the sky, notice that CMBR is blue-shifted in one direction and redshifted in the opposite one, and using Doppler shift you calculate the velocity of Earth relative to CMBR.

Then you may deduct the velocity of Earth's rotation, which will amount to some 0.5km/s (fluctuating daily), the velocity of Earth's revolution (30km/s fluctuating yearly), the velocity of Sun around the galactic centre (iirc ~240km/s fluctuating every 250 million years, so practically constant from our human perspective), the velocity of MW moving towards Andromeda Galaxy (110km/s) and you end up with some ~650km/s velocity of the Local Group w/r to the CMBR.

Another example, you look at the Andromeda galaxy, use doppler shift to find its approach velocity as seen from Earth, deduct the quickly changing velocity of rotation and revolution of the planet, and you end up with the velocity w/r to the Sun of about 300km/s (the "helio-radial velocity" in the wikipedia article on Andromeda). Then you may deduct the galactic orbital motion of the Sun to conclude that the actual speed of approach between the two galaxies is the 110km/s mentioned earlier.