Is the location of galaxy X in the universe constant?

[HZY]

If we look up the sky at galaxy X whose light took Y amount of time to reach us from distance Z, where is the galaxy X now?

 

[e.bar.goum]

If we look up the sky at galaxy X whose light took Y amount of time to reach us from distance Z, where is the galaxy X now?

It depends on the velocity of the galaxy! Happily, you can also measure the velocity of the galaxy by measuring its red(or blue) shift.

 

[Chronos]

Measure its peculiar mostion and extrapolate that out by its redshift distance [in light years] and you get a rough idea. Of course, that assumes the laws of physics are not conspiring to deceive us. We have no reason to believe that, but, plenty of reasons to believe we may be misdirected by logical constructs.

 

[ogg]

There's two answers to this. First is for nearby galaxies (with very small redshift). You just figure their apparent speed and multiply it by the time its taken light from there to get here (or if you understand the dynamics of the many body system it and the Milky Way are part of, you calculate it using those mutiple-body equations...Since we don't have a solid understanding of the distribution of Dark Matter, this is a bit of a reach, but not too much, its probably roughly correct). Second for large redshift galaxies, you calculate the time the light left the galaxy in billions of years, and multiply by ~3.3 light years/year. So in other words if a galaxy is 13.2 billion years away, it is now about 45 billion light years away. For galaxies which are "gravitationally bound" (nearby galaxies, aka "local galaxies") cosmological expansion can be ignored. For far away galaxies, the only significant effect has been cosmo. expansion (and relative velocities can be ignored). The distance to far away galaxies, depends on the rate at which the Universe has expanded since they were formed, but we THINK we have a fair understanding of that...But modern physics doesn't think in terms of "now". "Now" is relative, depending on your location and speed (acceleration, gravity, ..) In spacetime, "distance" can be measured in years and time can be measured in lightyears (or seconds and inches, etc.). We can never see "now", all of our measurements are of past events. Everything we see, feel, smell, touch, and taste is from an event which happened in the past. Nothing is "now". "Now" is a construct of our minds, not something which actually exists (not to get too philosophical or anything, ha-ha). Oh, and for galaxies at distances between nearby and far away, you'd look at both effects and either combine them, or chose to ignore the less important. Cosmological expansion is important when distances get to be 100's of millions of lightyears...and can be ignored for local distances (eg Andromeda at 250,000 ly).

 

[HZY]

There's two answers to this. First is for nearby galaxies (with very small redshift). You just figure their apparent speed and multiply it by the time its taken light from there to get here (or if you understand the dynamics of the many body system it and the Milky Way are part of, you calculate it using those mutiple-body equations...Since we don't have a solid understanding of the distribution of Dark Matter, this is a bit of a reach, but not too much, its probably roughly correct). Second for large redshift galaxies, you calculate the time the light left the galaxy in billions of years, and multiply by ~3.3 light years/year. So in other words if a galaxy is 13.2 billion years away, it is now about 45 billion light years away. For galaxies which are "gravitationally bound" (nearby galaxies, aka "local galaxies") cosmological expansion can be ignored. For far away galaxies, the only significant effect has been cosmo. expansion (and relative velocities can be ignored). The distance to far away galaxies, depends on the rate at which the Universe has expanded since they were formed, but we THINK we have a fair understanding of that...But modern physics doesn't think in terms of "now". "Now" is relative, depending on your location and speed (acceleration, gravity, ..) In spacetime, "distance" can be measured in years and time can be measured in lightyears (or seconds and inches, etc.). We can never see "now", all of our measurements are of past events. Everything we see, feel, smell, touch, and taste is from an event which happened in the past. Nothing is "now". "Now" is a construct of our minds, not something which actually exists (not to get too philosophical or anything, ha-ha). Oh, and for galaxies at distances between nearby and far away, you'd look at both effects and either combine them, or chose to ignore the less important. Cosmological expansion is important when distances get to be 100's of millions of lightyears...and can be ignored for local distances (eg Andromeda at 250,000 ly).

If you get on a spaceship and fly towards Galaxy X, what happens then? Will you ever catch up to it? If you do, what will you see?

 

[Chronos]

Any galaxy with a redshift of more than about 1.6 has left our cosmological horizon and no signal [or spacecraft ] sent now will ever reach it. You will simply see it redshift into obscurity like an astonaut approaching a black hole event horizon viewed from afar.

 

[HZY]

Any galaxy with a redshift of more than about 1.6 has left our cosmological horizon and no signal [or spacecraft ] sent now will ever reach it. You will simply see it redshift into obscurity like an astonaut approaching a black hole event horizon viewed from afar.

If the distance separating galaxy A and B is such that the expansion rate of space between them is exactly equal to c, what is that distance in light-year? What is the resulting measured red shift? Would observers either galaxies be able to see each other? If an observer in galaxy A got on a spaceship and travels at the speed of light c towards galaxy B, would galaxy B remain visible to that observer? What about galaxy A, would it be visible to the same observer?

 

[mfb]

If the distance separating galaxy A and B is such that the expansion rate of space between them is exactly equal to c, what is that distance in light-year?

This is the Hubble radius, currently about 14 billion light years.

What is the resulting measured red shift?

Measured when? For light currently reaching us (=emitted when the galaxies were closer), or for light currently emitted there (=reaching us in the distant future)?

Would observers either galaxies be able to see each other?

Light emitted there now will reach us in something like 30-40 billion years (didn't calculate it in detail). It won't make progress now (in terms of distance to us), but as the Hubble radius is increasing it will make progress towards us in the future.
If we try to answer then, our answer won't reach them any more as they will be outside the cosmological horizon by then.

If an observer in galaxy A got on a spaceship and travels at the speed of light c towards galaxy B, would galaxy B remain visible to that observer?

At nearly the speed of light. Yes. A would redshift into oblivion for this observer - the observer will never see the far distant future of A.

 

[rootone]

If the spaceship is traveling at c (or nearly) away from galaxy A in the direction of galaxy B which is receding at the same velocity from galaxy A...
Doesn't that mean the ship will never get closer to galaxy B, while at the same time the ship becomes disconnected from any possible communication with galaxy A?
Observers in both galaxies could never know that the spacecraft exists, and even the existence of the other galaxy becomes questionable since now all there is is a historical account, however trustworthy it may be, of something which is no longer visible.
Not a very nice prospect for any sentient observers on board the spacecraft .

 

[marcus]

If the spaceship is traveling at c (or nearly) away from galaxy A in the direction of galaxy B which is receding at the same velocity from galaxy A...
Doesn't that mean the ship will never get closer to galaxy B, while at the same time the ship becomes disconnected from any possible communication with galaxy A?
Observers in both galaxies could never know that the spacecraft exists, and even the existence of the other galaxy becomes questionable since now all there is is a historical account, however trustworthy it may be, of something which is no longer visible.
Not a very nice prospect for any sentient observers on board the spacecraft .

For definiteness let's assume that both A and B are at rest wrt CMB. (The Hubble law is about objects at rest with respect to CMB or equivalently wrt Hubble flow.) Galaxies typically move comparatively slowly, they are approximately at rest, so for simplicity we can neglect their individual motions in the space around them and say they are not moving.

Now you want to assume their separation (proper distance, this moment if you could pause expansion) is 14.4 Gly which is the Hubble distance. That means the distance between the two is increasing at c.

But how do you define the speed of the space ship? Relative to what? What does "traveling at c" mean?

If you define the speed by proper distance from A, then this can increase much faster than c. As soon as the ship is a substantial distance from home, that distance's expansion contributes. And the farther the ship gets, the more expansion contributes to that kind of "speed". After a while the distance from A to ship might be increasing at 2c, or 3c, and so on. It gets messy and unintuitive to use that kind of "speed".

I suspect your basic idea is to have the ship traveling nearly or approximately "at the limit". Almost as if it were a flash of light. If that is the idea then it would be good to specify that the ship is traveling nearly at c relative to CMB.

Then we can simply let Jorrie's calculator tell us.
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
Think of the ship as a flash of light that we, at A, send to B (which is receding at c because it is at the Hubble distance 14.4 Gly)
It's going to get there and Lightcone tells us it will take some 34+ billion years.
If you click on the link and have learned how to read the table you will see that for an arrival in year
13.7+34 = 47.7 billion the distance NOW should be about 14-some billion light years. Just look at the table as it comes up when you click on the link.
Look in the row of the table where the time T is 47.7 Gly. You don't have to do anything, just read the default table.

To get a more precise estimate put 0.121 in for S and you can reduce the number of steps to get a one-line table if you want. Press "calculate"
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 8.264&0.121&49.2196&17.2932&14.408&119.077&17.293&1.00&6.89\\ \hline \end{array}}$$
This gives distance_now as 14.4 Gly. And the time, you can see, is year 49.22 billion.

49.22 - 13.78 = 35.44.

That is when the flash of light arrives at galaxy B, and it is 35.44 billion years in the future,

so it would take around 35.4 billion years for the flash of light to get to a galaxy which today is receding from us at speed c.

I think this is what Mfb briefly said earlier, without going into so much detail. I wanted to show how to get a definite number and illustrate how to use the calculator.

 

[mfb]

Doesn't that mean the ship will never get closer to galaxy B, while at the same time the ship becomes disconnected from any possible communication with galaxy A?

It's the same as for light emitted there today: It won't make progress now (in terms of distance to us), but as the Hubble radius is increasing it will make progress towards us in the future.

That is when the flash of light arrives at galaxy B, and it is 35.44 billion years in the future,

I'm surprised how accurate the guess 30 to 40 billion years was :D.

 

[marcus]

If the spaceship is traveling at c (or nearly) away from galaxy A in the direction of galaxy B which is receding at the same velocity from galaxy A...
Doesn't that mean the ship will never get closer to galaxy B,...?

No, that's just the point I was making. The ship (think of a flash of light since it is traveling nearly the same speed) will get to B in some 35 billion years.

Observers on board the ship will be able to see galaxy B ahead of them all that time they are in transit. There is no question about the material existence of their destination. Of course galaxies suffer material change. Star-formation can exhaust available gas, stars can burn out, portions can undergo grav collapse. They will be able to watch the evolution of the matter comprising galaxy B all the time they are traveling towards it.
Although at the very start progress will seem extremely slow, effectively nil, after that they will always be getting closer to their destination.

 

[marcus]

...
I'm surprised how accurate the guess 30 to 40 billion years was :D.

Yes! It was remarkably close : ^)

 

[HZY]

Now, assume there exist three galaxies, Galaxy A, B, and C, such that the distance between Galaxy A and B is twice the Hubble radius, with Galaxy C located right at the midpoint between Galaxy A and B. If a spaceship takes off from Galaxy C and flies toward Galaxy B, which of the two galaxies, Galaxy A or Galaxy B, would be the first to disappear from the view of an observer on that ship when at the exact moment the speed of the ship reaches c? Would Galaxy B also disappear? Assume the rate of expansion of space between Galaxy A and B is c at the beginning of this scenario.

 

[HZY]

Now, assume there exist three galaxies, Galaxy A, B, and C, such that the distance between Galaxy A and B is twice the Hubble radius, with Galaxy C located right at the midpoint between Galaxy A and B. If a spaceship takes off from Galaxy C and flies toward Galaxy B, which of the two galaxies, Galaxy A or Galaxy B, would be the first to disappear from the view of an observer on that ship when at the exact moment the speed of the ship reaches c? Would Galaxy B also disappear? Assume the rate of expansion of space between Galaxy A and B is c at the beginning of this scenario.

Correction: Assume the rate of expansion of space between Galaxy A and C and between B and C is c at the beginning of this scenario.

 

[mfb]

Now, assume there exist three galaxies, Galaxy A, B, and C, such that the distance between Galaxy A and B is twice the Hubble radius, with Galaxy C located right at the midpoint between Galaxy A and B. If a spaceship takes off from Galaxy C and flies toward Galaxy B

Galaxy B would always stay in view for the spacecraft and it will arrive there in 35 billion years (as seen by B). A will redshift out of view soon (~2-3 billion years in the frame of the galaxies), C will do that later (~10 billion years?).

 

[HZY]

Galaxy B would always stay in view for the spacecraft and it will arrive there in 35 billion years (as seen by B). A will redshift out of view soon (~2-3 billion years in the frame of the galaxies), C will do that later (~10 billion years?).

Immediately upon arriving at Galaxy B, the ship quickly turns around and attempts a return trip back to Galaxy C. Could the ship make it back to Galaxy C in time to still be able to catch A if it were to continue flying pass Galaxy C? How long would each case take, first back to Galaxy C then further reaching Galaxy A?

 

[rootone]

What, they don't even take time to have a shower?
Anyway I am also interested to know what the more expert members think.

 

[HZY]

What, they don't even take time to have a shower?
Anyway I am also interested to know what the more expert members think.

There was simply no time. They are trying to stay Galaxy C visual, or at least get a final glimpse of it. Billions of light years of opportunity could potentially be lost while you take a show on planet Z, a decision probably not considered cosmologically wise.

 

[Jorrie]

Immediately upon arriving at Galaxy B, the ship quickly turns around and attempts a return trip back to Galaxy C. Could the ship make it back to Galaxy C in time to still be able to catch A if it were to continue flying pass Galaxy C? How long would each case take, first back to Galaxy C then further reaching Galaxy A?

I've been out of circulation for a while, so this may already have been answered (and it has been implied earlier in this thread), but there is no way your ship can ever make it back from B to C or A. By the cosmic time that it has reached B and is temporarily at rest in the CMB background, the other two will be far outside of the ship's cosmic horizon.

Incidentally, if your ship could go arbitrarily close to 'c' against the CMB background (without being fried), it could take very little ship time to reach Galaxy B. Even this will not help you for the return trip, because the other two galaxies would still be outside of its cosmic event horizon.

 

[HZY]

I've been out of circulation for a while, so this may already have been answered (and it has been implied earlier in this thread), but there is no way your ship can ever make it back from B to C or A. By the cosmic time that it has reached B and is temporarily at rest in the CMB background, the other two will be far outside of the ship's cosmic horizon.

Incidentally, if your ship could go arbitrarily close to 'c' against the CMB background (without being fried), it could take very little ship time to reach Galaxy B. Even this will not help you for the return trip, because the other two galaxies would still be outside of its cosmic event horizon.

During the return trip from Galaxy B back to Galaxy C, a new technology was invented that allows the mother ship (Ship 1) traveling at speed of light c relative Galaxy B to send out its shuttle ship (Ship 2) that can travel away from the mother ship at also the speed of light c. And the shuttle ship (Ship 2) itself has its own shuttle ship (Ship 3) that can also do the same by traveling away from the Ship 2 at speed of light c. Same goes for Ship 3, 4,5,6,...N in a Shuttle Ship Series. What is the value of N such that Galaxy C, which was outside of cosmic event horizon when was on Galaxy B, begins to reappear to an observer on Ship N?

 

[Jorrie]

During the return trip from Galaxy B back to Galaxy C, a new technology was invented that allows the mother ship (Ship 1) traveling at speed of light c relative Galaxy B to send out its shuttle ship (Ship 2) that can travel away from the mother ship at also the speed of light c. And the shuttle ship (Ship 2) itself has its own shuttle ship (Ship 3) that can also do the same by traveling away from the Ship 2 at speed of light c. Same goes for Ship 3, 4,5,6,...N in a Shuttle Ship Series. What is the value of N such that Galaxy C, which was outside of cosmic event horizon when was on Galaxy B, begins to reappear to an observer on Ship N?

These sort of 'games' quickly enter the realm of Sci-Fi - and it is in any way no longer a cosmological issue, but one of special relativity. Please stick to cosmology questions here.

The speed of an observer against the CMB rest frame does not influence what is inside or outside if its cosmic event horizon, only the perceived distances to things - the distance ratios stay the same. And incidentally, none of your 'staggered probes' can exceed 'c' relative to the CMB background - and that speed is all that counts.

 

[mfb]

Things outside the horizon never reappear. It doesn't matter if your ships travel at .9999 c, .9999999c, .99999999999c or whatever your series of ships would produce.
I suggest you start learning special relativity before you ask the same (GR) cosmology question over and over with different words.