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jdmack
2006-Nov-02, 08:07 PM
1. Our Milky Way galaxy, and most other galaxies, are said to have
billions of stars. How is that number derived? Photos of galaxies
look like white blurs to me. Why is it not millions, or tens of
millions? Billions is a *far* greater number than millions.

2. I am still trying to get my head around the idea of an expanding
universe. Let me ask this. The nearest star to Earth other
than our sun is Proxima Centauri, which is 4.3 light years from us
(from the sun, actually, but close enough). If I were to shoot a
laser beam towards Proxima Centauri, how long would it take for the
light to get there? Would it be 4.3 years, or something greater
than that when accounting for the expansion of the universe?

Apologies in advance if these questions have been covered before. Thanks in advance to anyone who chimes in with an answer!

J. D.

Squashed
2006-Nov-02, 08:22 PM
...

2. I am still trying to get my head around the idea of an expanding
universe. Let me ask this. The nearest star to Earth other
than our sun is Proxima Centauri, which is 4.3 light years from us
(from the sun, actually, but close enough). If I were to shoot a
laser beam towards Proxima Centauri, how long would it take for the
light to get there? Would it be 4.3 years, or something greater
than that when accounting for the expansion of the universe? ...

It would take 4.3 years. For the 1st half of the trip the expansion would hinder the laser's travels and for the 2nd half of the trip the expansion would expedite the laser's travels - the two effects would offset each other and the result would be the distance between the two at the moment the laser was fired.

Cougar
2006-Nov-02, 09:10 PM
It would take 4.3 years.
It would be interesting to figure out just how much farther (proper distance?) Proxima Centauri would be from us after a duration of 4.3 years, considering the expansion to progress at ~70 km/sec per Mpc. Anyone numerically minded passing through? ;)

Casus_belli
2006-Nov-02, 09:13 PM
. Anyone numerically minded passing through? ;)

Who me?:eh:

antoniseb
2006-Nov-02, 09:16 PM
Let's imagine that you knew that the distance was 4.0000000000 light years to some target, and that you and that target both with little mass in the middle of some intergalactic void, and both at rest relative to the CMB. If you sent a pulse of photons to the target, they would arrive about 6 milli-seconds late because of universal expasion.

Proxima Centauri, on the other hand has a lot of factors having to do with being graviationally bound to the Milky Way, and some relative motion with respect to the Sun... And we don't know the distance to 10 significant digits.

Squashed
2006-Nov-02, 09:57 PM
Let's imagine that you knew that the distance was 4.0000000000 light years to some target, and that you and that target both with little mass in the middle of some intergalactic void, and both at rest relative to the CMB. If you sent a pulse of photons to the target, they would arrive about 6 milli-seconds late because of universal expasion.

Proxima Centauri, on the other hand has a lot of factors having to do with being graviationally bound to the Milky Way, and some relative motion with respect to the Sun... And we don't know the distance to 10 significant digits.

I figured the two would separate by 12,245,028 meters during the 4.3 years

I converted a light-year into meters:

299,792,458 * 60 * 60 * 24 *365.25 = 9.46073 * 1015 meters

I converted the 4.3 light-years to meters:

4.3 * 9.46073 * 15 = 4.06811 * 1016 meters

The expansion can be expressed as 70 parts per trillion per year as Peter (http://www.bautforum.com/showpost.php?p=669546&postcount=3) points out which equals = 7 * 10-11

and then

(4.3*(1 + 7 * 10-11)4.3) - 4.3 = 3.01 * 10-10 to get the decimal change in 4.3 years which when multiplied by the distance gives:

3.01 * 10-10 * 4.06811 * 1016 meters = 12,245,028 meters.

- - - - - - - - - - - - - -

Feel free to correct any errors cause this was my first time doing such a feat.

antoniseb
2006-Nov-02, 10:22 PM
I figured the two would separate by 12,245,028 meters during the 4.3 years

That seems about right. My 6 milli-seconds answer is 18 million meters. I just figured that space expanded one part in 13.7 billion per year.

Kaptain K
2006-Nov-02, 10:53 PM
1. Our Milky Way galaxy, and most other galaxies, are said to have
billions of stars. How is that number derived? Photos of galaxies
look like white blurs to me. Why is it not millions, or tens of
millions? Billions is a *far* greater number than millions.
We know the luminosity range of stars.
We know the distribution of luminosities of stars.
We know the total luminosity of galaxies.
It is easy to calculate the total number of stars in a galaxy.
Also, we know the mass range of stars and from the rotation curves of galaxiies we can derive the total mass of the galaxies
Either way, we come up with total numbers of stars in the billions to trillions of stars.

2. I am still trying to get my head around the idea of an expanding
universe. Let me ask this. The nearest star to Earth other
than our sun is Proxima Centauri, which is 4.3 light years from us
(from the sun, actually, but close enough). If I were to shoot a
laser beam towards Proxima Centauri, how long would it take for the
light to get there? Would it be 4.3 years, or something greater
than that when accounting for the expansion of the universe?
The expansion of the universe does not affect the distance to Proxima Centauri. Nor any other stars in the Milky Way. Nor any galaxies in the Local Group. Nor any clusters of galaxies in the local super cluster (Virgo group). All of these are gravitationally bound. The expansion is only over cosmological distances - billions of light years.

Cougar
2006-Nov-02, 11:25 PM
...you and that target both with little mass in the middle of some intergalactic void, and both at rest relative to the CMB...
Right, right. That's the problem I was interested in. The Kaptain is quite right that local gravitation swamps the effect.

Feel free to correct any errors cause this was my first time doing such a feat.
Thanks. I appreciate the effort.

(4.3*(1 + 7 * 10-11)4.3) - 4.3
Where the heck did this form come from? :o

Ken G
2006-Nov-03, 01:16 AM
He didn't mean the 4.3 in the exponent. Also, if you follow his math, you'll see that he multiplied by 4.3 twice, when it should only be done once. For some reason I haven't followed up, his answer still came out close to antoniseb's. But it's all academic, as it has already been pointed out that the expansion does not appear within galaxies.

Squashed
2006-Nov-03, 01:23 PM
...
Where the heck did this form come from? :o

This part: (4.3*(1 + 7 * 10-11)4.3) - 4.3 is like an interest calculation except that the "interest" is expansion and so since the expansion rate that you defined as 70 km/sec per Mpc when converted to a rate of change equals 7 * 10-11 per year then since this is an annual rate of change it is added to 1.0 and the sum is to the power 4.3 since it is over that many years that the change is for.

Then I multiplied the total "interest" change by the 4.3 and then subtracted the 4.3 since we are only interested in the change due to expansion and not the actual distance.

I'll have to re-check the math to make sure I did not multiply by 4.3 twice like Ken G claims but I can't do it right now.

Ken G
2006-Nov-03, 01:38 PM
The problem is that having the power 4.3 there effectively already multiplies the 70 parts per trillion by 4.3. Then you multiply by 4.3 again, subtract 4.3, and then actually multiply by 4.3 a third time in your calculation (when you multiply by 4 times 10 to the 16 m). So that's actually 3 times, when you only want to multiply twice (once for the amount of expansion in 4.3 years, and again for how much expansion over 4.3 LY of distance).

2006-Nov-03, 02:02 PM
The expansion of the universe does not affect the distance to Proxima Centauri. Nor any other stars in the Milky Way. Nor any galaxies in the Local Group. Nor any clusters of galaxies in the local super cluster (Virgo group). All of these are gravitationally bound. The expansion is only over cosmological distances - billions of light years.

Aren't any of you bothered by our lack of knowledge of the variability of the cosmological coefficient of expansion (as a function of time and maybe volume),aka Hubble Constant, and the effect this would have on our estimate of the age of the universe since the BB, and how we conveniently invoke or dismiss the expansion effects without so much as a hunch as to what, how, when, and where activates (it is activated) it?

StupendousMan
2006-Nov-03, 03:30 PM
Aren't any of you bothered by our lack of knowledge of the variability of the cosmological coefficient of expansion (as a function of time and maybe volume),aka Hubble Constant, and the effect this would have on our estimate of the age of the universe since the BB ...

Many astronomers (including me) are bothered by our lack of knowledge of the long-term history of the universe and its expansion. That's why we keep applying for time at big telescopes, and designing missions for space telescopes, and devising new ideas which we can test against the measurements.

If we weren't bothered, we would stop investigating.

Squashed
2006-Nov-03, 07:02 PM
I figured the two would separate by 12,245,028 meters during the 4.3 years

I converted a light-year into meters:

299,792,458 * 60 * 60 * 24 *365.25 = 9.46073 * 1015 meters

I converted the 4.3 light-years to meters:

4.3 * 9.46073 * 15 = 4.06811 * 1016 meters

The expansion can be expressed as 70 parts per trillion per year as Peter (http://www.bautforum.com/showpost.php?p=669546&postcount=3) points out which equals = 7 * 10-11

and then

(4.3*(1 + 7 * 10-11)4.3) - 4.3 = 3.01 * 10-10 to get the decimal change in 4.3 years which when multiplied by the distance gives:

3.01 * 10-10 * 4.06811 * 1016 meters = 12,245,028 meters.

- - - - - - - - - - - - - -

Feel free to correct any errors cause this was my first time doing such a feat.

The confusing part of this whole problem is the fact that the 4.3 is the number of light-years (distance) and the 4.3 is also the number of years that the laser travels.

I figured the two would separate by 12,245,028 meters during the 4.3 years

I converted a light-year into meters:

299,792,458 * 60 * 60 * 24 *365.25 = 9.46073 * 1015 meters

I converted the 4.3 light-years to meters:

4.3 * 9.46073 * 15 = 4.06811 * 1016 meters

The expansion can be expressed as 70 parts per trillion per year as Peter (http://www.bautforum.com/showpost.php?p=669546&postcount=3) points out which equals = 7 * 10-11

and then

(1 + 7 * 10-11)4.3 - 1.0 = 3.01 * 10-10 to get the decimal change in 4.3 years which when multiplied by the distance gives:

3.01 * 10-10 * 4.06811 * 1016 meters = 12,245,028 meters.

- - - - - - - - - - - - - - - - - -

Okay, I did this using an excel spreadsheet but while transcribing the formulas to the previous post I screwed up the actual math that I used.

Hopefully this is correct ... back to you, Ken G, and your checking skills.

Ken G
2006-Nov-03, 10:51 PM
Aren't any of you bothered by our lack of knowledge of the variability of the cosmological coefficient of expansion (as a function of time and maybe volume),aka Hubble Constant, and the effect this would have on our estimate of the age of the universe since the BB, and how we conveniently invoke or dismiss the expansion effects without so much as a hunch as to what, how, when, and where activates (it is activated) it?

It's not clear that you are aware that the theory of general relativity completely explains the "variability" of the coefficient of expansion, in terms of what is happening over galactic and intergalactic scales. We are not "invoking" the expansion at will, we are using observations to constrain the unknown parameters, within the context of general relativity. Your question sounds like, aren't we bothered that Newton's laws don't tell us the trajectory of a cannon ball, until we observe its muzzle velocity and direction?

Ken G
2006-Nov-03, 10:54 PM
I figured the two would separate by 12,245,028 meters during the 4.3 years

That looks OK, and is the calculation you did before, though the calculation you said you did had an extra 4.3 in it. No matter, this does seem right now, taken as a "what if" there was no gravitational binding.

Squashed
2006-Nov-06, 01:54 PM
Let's imagine that you knew that the distance was 4.0000000000 light years to some target, and that you and that target both with little mass in the middle of some intergalactic void, and both at rest relative to the CMB. If you sent a pulse of photons to the target, they would arrive about 6 milli-seconds late because of universal expasion.

Proxima Centauri, on the other hand has a lot of factors having to do with being graviationally bound to the Milky Way, and some relative motion with respect to the Sun... And we don't know the distance to 10 significant digits.

I would contend that the laser arrives exactly at 4.3 years.

If there was a reflector attached to the target then the reflection would have to travel the additional 12,245,028 meters back to earth which would add

12,245,028 / 299,792,458 = 0.040845017 seconds

to the return leg of the round trip.

This all happens because of the way the situation develops.

Prior to emitting the photon there are only two entities, the emitter and the receiver, with one distance separating the two entities.

At the moment that the photon is created there are now three entities with two separating distances, the sum of both separating distances equals the original single separating distance.

At the moment of photon creation these two distance values equals 4.3 light-years in front and zero light-years behind.

At the quarter-way distance, the distance behind is equal to:

((1 + 7 * 10-11)4.3*1/4) * 1/4 * 4.06811 * 1016 meters = 1/4 * 4.3 light-years + 765,314 meters.

and the distance in front is equal to:

((1 + 7 * 10-11)4.3*1/4) * 3/4 * 4.06811 * 1016 meters = 3/4 * 4.3 light-years + 2,295,942 meters.
.
.
.
At the half-way distance, the distance behind is equal to:

((1 + 7 * 10-11)4.3*2/4) * 2/4 * 4.06811 * 1016 meters = 2/4 * 4.3 light-years + 3,061,257 meters.

and the distance in front is equal to:

((1 + 7 * 10-11)4.3*2/4) * 2/4 * 4.06811 * 1016 meters = 2/4 *4.3 light-years + 3,061,257 meters.
.
.
.
At the three-quarters-way distance, the distance behind is equal to:

((1 + 7 * 10-11)4.3*3/4) * 3/4 * 4.06811 * 1016 meters = 3/4 *4.3 light-years + 6,887,828 meters.

and the distance in front is equal to:

((1 + 7 * 10-11)4.3*3/4) * 1/4 * 4.06811 * 1016 meters = 1/4 * 4.3 light-years + 2,295,943 meters.
.
.
.
At the receiver,Proxima Centauri, the distance in front equals:

zero

and the distance behind equals:

((1 + 7 * 10-11)4.3*4/4) * 4/4 * 4.06811 * 1016 meters = 4/4 * 4.3 light-years + 12,245,028 meters.

At the beginning of the trip the laser seems to be "slow" because the distance in front grows faster** than the distance behind but after the halfway point the laser seems to be "fast" because the distance in front grows slower** than the distance behind.

** Even though the rate of change is equal for both distances since the size of the distances being factored by this rate of change varies then it appears like a varying rate of change.

antoniseb
2006-Nov-06, 02:33 PM
You've done a nice job of showing that the extra 12 million meters is traversed by the photon begin carried by the expansion. Another way to think about it is this. In the time it takes for the photon to get half way there, that first half only expanded half of its 6 million extra meters, so it didn't take the whole extra time that light would normally need to go 12 million meters.

closetgeek
2006-Nov-15, 05:02 PM
Alright, here is a question that may seem a bit simple but; let's say Proxima Centauri was bumped out of it's galactic orbit by something inconsequential to the question. Just accept that it was given a new path without arguing logistics. Say it is heading toward Earth at .5 c. (did I symbolize half the speed of light correctly?). Knowing that we are still seeing the object as it was in the past, is there a point, as it crosses the threshhold of LY distance to say AU distance that it would appear to increase in speed in a major leap or would the increase be gradual since the distance is slowly closing, if it appears to increase at all?

antoniseb
2006-Nov-15, 06:15 PM
...is there a point, as it crosses the threshhold of LY distance to say AU distance that it would appear to increase in speed in a major leap...

In the scenario you describe (Proxima Cent. suddenly starts coming toward us at 0.5c) we would see the event that caused the change 4.3 years after it happened, and from that point on, we would see Proxima coming toward us at 0.5 c (judged by redshift and parallax). So, 6.45 years after the event, we would see Proxima half the distance to Earth on its deadly journey, even though in some objective reality, it would already be three quarters of the way there... the light we'd be seeing at that time would be the light emitted when Proxima was half way. Thus, we would see Proxima in our Solar neighborhood 4.3 years after we saw the event.

closetgeek
2006-Nov-17, 03:52 PM
Okay, thanks. Still trying to grasp that light/time concept. I need visuals.

In the scenario you describe (Proxima Cent. suddenly starts coming toward us at 0.5c) we would see the event that caused the change 4.3 years after it happened, and from that point on, we would see Proxima coming toward us at 0.5 c (judged by redshift and parallax). So, 6.45 years after the event, we would see Proxima half the distance to Earth on its deadly journey, even though in some objective reality, it would already be three quarters of the way there... the light we'd be seeing at that time would be the light emitted when Proxima was half way. Thus, we would see Proxima in our Solar neighborhood 4.3 years after we saw the event.

antoniseb
2006-Nov-17, 04:07 PM
Okay, thanks. Still trying to grasp that light/time concept. I need visuals.

Without dealing with any relativity concepts at all, you can lay this out on graph paper, using a ruler or meter stick, and some different colored tokens like the ones in the game Risktm.

Use the use a large coin to represent the Sun, and a small copper coin to represent Proxima, and the colored tokens to represent photons. Show the placement of Proxima and the circles of photons for in two year intervals starting with the event that starts it moving toward us. I think you'll rapidly figure out how this all works.