B What process allows us to 'see' lightyears of distance with the natural eye?

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Leavitt's Law allows us to determine how far stars are from us by calculating their variable magnitude of brightness. Please explain how it's possible then for us to see, with the 'natural eye', the distances from one star to another, from one point in the night sky to the opposite, that would take x-# of lightyears traveling at the 'SOL' to reach? (What process allows us to 'see lightyears of distance' with the natural eye?)
 

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I'm sorry, your model is inside-out. You are seeing 'old' light from those sources.

It's travelled a second and a half from the Moon, eight minutes from the Sun, three years and change from the Alpha Centauri triplet, eight and a half from Sirius A...

A quasar's light may have been travelling since early in the universe...
 

Drakkith

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Please explain how it's possible then for us to see, with the 'natural eye', the distances from one star to another, from one point in the night sky to the opposite, that would take x-# of lightyears traveling at the 'SOL' to reach? (What process allows us to 'see lightyears of distance' with the natural eye?)
I'm not quite sure what you're asking. We see distant stars simply because the starlight has been traveling for long enough to reach us. Does that answer your question, or were you asking something else?
 

BillTre

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Dark adapted rods (low light level light receptors in your retina) in your eyes can detect single photons under good conditions.
 
I'm sorry, your model is inside-out. You are seeing 'old' light from those sources.

It's travelled a second and a half from the Moon, eight minutes from the Sun, three years and change from the Alpha Centauri triplet, eight and a half from Sirius A...

A quasar's light may have been travelling since early in the universe...
Thank you for your response. Yes, I understand we are seeing 'old' light from stars. Some of which may have in fact died long ago, so were actually seeing the light traveling from them, after they burned out, not the actual star. But aren't we 'seeing' light from stars only when it comes within a certain distance for our eyes ability to see a certain distance? The light has traveled thousands of light years and trillions of millions until we are able to precieve it visually! Right? That light comes to us in a straight line, for the most part, i.e., light bends around massive objects due to gravity on it's way to us! But, we are still seeing the 'light', be it 'old light' or 'not old light'. My misunderstanding comes from the precieved viewed distance we see from one star in the night sky to another star 'in the opposite point in the sky!' How are we able to visually see those 'lightyears of DISTANCE' with the natural/naked eye 'between' stars represented in our filed of view from earth? Is it the same thing? Is that what your saying? How is it possible for us to visually see those vast 'DISTANCES', 'BETWEEN' stars that would take us thousands of lightyears to travel even if we could travel at the speed of light!? (20% s.o.l., photon propulsion not withstanding, some day!) Is their a computer graphfic you could point me to that displays a visual explanation of what were seeing, for a better understanding? Thank you.
 

Drakkith

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But aren't we 'seeing' light from stars only when it comes within a certain distance for our eyes ability to see a certain distance?
Nope. The only requirement is that the path of the light takes it through your pupil and onto your retina, where it is then detected. It doesn't matter how far or for how long the light has traveled. If it enters your eye, it can be detected. This means that there is no maximum distance that our eyes can see. The only requirement is that the object is bright enough that the incoming light is still sufficiently bright for our eyes to see after its long travel.

This is why we can see stars like Betelgeuse, which is 600+ light years away, with the naked eye, but we need a telescope to see Proxima Centauri, which, at 4.2 light years, is the nearest star to us after the Sun. Proxima Centauri is MUCH dimmer than Betelgeuse, so we would need to be much closer to see it with the naked eye.
 
I'm not quite sure what you're asking. We see distant stars simply because the starlight has been traveling for long enough to reach us. Does that answer your question, or were you asking something else?
Drakkith, Thank you. Well said! OK, I get that. But what I'm not getting is the 'distance' between the stars (thousands of light years) from one star to another that we see when we look at one point of light, (a star) in the sky, and then scan our eyes to the opposite point in the night sky to another star. All I can conclude is the 'separation' I see is what we call distance! That separation represents thousands of lightyears of distance as we look back and forth between them, right? I believe the sicence, I just can't understand how we can see that many lightyears of distance between point 'A' star and point 'B' star, on a horizontal/elipse plain with the naked eye, when it would take thousands of light years, traveling at the 'sol' to actually travel there! Did I make that clear? What am I missing?
 

BillTre

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I believe the sicence, I just can't understand how we can see that many lightyears of distance between point 'A' star and point 'B' star, on a horizontal/elipse plain with the naked eye, when it would take thousands of light years, traveling at the 'sol' to actually travel there! Did I make that clear?
A star as a light source emits light in the form of photons.
They move in (mostly) straight lines (within the constraints of relativity) until they interact with something.
The brighter a light source is the more light it emits per unit time.
The brightness of the light observed decreases the further the observer is from the light source. This is because the light is spreading out in all directions, diluting the density of photns that might be observed. This results in a reduction of the number of photons that might hit your eye (or go into a telescope), but the few that are are still going in straight lines from their source, unless perturbed in some way.

If the number of photons becomes too few for direct human observation (as said above, your photo-receptors can detect single photons), than a telescope (with a larger opening and therefore a larger surface for collecting more photons) can be used to increase sensitivity. Telescope cameras can also be left to collect more photons over longer periods of time to collect enough photons to make an image. A single photon on a retina will evoke a flash visually, but unless another one comes along quickly it will not produce a continuous visual image that would be interpreted as a star.

Until the photons interact with something they will proceed on their course unaltered so you can see old photons generated long ago from far away.
What you are seeing may not even exist anymore, but you are seeing as it was when the light was emitted.
 

russ_watters

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Drakkith, Thank you. Well said! OK, I get that. But what I'm not getting is the 'distance' between the stars (thousands of light years) from one star to another that we see when we look at one point of light, (a star) in the sky, and then scan our eyes to the opposite point in the night sky to another star. All I can conclude is the 'separation' I see is what we call distance! That separation represents thousands of lightyears of distance as we look back and forth between them, right? I believe the sicence, I just can't understand how we can see that many lightyears of distance between point 'A' star and point 'B' star, on a horizontal/elipse plain with the naked eye, when it would take thousands of light years, traveling at the 'sol' to actually travel there! Did I make that clear? What am I missing?
What you are describing is the angle between them. If two objects are each 1m away from you and to your eyes are 45 degrees apart, they are 1m away from each other. Or scale that up to a million light years. It gets more complicated if the stars are different distances from us, but either way, it's just triangles.

Think about a photo of Jupiter vs the real Jupiter. The real Jupiter is so small looking because it is far away. In the photo it looks big because it is closer and subtends a larger angle, even though the photo is smaller than the real thing.
 
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Are you simply asking how can we figure out how far apart two stars are? None of that is done with the naked eye, it requires extremely precise measurements.

The closest stars we determine their position through parallax. If you take two objects that are different distances from your eye and move your head, these objects will change position relative to your eyes. That change is related to how far apart they are and how much you are moving your head. The earth moves back and forth about 300 million kilometers every year, this cause the positions of the closest stars to change ever so slightly, but by a large enough amount that we can measure them.
 

Drakkith

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Drakkith, Thank you. Well said! OK, I get that. But what I'm not getting is the 'distance' between the stars (thousands of light years) from one star to another that we see when we look at one point of light, (a star) in the sky, and then scan our eyes to the opposite point in the night sky to another star. All I can conclude is the 'separation' I see is what we call distance! That separation represents thousands of lightyears of distance as we look back and forth between them, right? I believe the sicence, I just can't understand how we can see that many lightyears of distance between point 'A' star and point 'B' star, on a horizontal/elipse plain with the naked eye, when it would take thousands of light years, traveling at the 'sol' to actually travel there! Did I make that clear? What am I missing?
I'm sorry but I don't really understand your question. The arrangement of stars in the sky and both their real and apparent separation is due to a combination of chance and geometry. The fact that we can see that entire real separation is due to geometry and the physics of how light travels. I'm not sure if that helps or not, but I'm having trouble understanding what you're asking about.
 
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I think he might be touching on the "Sweep a laser pointer across the sky" scenario.
 
Yes, it is difficult to state simply. But once you see what I mean you'll get that (Ah, that's what he means, moment!) Like I'm trying for with this question! LOL! Try this senario, please. You're standing outside on a clear night. You look up and see a sky full of stars. You pick one bright star on the far right side of the night sky, (star A) and one star on the far left side, opposite of the first star, (star B). The distance between those two stars, (A & B), has been determined to be five thousand lightyears! So the question is: How can we see star A and star B which are five thousand lightyears apart in space, from a vantage point from earth, that's 50 to 100 miles from horizon to horizon over our head? How are you and I able to 'see' 'five thousand lightyears which would take us five thousand years, traveling at the sol to actually travel from star A to star B? We know it's true, you and I are able to see those two stars, and they are five thousand lightyears from one another, and we can see them in the space overhead! I just don't know how that works? Is it the distance the stars are from us, from themselves, our perspective, focus, what? Does that help? There has to be a basic astronomical fundamental principle, axiom or visual scientific explanation term for what you and I are seeing and I'm trying to describe. I just can't find the right words for it. Thanks again!
 

Drakkith

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So the question is: How can we see star A and star B which are five thousand lightyears apart in space, from a vantage point from earth, that's 50 to 100 miles from horizon to horizon over our head?
We can see the stars simply because the light has made its way to us from each star. The 2nd part is confusing. The stars are not at the horizon, and the horizon is not over our head, so the 50-100 miles from horizon to horizon is meaningless.

How are you and I able to 'see' 'five thousand lightyears which would take us five thousand years, traveling at the sol to actually travel from star A to star B?
The distance between the two stars has nothing to do with our ability to see them. One is to the left simply because that is where it is located in space relative to ourselves. The other is to the right for exactly the same reason.

Is it the distance the stars are from us, from themselves, our perspective, focus, what?
Yes, it is only the star's relative position to us and its distance from us that matters. Where the other star is located is irrelevant in regards to seeing the 1st.
 

russ_watters

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How can we see star A and star B which are five thousand lightyears apart in space.... How are you and I able to 'see' 'five thousand lightyears which would take us five thousand years, traveling at the sol to actually travel from star A to star B?
We don't see time or distance, we see light that enters our eyes. I can't imagine why you would think the distance between the stars matters. The light doesn't travel from one star to the other and then to you (not sure if you are thinking that...), it just travels from each star to you.

Try this: You're holding a party at your house, and it starts at 7:00pm. One of your friends lives 20 miles east of you and the other lives 90 miles west of you. Both arrive at the party on time. How is this possible when they live 110 miles apart?

Or:
I just looked at a meter stick and then I looked at the moon. The moon is bigger than the meter stick. How is it possible that I could see the moon?

Do these questions even make sense?
 
We don't see time or distance, we see light that enters our eyes. I can't imagine why you would think the distance between the stars matters. The light doesn't travel from one star to the other and then to you (not sure if you are thinking that...), it just travels from each star to you.

Try this: You're holding a party at your house, and it starts at 7:00pm. One of your friends lives 20 miles east of you and the other lives 90 miles west of you. Both arrive at the party on time. How is this possible when they live 110 miles apart?

Or:
I just looked at a meter stick and then I looked at the moon. The moon is bigger than the meter stick. How is it possible that I could see the moon?

(Reply) You lost me with that anlogy? Unless your being sarcastic? Of course the moon is bigger than a meter. How could I not see it based on what you said? (See, your analogy made sense to you, but I don't see what you're trying to make me see by it, much like my question, I guess! I'm not explaining my question adequately and I may be frustrating someone who has a lot more astronomy knowledge than I do!
OK, using your meter stick analogy, the moon is about 240K miles from earth. Yes, I see what your saying, but stars in the sky are thousands of lightyears from one another, how can I see the span of lightyears between them precieved by us as distance? See what I'm saying? The stars are infinately farther than the moon, some are thousands of lightyears from one to another, but I can still see that span, isn't that the same argument?
If I may respectfully address your comments. (Reply) 1. You can't imagine why I would think the distance between stars would matter? Then why did they call it Leavitt's Law? Isn't that why do astronomers tell us that certain stars and galaxies are 4, 20, 500, 1000's of lightyears away from us?) 3. Doesn't light from a star travel in all directions from the source? We happen to be the only ones who can see it, as far as we know! 4. I don't think light travels from one star to another and then to us! 5. The party scenario: I guess the friend who lives 90 miles away had to either leave from his home earlier than the friend who lives 20 miles away for both to arrive on time. Or he drove 4 or 5 times faster than the friend who lives closer. It's the distance each has to travel, times the speed they travel, that determines the time it takes each to arrive at the same time. (D=S*T) And it wouldn't make any difference what direction they lived from my house. But I'm not sure what you're leading me to correlate with you're analogy.

We can see the stars simply because the light has made its way to us from each star. The 2nd part is confusing. The stars are not at the horizon, and the horizon is not over our head, so the 50-100 miles from horizon to horizon is meaningless.
(Reply) What I was trying to express what we see overhead in the nightsky. Where the sky meets the curve of the earth isn't the horizon? There are no visible stars there? The horizon isn't part of whta's overhead? I'm not sure what YOU mean?

The distance between the two stars has nothing to do with our ability to see them. One is to the left simply because that is where it is located in space relative to ourselves. The other is to the right for exactly the same reason. (Reply) I get it, there's no up, down, N.S.E.W., left or right in space! I was giving a point of reference from earth as we see the nightsky.

Yes, it is only the star's relative position to us and its distance from us that matters. Where the other star is located is irrelevant in regards to seeing the 1st.


(Reply) I'm not sure what you're saying here?
OK, let me try this. Let me ask you a few questions. You respond and answer just the question I ask without going into the minutia. Maybe that will help me understand what I can't seem to convey here.
Are you simply asking how can we figure out how far apart two stars are? None of that is done with the naked eye, it requires extremely precise measurements.

Reply: No, I'm not asking how we can figure out how far apart two stars are. I'm asking, if we 'already know', by calculation, the distance between two stars is 5 thousand lightyears, and we can see both stars together in the night sky, then we are seeing the 'five thousand lightyears between those two stars', implied by the span between them, right? (Please answer, yes or no, right or wrong?) And then explain!

(The question is not that one doesn't believe it, yes, we see the two stars light and yes we see the span between them.) My response to your answer of 'yes', is, one of incredulousness!) (I would assume you would say, "yes, amazing ain't it, those two stars were looking at are five 5 thousand lightyears apart, as represented but the distance of the span between them!" I would say: "So the span between those two stars we're looking at represents 'five thousand lightyears'?" "But if those two stars we're looking at are five thousand lightyears apart, how can we be seeing five thousand lightyears with the naked eye?" "Wouldn't the have to be super-massive stars to understand that the 'span' between them represents five or more lightyears?" (Some stars are super-massive stars, but not all the ones we see!)
What I have a hard time comprehending is being able to see a span between two stars and understand that span represents and is five or whatever # of lightyears that I can see, with or without a telescope! It's mind-blowing and unimaginable the distance and size when you get those momentary glimpses in your mind of how big space, the cosmos and the universe really is.
Isn't there a scientific/astronomical term for what I'm describing?

I don't know how much more clear I can explain it, respectfully!? Does this help and make my question more understandable? Thank you. I appreciate your help.


The closest stars we determine their position through parallax. If you take two objects that are different distances from your eye and move your head, these objects will change position relative to your eyes. That change is related to how far apart they are and how much you are moving your head. The earth moves back and forth about 300 million kilometers every year, this cause the positions of the closest stars to change ever so slightly, but by a large enough amount that we can measure them.
 

russ_watters

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The quoting is a mess here; hopefully I can sort it out...
You lost me with that anlogy? Unless your being sarcastic?
My reply was not intended to be sarcastic. My goal was to pick examples of a similar type and level of absurdity so that you may recognize and connect them to your example and see why the problem you posed doesn't make sense.
OK, using your meter stick analogy, the moon is about 240K miles from earth. Yes, I see what your saying, but stars in the sky are thousands of lightyears from one another, how can I see the span of lightyears between them precieved by us as distance? See what I'm saying?
No, I don't. How does the difference actually matter? Light from opposite edges of the moon are separately traveling to your eye. Light from different stars are separately traveling to your eye. There is no difference between these scenarios and no reason to believe the distance between the points on the moon or stars matters - or at least you haven't stated one, you just keep saying "how"? without explaining "why not".
The stars are infinately farther than the moon, some are thousands of lightyears from one to another, but I can still see that span, isn't that the same argument?
It is indeed exactly the same, which is why if you have no problem with accepting that you see the whole moon you should have no problem accepting that you see two different stars.
1. You can't imagine why I would think the distance between stars would matter? Then why did they call it Leavitt's Law?
This has nothing to do with your question. Your question asked how it is possible to see two stars at the same time when they are far apart. My answer to that question is that it doesn't matter how far apart they are. That answer cannot be interpreted to mean that there aren't other contexts where the distance between stars might be interesting to know.
What I have a hard time comprehending is being able to see a span between two stars and understand that span represents and is five or whatever # of lightyears that I can see, with or without a telescope! It's mind-blowing and unimaginable the distance and size when you get those momentary glimpses in your mind of how big space, the cosmos and the universe really is.
Isn't there a scientific/astronomical term for what I'm describing?

I don't know how much more clear I can explain it, respectfully!? Does this help and make my question more understandable? Thank you. I appreciate your help.
I think you used the right word: imagination. There is no logic behind your inability to imagine this, but that's ok. There's a lot of things that happen in the universe that are difficult to picture in our imagination. That doesn't mean we should let that limit our understanding of them.

Let's try another one:
Sometimes the moon and Venus are in the sky at the same time and we can see them both even though they are 40 million miles apart. Sometimes Venus and Jupiter are in the sky and visible together even though they are 500 million miles apart. Sometimes Venus and Neptune are near each other in the sky and both are visible (Neptune, barely) even though they are almost 5 billion miles apart.

How far apart do two objects that appear to be near each other have to be before your imagination starts to have difficulty processing/accepting the distance between them?
 

Drakkith

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3. Doesn't light from a star travel in all directions from the source? We happen to be the only ones who can see it, as far as we know!
I don't know what you're getting at here. It's true that we are the only ones who can see it as far as we know in the sense that we don't know if other lifeforms exist elsewhere to see it, but if you and I were placed 100 light years on the other side of the star we would certainly still see it.

This is my problem with your questions. You ask a concrete question (light traveling in all directions) and then follow it up with something completely vague (is the part about we being the only ones who can see it a statement about extraterrestrial life, or is it a reference to a question about how light travels).

I feel you have some misunderstanding about physics that I would like to address, but I can't say exactly what it is yet.

4. I don't think light travels from one star to another and then to us!
That is correct. For the vast majority of the light it does not. There might be a few photons from one star scattered off of another star and into our direction every now and then, but this occurs so infrequent that it's contribution is almost nil.

Reply: No, I'm not asking how we can figure out how far apart two stars are. I'm asking, if we 'already know', by calculation, the distance between two stars is 5 thousand lightyears, and we can see both stars together in the night sky, then we are seeing the 'five thousand lightyears between those two stars', implied by the span between them, right? (Please answer, yes or no, right or wrong?) And then explain!
Sure. Using those two stars as starting and end points, we can find the distance between them and say that the path traveled when moving directly from one star to the other is 5000 light years. That is certainly true. However, that's only true for that exact path. Any deviation, no matter how small, will be another path which, depending on where you eventually stop, will be shorter or longer than the original.

And, really, we don't actually need those two stars as starting and end points. We could use any physical objects. Or none at all. If I find the angle between the stars (in this case 180 degrees) and place successive start and end points upon lines starting at myself and ending on the stars, then the distance between these points will increase as my points move away from me and towards the stars. So I can 'see' a path that's 2500 light years long despite the fact that my starting and end points are nowhere near either star yet.

So what I'm getting at is that the stars themselves have nothing to do with this except as convenient and visible starting and end points.
 
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"Did I make that clear? What am I missing?"

This isn't CGI, building a scene via careful ray-tracing between light-source and object and eye.

As I said earlier, your model is back-to front. IMHO, your misconception echoes a 'classical' notion of vision, where-in 'something' emitted from eyes provides sight. How they 'explained' not being able to see in the dark matches 'Flat Earth' logic...

We know a bit better. That light, those photons were already on the way.
Bright stuff gives off light. That goes hither and yon, never faster than 'c', interacting variously. If you happen to be looking in the right direction, and your eyes respond to the photon flux, you 'see the light'. A telescope's 'light bucket' optics will let you see more than an unaided eye. Beyond a rainbow's pretty range, you must rely on instruments ranging from planet-wide radio-telescope arrays at one end to grazing reflectors at the other...

For a gentle deconstruction of your fallacy, albeit in slo-mo, consider a coastal light-house with a revolving beam. A ship far to its West may glimpse it on the horizon. Then, as the lantern's lens(es) swing, a ship far to its East may glimpse it likewise. Even if a sea-mist and/or the Earth's curvature blocks the ships' view of each other, so no light from one ship can reach the other, they'll still glimpse the light-house beam by turn...
 

phyzguy

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5. The party scenario: I guess the friend who lives 90 miles away had to either leave from his home earlier than the friend who lives 20 miles away for both to arrive on time. Or he drove 4 or 5 times faster than the friend who lives closer. It's the distance each has to travel, times the speed they travel, that determines the time it takes each to arrive at the same time. (D=S*T) And it wouldn't make any difference what direction they lived from my house. But I'm not sure what you're leading me to correlate with you're analogy.
Why isn't russ_waters party analogy exactly the same as what you are asking? If you look up in the sky and see two stars, one that is 4 light-years away, and one right next to it that is 1000 light-years away, the light left the first star 4 years ago, and the light left the second star 1000 years ago, so they both arrive at your eye at the same time. What is it about this that bothers you?
 
I think there has been some has misunderstanding of my question, or I'm not explaining it well. It appears people are responding and answering different questions I never asked on different topics I did not ask about! I'll try one more time! My apologies for my lack of understanding of light, photons, physics, stars etc.

Darkkith, is this the response you sent me below?
Are you simply asking how can we figure out how far apart two stars are? None of that is done with the naked eye, it requires extremely precise measurements.

The closest stars we determine their position through parallax. If you take two objects that are different distances from your eye and move your head, these objects will change position relative to your eyes. That change is related to how far apart they are and how much you are moving your head. The earth moves back and forth about 300 million kilometers every year, this cause the positions of the closest stars to change ever so slightly, but by a large enough amount that we can measure them.





Why isn't russ_waters party analogy exactly the same as what you are asking? If you look up in the sky and see two stars, one that is 4 light-years away, and one right next to it that is 1000 light-years away, the light left the first star 4 years ago, and the light left the second star 1000 years ago, so they both arrive at your eye at the same time. What is it about this that bothers you?

Surayabay - My response:

I'm not bothered by it! I'm sure russ waters is correct, his thoughtful answer just isn't related to my question!

My Question:

I pick two stars in the sky. Assume we already know the distance between them is five thousand lightyears, done by calculation.
When I look at those two stars I see a separation between them, (I call that the distance between them.)
Doesn't that separation/distance I see between those two stars represent five thousand lightyears, even though I can't actually see five thousand lightyears of distance, what I am seeing is what five thousand lightyears looks like from earth. (yes or no, right or wrong, please.) Then please explain what I got mixed-up. Thanks! I will have follow-up questions too!
 
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I think you're asking about just basic trigonometry. You're asking how can we see the span between two stars that are many light years apart.

triangle.gif


You are at the point at angle B, the stars are at A and C. Are you asking how it's possible that we can see the entirety of length b? It's all geometry, either wide angle photography (make the angle of B bigger) or just have a and c be long enough that b fits inside the angle B. Your terminology is what is confusing people. The DISTANCE between the two stars in b, the ANGULAR SEPERATION is B.

Here is a photograph of the Andromeda Galaxy.
dromeda-Galaxy-Josh-Blash-7-23-2014-e1473897834535.jpg

A star on the left side of the galaxy in this image is about 200,000 light years away from a star on the right side of the galaxy. It fits inside a space a little smaller than the full moon because it's about 2 million light years away.

See that bright red dot at the 5-o'clock position of the galaxy? It angular from the galaxy is less than a degree, but it’s distance is over two million light years.



Imagine a perfectly straight set of train tracks. Put a penny on one side of the tracks and another on the other side. They’re separated by few feet and you can see both. Now slide the pennies along the track. As long as you are in the track looking down them, you can always see both pennies. It makes no difference is they are both two feet from you or if one is two feet from you and the other is two hundred miles (assuming you have perfect vision.)
 
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Drakkith

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When I look at those two stars I see a separation between them, (I call that the distance between them.)
Doesn't that separation/distance I see between those two stars represent five thousand lightyears, even though I can't actually see five thousand lightyears of distance, what I am seeing is what five thousand lightyears looks like from earth. (yes or no, right or wrong, please.)
Of course you can see 5000 thousand light years of distance. It's no different than seeing 5 feet of distance or 5 miles of distance.

Darkkith, is this the response you sent me below?
Nope.
 

phyzguy

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... even though I can't actually see five thousand lightyears of distance, what I am seeing is what five thousand lightyears looks like from earth. (yes or no, right or wrong, please.)
Wrong.

newjerseyrunner has nailed what your problem is. You are confusing linear distance with angular separation. Try this Wikipedia article:

 

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• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
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