Inverse square law explains Olbers' paradox?

[Drakkith]

I was of course referring to apparent size. Let me try again. If the angular diameter of a star can not be resolved and the distance from the star is increased, then its apparent size can not get any smaller, only its apparent color can get dimmer. True?

Apparent size/angular diameter does not depend on our ability to resolve an object. Consider that the resolving power of an optical system is highly variable. Very small diameter telescopes have MUCH less resolving power than very large telescopes. Resolving power has nothing to do with apparent size/angular diameter, as the latter is purely a function of object size and distance. This is why it helps to look at the paradox using hypothetical "perfect" optical systems that can resolve whatever object we want to talk about. We can ignore what doesn't apply to the paradox.

That arc-second will not correspond to the same surface area if the distance is increased, but larger area, so yes. I guess that example is supposed to represent a "wall of stars" relating to Olbers' paradox, but it's misleading as those stars are not in the same plane perpendicular to the line of sight.

It doesn't matter if it's in the same plane or not, the light still comes out the same. That's what we've been trying to get you to understand. It's not misleading, it's the way it works.

 

[humbleteleskop]

Let me say it again: The angular size of an object is what it is, independent of whether or not we can resolve an object of this size or not. The size of an object is not determined by our ability to measure.

Apparent size/angular diameter does not depend on our ability to resolve an object. Consider that the resolving power of an optical system is highly variable.

"In astronomy the sizes of objects in the sky are often given in terms of their angular diameter as seen from Earth, rather than their actual sizes."
http://en.wikipedia.org/wiki/Angular_size


"Mathematically an object may be considered a point source if its angular size is much smaller than the resolving power of the telescope."
http://en.wikipedia.org/wiki/Point_source

 

[Bandersnatch]

Look, if your detector has got a very low resolution, less than 0.5 degree in the case of the picture with the Sun you've posted, it won't be able to tell how big the source of light is. It would record the same brightness whether it's a 0.5 degree diametre stellar disc of X brightness, or a point source of the same brightness. But it's actual physical size, as well as the resultant angular size on the sky remains the same.

Is that what you can't understand? It's hard to guess when you just post a bunch of wiki quotes, that all agree with everything that has been said, without pointing out the problem you've got with understanding them.


I agree with others, you need to show a bit of good will here. This is not a debate, so it's not about winning or losing an imaginary argument. You either learn or you don't.

 

[Drakkith]

I'm done. The OP has shown a clear unwillingness to actually consider what has been said and learn. Requesting this thread be closed, as the question of whether the inverse-square law explains Olber's paradox has been hammered to death repeatedly.

 

[humbleteleskop]

Resolving power has nothing to do with apparent size/angular diameter, as the latter is purely a function of object size and distance.

Mathematically an object may be considered a point source if its angular size is much smaller than the resolving power of the telescope. Ok? So what happens to apparent brightness of an object which you can not resolve and you move away to a point that is twice your current distance? Can its apparent size get any smaller? Or will its color instead get four times dimmer? Or what?

It doesn't matter if it's in the same plane or not, the light still comes out the same.

http://en.wikipedia.org/wiki/Apparent_brightness

Haven't we agreed just in our previous exchange that apparent brightness varies with distance?

So if apparent brightness varies with distance, how can possibly the amount of light received be the same from objects in the same plane perpendicular to the line of sight and from those which are not?

 

[Drakkith]

If you're willing to listen and not just link random wikipedia articles I'll help explain it to you. If something doesn't make sense, ASK for more detail on it, don't just find something that you think supports your understanding.

 

[Bandersnatch]

So if apparent brightness varies with distance, how can possibly the amount of light received be the same from objects in the same plane perpendicular to the line of sight and from those which are not?

We were talking about Olber's paradox, weren't we? It says there ought to be more stars farther away to compensate for the reduced brightness of each single star.

 

[humbleteleskop]

Look, if your detector has got a very low resolution, less than 0.5 degree in the case of the picture with the Sun you've posted, it won't be able to tell how big the source of light is. It would record the same brightness whether it's a 0.5 degree diametre stellar disc of X brightness, or a point source of the same brightness. But it's actual physical size, as well as the resultant angular size on the sky remains the same.

I don't think I said anything contrary to that. Please note Wikipedia does not define a point source in regards to low resolution sensor or blind people, it explicitly mentions telescope, so I suppose that has some relevance in which case it would render your example in relation to it invalid.

Is that what you can't understand? It's hard to guess when you just post a bunch of wiki quotes, that all agree with everything that has been said, without pointing out the problem you've got with understanding them.

I'm asking a question. I can't tell you what I understand or not unless we establish correct answer first.

QUESTION: What happens to apparent brightness of a star which is thousand million light years away, which apparent size you can not resolve with a telescope and you move away to a point that is twice your current distance? Can its apparent size get any smaller? Or will its color instead get four times dimmer? Or what?

 

[Bandersnatch]

Both. It's angular size will get smaller, which will result in less light reaching the detector.

 

[humbleteleskop]

Both. It's angular size will get smaller, which will result in less light reaching the detector.

How do you measure the difference in angular size if it is smaller than the resolving power of the telescope?

 

[Bandersnatch]

You don't. At that point you can only measure the total brightness of the area.

 

[humbleteleskop]

If you're willing to listen and not just link random wikipedia articles I'll help explain it to you. If something doesn't make sense, ASK for more detail on it, don't just find something that you think supports your understanding.

Please do explain. If apparent brightness varies with distance, how can possibly the amount of light received be the same from objects in the same plane perpendicular to the line of sight and from those which are not?

 

[Bandersnatch]

If apparent brightness varies with distance, how can possibly the amount of light received be the same from objects in the same plane perpendicular to the line of sight and from those which are not?

It's not true for individual stars. It's true for light coming from any area of the sky in Olber's paradox, as the stars fill the sky completely. Once again, it's not about individual stars - it's about the total contribution of all visible stars to the brightness of the sky.

 

[humbleteleskop]

You don't. At that point you can only measure the total brightness of the area.

Houston, we have an agreement.

We were talking about Olber's paradox, weren't we?

Does answer depend on it? We are talking about facts of reality, they should hold true in our hypothetical scenarios just like in the real world.

It says there ought to be more stars farther away to compensate for the reduced brightness of each single star.

It says total intensity received from each shell is the same, and we all agree. It does not mention any other kind of compensation or pixel saturation related to individual stars as suggested earlier on, but that doesn't bother me. Is that what you are referring to?

 

[Bandersnatch]

Does answer depend on it? We are talking about facts of reality, they should hold true in our hypothetical scenarios just like in the real world.

Answers you get depend on the setup you start with. The sky looks different if you start with an eternal, infinite universe, and different when you start with a finite one.

Yes, the physics is the same here and there, but the initial conditions are also improtant.

During this overly long discussion, there has been talk about both the physics of what makes stars less bright, and the end result of having infinitely many shells of equal brightness. I believe you've had them mixed at least once, which seems to be the source of the confusion.

It says total intensity received from each shell is the same, and we all agree. It does not mention any other kind of compensation or pixel saturation related to individual stars as suggested earlier on, but that doesn't bother me. Is that what you are referring to?

It also says there's an infinite number of shells. Which leads to pixel saturation.

 

[russ_watters]

Ok, that's enough. These are the same issues that were covered -- many of which were then ignored instead of resolved -- exactly 24 hours ago. Since this thread is going in ever tightening circles, it is locked.