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#1
09-18-2019, 12:12 PM
 Guest Join Date: Dec 2007 Posts: 112

## Does the inverse square law remain true for large distances?

The inverse square law applies because as you recede from a light source the area that must be illuminated increases with the square of the distance. But if you are viewing a star that is a thousand light years away that means the universe has had a thousand years to expand. Seems to me the area to be illuminated is now slightly larger than the distance squared. Perhaps the discrepancy is too small to matter?
#2
09-18-2019, 12:24 PM
 Guest Join Date: Oct 2018 Posts: 152
Quote:
 Originally Posted by Carlarm The inverse square law applies because as you recede from a light source the area that must be illuminated increases with the square of the distance. But if you are viewing a star that is a thousand light years away that means the universe has had a thousand years to expand. Seems to me the area to be illuminated is now slightly larger than the distance squared. Perhaps the discrepancy is too small to matter?
I'm going to guess that you are right, that 1000 light years of distance is not enough for the expansion of the space between you and the light source to be appreciable. Maybe you could factor this in but it should be a tiny, negligible effect.

The space expansion effect should be factored in for very very distant objects, millions or billions of light years distant, at scales separating galaxies from each other. I'm not a professional astronomer, but I'd bet that the idea of red shift is connected to this space-expanding effect.

Indeed, Wikipedia's entry for red shift says that it is caused by objects moving apart from each other, also due to the expansion of space itself: https://en.wikipedia.org/wiki/Redshift (The third reason is strong gravitational effects, but I think we might neglect that for this discussion.)

Last edited by Limmin; 09-18-2019 at 12:24 PM.
#3
09-18-2019, 01:30 PM
 Charter Member Join Date: Jan 2001 Location: Mid Atlantic, USA Posts: 9,579
I think you're right in principle, that there's a deviation at large distances because of the expansion. But I don't think 1000 light years is far enough. At 1000 light years, star motions are dominated by the dynamics of our galaxy and its myriad component populations. If you went to 1,000,000 light years you might have that effect, or maybe you'd have to go to 1,000,000,000 light years. You have more than an order of magnitude available beyond that before things get too distant to interact with.
#4
09-18-2019, 01:59 PM
 Member Join Date: Dec 2009 Location: Continental Divide Posts: 5,420
There is no decrease to a Newtonian approximation for cosmological observations due to expansion. We are co-moving so the distance and angular diameter remains constant for the observer, which in this case are point light sources. Note that even under Newtonian mechanics the inverse square law only holds for spherically symmetric objects which works for "point source". These observations were already point sources and even if we weren't co-expanding they would still act like point sources.

The Inverse square law is one of the correct predictions of general relativity if you are dealing with low speed and weak gravity approximations. It arises because we are in four-dimensional spacetime but is itself not a fundamental property in modern physics.

The fact that we can simplify to that level is more than convenient.

Last edited by rat avatar; 09-18-2019 at 02:00 PM.
#5
09-18-2019, 02:21 PM
 Member Join Date: Dec 2009 Location: Continental Divide Posts: 5,420
For those who want the math behind how this reduces to the simplified model I found this "paper" which is actually lecture notes.

https://arxiv.org/abs/1712.10315

Section 6.7 has a fairly simple and standard way of explaining why it simplifies to the ordinary, non-expanding, Euclidean-space form.
#6
09-18-2019, 05:01 PM
 Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 85,131
Once you get to cosmological scales, there are multiple different things you can define as "distance", which will give you different answers to questions like this.

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