<p>I'm trying to understand the point where the expansion of space dominates over gravity, but I'm coming up empty handed when searching the internet. Specifically, I'm trying to find the math for it. I'm wondering if there might be some sort of Hill sphere-like thing surrounding galaxies or clusters, inside which gravity keeps things together and there is no effect, or very little effect, from the expansion of space. Does anyone know where I can find the math for this or whether there is even such a point in space?</p>

CC BY-SA 4.0
2022-07-26T16:55:24.730Z
This post from our sister site doesn't exactly answer your question, but it's got lots of great info (& references) about expansion: https://physics.stackexchange.com/a/63780/123208
PM 2Ring
CC BY-SA 4.0
2022-07-26T18:11:43.413Z
Are you asking for details of the turnaround radius?  This is the surface around a mass where there is neither expansion away or infall towards the gravitating object.
eshaya
CC BY-SA 4.0
2022-07-27T03:26:25.487Z
Thanks @eshaya. This should be the answer. It's is exactly what I meant. I'm glad it has a name! Here's a reference paper https://arxiv.org/pdf/1912.08216.pdf.
Richtopia
CC BY-SA 4.0
2022-07-27T12:23:06.633Z
Feel free to write your own answer, based on that paper.  We encourage self learners!
James K
CC BY-SA 4.0
2022-07-27T15:26:14.080Z
This pair of papers on Perturbations of the Hubble flow provide a lot of math on growth of overdensities for professionals.  In particular, the appendix of the second paper has turnaround equations.
https://ui.adsabs.harvard.edu/abs/1980A&A....86..212O/abstract https://ui.adsabs.harvard.edu/abs/1982A&A...107..172O/abstract
eshaya
<gravity><expansion>
Calculating the "Turnaround Point," where expansion dominates over gravity
Richtopia
# Calculating the "Turnaround Point," where expansion dominates over gravity

(Asked by: username_0 on 2022-07-26)

I'm trying to understand the point where the expansion of space dominates over gravity, but I'm coming up empty handed when searching the internet. Specifically, I'm trying to find the math for it. I'm wondering if there might be some sort of Hill sphere-like thing surrounding galaxies or clusters, inside which gravity keeps things together and there is no effect, or very little effect, from the expansion of space. Does anyone know where I can find the math for this or whether there is even such a point in space?

**Tags:** gravity, expansion
> **Comments:**
> **username_1**: This post from our sister site doesn't exactly answer your question, but it's got lots of great info (& references) about expansion: https://physics.stackexchange.com/a/63780/123208  
> **username_2**: Are you asking for details of the turnaround radius?  This is the surface around a mass where there is neither expansion away or infall towards the gravitating object.  
> **username_0**: Thanks @eshaya. This should be the answer. It's is exactly what I meant. I'm glad it has a name! Here's a reference paper https://arxiv.org/pdf/1912.08216.pdf.  
> **username_3**: Feel free to write your own answer, based on that paper.  We encourage self learners!  
> **username_2**: This pair of papers on Perturbations of the Hubble flow provide a lot of math on growth of overdensities for professionals.  In particular, the appendix of the second paper has turnaround equations. https://ui.adsabs.harvard.edu/abs/1980A&A....86..212O/abstract https://ui.adsabs.harvard.edu/abs/1982A&A...107..172O/abstract  

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