Why Does 'a' Being Smaller Than 'a0' Eliminate μ in MOND?

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Discussion Overview

The discussion revolves around the Modified Newtonian Dynamics (MOND) theory, specifically addressing why the condition of 'a' being smaller than 'a0' leads to the elimination of the function μ in the context of gravitational dynamics. Participants explore the implications of MOND on galaxy rotation curves and the nature of the interpolation function μ, as well as comparisons with dark matter theories.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants express confusion about the role of the function μ in MOND, particularly how it behaves when 'a' is smaller than 'a0'.
  • Others clarify that μ is defined as a function of x, with specific behaviors for large and small values of x, suggesting that μ(x) = 1 when x is much larger than 1 and μ(x) = x when x is around 1 or smaller.
  • One participant proposes an example of μ(x) = x/(1+x) to illustrate the concept.
  • Concerns are raised about the nature of MOND as a "fudge factor" in gravity equations, with some arguing that it fails to provide a consistent explanation across different galaxies.
  • Another participant notes that MOND has shown success in predicting behaviors for certain galaxies, particularly Low Surface Brightness galaxies, but struggles at larger and smaller scales without additional adjustments.
  • Some participants compare MOND to dark matter theories, suggesting that both may serve as "fudge factors" to reconcile observations with existing gravitational models.
  • There is a mention of the "tooth fairy rule" in theoretical astrophysics, highlighting the acceptance of one significant assumption to make a theory work, but questioning the validity of multiple assumptions in MOND.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement regarding the effectiveness of MOND compared to dark matter theories. While some believe MOND is successful at the galactic scale, others argue that it lacks a solid theoretical foundation and fails to consistently explain observations across different contexts.

Contextual Notes

Participants note that MOND's success is primarily empirical, with ongoing discussions about its theoretical underpinnings and the variability of the "fudge factor" across different galaxies. There are unresolved questions about the relationship between MOND and Newtonian mechanics, particularly in how they relate to dark matter theories.

  • #31
mesa said:
I'm a little surprised that would work, how is the integretion setup? Is it a function of the gravity of each sun and it's affect on the next by putting together an artificail layout based on average distances apart or is it simply the sum of all the masses thrown into the center for the swept area of the galaxy by a particular star?

I was told by an astrophysicist that it has only been recently that papers were published changing the model from a spherical density to a more disc like shape, I found this surprising as well.

I don't know the practical details. For a simple case, I guess one could assume one could treat the mass as a series of rings of varying density surrounding a spherical nucleus. In a more complex cases one could use numerical methods to sum the effects of mass density over a modeled shape of the galaxy consistent with the observations. There's certainly no need to model the individual stars, because from sufficient distance the gravitational effect is essentially the same as that of a continuous medium with an appropriate average density.
 
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  • #32
Jonathan Scott said:
I don't know the practical details. For a simple case, I guess one could assume one could treat the mass as a series of rings of varying density surrounding a spherical nucleus. In a more complex cases one could use numerical methods to sum the effects of mass density over a modeled shape of the galaxy consistent with the observations. There's certainly no need to model the individual stars, because from sufficient distance the gravitational effect is essentially the same as that of a continuous medium with an appropriate average density.

Where do you think would be a good place to start to find the actual formulas used for these calculations? I looked online and came up with very little. Are there members on the board that would be helpful?

I am going to quiz the proffesors at school again and see if I can get a more complete answer. I was told by one it was basically the same as you stated originally; the mass is essentially summed and put into the center and then calculated.

That seems overly simplified and frankly I don't see how that could calculate anything properly.
 

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