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I Galaxy Rotation Curves and Mass Discrepancy

  1. Oct 9, 2017 #1
    I apologize for the simple question, but I am trying to understand the Mass Discrepancy-Acceleration Relation and its relationship to ##\mu(x)## (from https://arxiv.org/pdf/astro-ph/0403610.pdf).

    The mass discrepancy, defined as the ratio of the gradients of the total to baryonic gravitational potential, can be described by a simple function of centripetal acceleration:

    ##D(x) = \frac{\Phi'}{\Phi'_{b}} ##

    Where ##x = a/a0## and ##D(x)## is the inverse of the following equation:

    ##\mu(x) = \frac{x}{\sqrt{1+x^2}}##

    It's not clear to me how ##D(x)## is the inverse of the equation ##\mu(x) = \frac{x}{\sqrt{1+x^2}}##.

    For example, how would one substitute ##\mu(x)## for ##D(x)##?
     
  2. jcsd
  3. Oct 10, 2017 #2

    haruspex

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    If it means merely that D() is the inverse function of ##\mu(x)## then that would be ##D(x)=\frac x{\sqrt{1-x^2}}##.
     
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