Cuts

On Rotation Curve Analysis

“…In the light of his counterexample, Saari calls for new justifications for the use of Equation 1 and other continuous approximations (Saari 2016). But there are a number of misconceptions embedded in this challenge-first and foremost, the notion that Equation 1 is typically used to model galaxies.…”

“…Broadly speaking, Saari attributes the failure of Equation 1 to a "reductionist" approach: by analogy to Arrow's theorem, he argues that by simplifying a problem into individual component parts and solving each part separately, information that is otherwise preserved by a holistic treatment of the system is lost. In the specific case of dark matter, he argues that, by treating galaxies as continuous distributions instead of discrete N -body problems, astronomers have smoothed over and ignored the "connecting links" between bodies (Saari 2016). His contention is that when two bodies closely approach each other while traveling in their circular orbits, as in Figure 2, the inner body (A) 'tugs' on the outer body (B) in such a way that the outer body's rotational velocity increases, and that this 'tugging' is ignored by the continuous treatment of the N-body problem (Saari 2015).…”