N-BODY SOLUTIONS AND COMPUTING GALACTIC MASSES

Abstract

A classical approach used to determine the mass distribution of a galaxy in terms of observed rotational velocities is applied to analytic solutions of Newtonian systems of N discrete bodies (so mass distributions are known). Predictions significantly exaggerate the amount of mass distributed at larger distances from the center; e.g., rather than the actual 5% of mass on the outer edges, the method could predict over 80%. Explanations are given for the differences.

Spiderweb Central Configurations

“…From our many numerical experimentations we are led to believe that the n × and n × + 1 spiderweb central configurations not only exist, but are unique in the sense of Section 2.1. Saari stated the same result in his papers [9] and [10].…”

“…The proof is a completion of Saari's proof given in [10] for the existence of spiderweb central configurations when n ∈ {3, 4}. It makes an essential use of all properties proved in Lemma 2.4 and Corollary 2.5.…”

“…m n for m 0 = 0, while Saari treated the general case, releasing the restrictions on the masses with a different method in [9] and [10]. We became interested in the problem and decided to study numerically the distribution M (η) of mass depending of the distance η to the origin for large values of and n. At the same time we considered the proofs of the results appearing in [1], [9] and [10]: to our surprise, these proofs are incomplete and we started working on completing them. We could give some complete proofs, but not for all values of n, and of the masses.…”

“…In [10], Saari proposed a proof of the existence of spiderweb central configurations in the general case. There, again, the proof was by induction on n, and used continuity arguments, which had to rely on the implicit function theorem.…”

On Rotation Curve Analysis

“…In both cases, a successful skepticism regarding the connection between galactic rotation curves and dark matter would require us to reevaluate these methods and our expectations for the future of cosmological research. I will endeavor to show that such a radical reevaluation is unnecessary-at least on the basis of the considerations presented in (Saari 2015).…”