ON THE SUNDMAN-SPERLING ESTIMATES FOR THE RESTRICTED ONE-CENTER-TWO-BODY PROBLEM

Ku-Jung Hsu, Lei Liu

correcthigh confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s Theorem 1.1 establishes angle monotonicity and Sundman–Sperling asymptotics for minimizers near a three-body collision, with α* determined by algebraic balances; the candidate solution derives the same conclusions via a direct Euler–Lagrange/polar-coordinate blow-up. Aside from a likely sign typo in Theorem 1.1’s equation (8) (the α∈(0,1) branch should have a plus sign, as is consistent with hm/µ(a,π)=0 later in the paper), the arguments coincide in substance (cf. Theorem 1.1 and Lemma 4.13) . The paper also rigorously excludes intermediate two-body collisions for minimizers before applying the analysis, which the model implicitly assumes .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The work gives sharp Sundman–Sperling-type asymptotics for action minimizers at a three-body collision in a restricted setting, balancing variational and analytic techniques. It closes a gap by proving monotonicity and limit classification for the angle and scaling ratio, and applies these to existence results with prescribed angles. Aside from a minor sign typo in the theorem statement, the presentation is rigorous and well-structured, and the results should be of interest to researchers in celestial mechanics and variational methods.