SEMI-ANALYTICAL ESTIMATES FOR THE ORBITAL STABILITY OF EARTH’S SATELLITES

Irene De Blasi, Alessandra Celletti, Christos Efthymiopoulos

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:55 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The candidate reproduces the paper’s three core claims with the same logic: (A) J2 is neither convex nor quasi-convex while satisfying the three-jet test; the geolunisolar normal form is non-convex but quasi-convex (Tables 6–9 and Definition 10/11). (B) The semimajor-axis stability time bound T2 follows from dL/dt = −∂H/∂λ and a sup-norm/mean-value estimate (eqs. (47)–(52)). (C) In the resonant normal form, I1+I2 is exactly conserved, implying near-conservation of I ≈ (e^2+i^2)/2 up to the remainder (eqs. (53)–(56)). Minor discrepancies are purely expository (e.g., “det A ≡ 0” vs. “≈ 0 within precision” and the dimensionality of u in the three-jet test).

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript combines high-order normal forms with concrete sup-norm bounds to deliver long-term stability estimates for orbits across practically relevant altitudes, and it documents non-degeneracy properties indicative of Nekhoroshev-type behavior. The methodology is standard but carefully implemented; numerical evidence is convincing. Small clarifications (numerical precision for det A in J2; vector dimensionality in the three-jet test) would further improve readability.