Daily Papers

In this work, we consider the generalized Benjamin-Bona-Mahony equation $partial_t u+partial_x u+partial_x( |u|^pu)-partial_t partial_x^{2}u=0, quad(t,x) in R times R, with p>4. This equation has the traveling wave solutions \phi_{c}(x-ct), for any frequency c>1. It has been proved by Souganidis and Strauss Strauss-1990 that, there exists a number c_{0}(p)>1, such that solitary waves \phi_{c}(x-ct) with 1<c<c_{0}(p) is orbitally unstable, while for c>c_{0}(p), \phi_{c}(x-ct) is orbitally stable. The linear exponential instability in the former case was further proved by Pego and Weinstein Pego-1991-eigenvalue. In this paper, we prove the orbital instability in the critical case c=c_{0}(p)$.

Context: The Solar System giant planets harbour a wide variety of moons. Moons around exoplanets are plausibly similarly abundant, even though most of them are likely too small to be easily detectable with modern instruments. Moons are known to affect the long-term dynamics of the spin of their host planets; however, their influence on warm exoplanets (i.e.\ with moderately short periods of about 10 to 200~days), which undergo significant star-planet tidal dissipation, is still unclear. Aims: Here, we study the coupled dynamical evolution of exomoons and the spin dynamics of their host planets, focusing on warm exoplanets. Methods: Analytical criteria give the relevant dynamical regimes at play as a function of the system's parameters. Possible evolution tracks mostly depend on the hierarchy of timescales between the star-planet and the moon-planet tidal dissipations. We illustrate the variety of possible trajectories using self-consistent numerical simulations. Results: We find two principal results: i) Due to star-planet tidal dissipation, a substantial fraction of warm exoplanets naturally evolve through a phase of instability for the moon's orbit (the `Laplace plane' instability). Many warm exoplanets may have lost their moon(s) through this process. ii) Surviving moons slowly migrate inwards due to the moon-planet tidal dissipation until they are disrupted below the Roche limit. During their last migration stage, moons -- even small ones -- eject planets from their tidal spin equilibrium. Conclusions: The loss of moons through the Laplace plane instability may contribute to disfavour the detection of moons around close-in exoplanets. Moreover, moons (even those that have been lost) play a critical role in the final obliquities of warm exoplanets. Hence, the existence of exomoons poses a serious challenge in predicting the present-day obliquities of observed exoplanets.

In the era of mega-constellations, the need for accurate and publicly available information has become fundamental for satellite operators to guarantee the safety of spacecrafts and the Low Earth Orbit (LEO) space environment. This study critically evaluates the accuracy and reliability of publicly available ephemeris data for a LEO mega-constellation - Starlink. The goal of this work is twofold: (i) compare and analyze the quality of the data against high-precision numerical propagation. (ii) Leverage Physics-Informed Machine Learning to extract relevant satellite quantities, such as non-conservative forces, during the decay process. By analyzing two months of real orbital data for approximately 1500 Starlink satellites, we identify discrepancies between high precision numerical algorithms and the published ephemerides, recognizing the use of simplified dynamics at fixed thresholds, planned maneuvers, and limitations in uncertainty propagations. Furthermore, we compare data obtained from multiple sources to track and analyze deorbiting satellites over the same period. Empirically, we extract the acceleration profile of satellites during deorbiting and provide insights relating to the effects of non-conservative forces during reentry. For non-deorbiting satellites, the position Root Mean Square Error (RMSE) was approximately 300 m, while for deorbiting satellites it increased to about 600 m. Through this in-depth analysis, we highlight potential limitations in publicly available data for accurate and robust Space Situational Awareness (SSA), and importantly, we propose a data-driven model of satellite decay in mega-constellations.