Exponential growth of eccentricity in secular theory

Boaz Katz; Subo Dong

Home/Archive/arXiv

arXiv · 1105.3953

Exponential growth of eccentricity in secular theory

Boaz Katz·Subo Dong

View original source ↗Read source document ↗Export metadata ↓

Abstract

The Kozai mechanism for exponentially exciting eccentricity of a Keplerian orbit by a distant perturber is extended to a general perturbing potential. In particular, the case of an axisymmetric potential is solved analytically. The analysis is applied to orbits around an oblate central object with a distant perturber. If the equatorial plane of the central object is aligned with the orbit of the distant perturber (axisymmetric potential), a single instability zone, in which eccentricity grows exponentially, is found between two critical inclinations; if misaligned (non-axisymmetric potential), a rich set of critical inclinations separating stable and unstable zones is obtained (Vashkoviak 1974). The analysis is also applied to a general quadratic potential. Similarly, for non-axisymmetric cases, multiple stability and instability zones are obtained. Here eccentricity can reach very high values in the instability zones even when the potential's deviation from axisymmetry is small.

Explore related subjects

astro-ph.EP physics.class-ph

Keep this discovery

BibTeX RIS

Boaz Katz, Subo Dong. 2011-05-19. Exponential growth of eccentricity in secular theory. https://arxiv.org/abs/1105.3953

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Planetary Accretion Is Less Frequent in Wide Binaries: Evidence from Metal-Enriched White Dwarfs in DESI DR1

Binary stars are common in the Galaxy, and understanding how stellar binarity influences the formation and evolution of planetary systems is an active area of research. In this study, we use metal-enriched white dwarfs in wide binaries as tracers of long-lived planetary systems. With Data Release 1 from the Dark Energy Spectroscopic Instrument (DESI), we find that the fraction of cool metal-enriched white dwarfs in wide binaries is 9.8\,$\pm$\,2.1\%, significantly lower (4.7\,$\sigma$) than the 20.5\,$\pm$\,0.9\% in a control sample of single systems. Furthermore, we identify a tentative dependence of metal enrichment on projected separation and white dwarf effective temperature, where enrichment fraction decreases at smaller separations and lower temperatures. These findings indicate that, compared to single stars, binary systems either start with smaller initial planetary reservoirs due to suppressed planetesimal formation or undergo more rapid depletion of planetary material during the initial part of the white dwarf stage.

astro-ph.EP↗

arXiv2026

The Mysterious Inspiral of WASP-12b: Why Obliquity Tides Cannot Drive Orbital Decay

WASP-12b's orbit is decaying, for unknown reasons. The planet's period is shrinking more rapidly than can be attributed to equilibrium tides or dynamical tides in a main-sequence star. Planetary obliquity tides could be sufficiently dissipative to drive WASP-12b's inspiral, but would also damp the planet's obliquity, halting the decay. Millholland & Laughlin proposed that a nearby, low-mass planet ($\sim 10$ M$_\oplus$) is maintaining a large obliquity for WASP-12b, sustaining the dissipation. We re-evaluated this hypothesis, finding that the companion must be more massive than originally proposed ($\gtrsim 65$ M$_\oplus$) to absorb WASP-12b's orbital angular momentum. Radial velocity data allowed us to rule out a companion of this type. Any companions within $3$ AU have $K \lesssim 14$ m/s at $95$% confidence.

astro-ph.EP↗

arXiv2026

Lava Tube Exploration with LunarLeaper

Lunar pits, some of which are interpreted as collapse features into underlying lava tubes, expose otherwise inaccessible stratigraphy and may provide entry points to subsurface voids that preserve records of lunar volcanism and offer potential sites for future human exploration. We synthesize the current state of knowledge on lunar pits and lava tubes, covering their morphological characteristics, classification, proposed formation mechanisms, mechanical stability, and detection from orbit. We then review the open science questions that pit and pit-wall investigation is uniquely placed to address, spanning the volcanic stratigraphy of the lunar maria, the structure and lateral variability of the regolith, and the dimensions and accessibility of subsurface conduits. To evaluate how these questions can be tackled in situ, we assess the feasibility and expected performance of geophysical and remote-sensing investigations for subsurface voids and surface exposures, mainly focusing on gravity measurements, ground-penetrating radar, high-resolution imaging, and spectroscopy. Building on this, we present LunarLeaper, a small legged robot mission concept combining a gravimeter, ground-penetrating radar, high-resolution imager, spectrometer, and leg-based geomechanical experiments to deliver the first in situ investigation of a mare pit. The concept targets the Marius Hills Pit and its associated rille, with a mobility architecture optimized for the rugged terrain encountered at pit edges and funnel slopes.

astro-ph.EP↗