Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1612.05329

A study of symplectic integrators for planetary system problems: error analysis and comparisons

David M. Hernandez·Walter Dehnen
View original source ↗Read source document ↗Export metadata ↓

Abstract

The symplectic Wisdom-Holman map revolutionized long-term integrations of planetary systems. There is freedom in such methods of how to split the Hamiltonian and which coordinate system to employ, and several options have been proposed in the literature. These choices lead to different integration errors, which we study analytically and numerically. The Wisdom-Holman method in Jacobi coordinates and the method of Hernandez, H16, compare favorably and avoid problems of some of the other maps, such as incorrect center-of-mass position or truncation errors even in the one-planet case. We use H16 to compute the evolution of Pluto's orbital elements over 500 million years in a new calculation.

Explore related subjects

astro-ph.EPastro-ph.IM

Keep this discovery

BibTeXRIS

David M. Hernandez, Walter Dehnen. 2017-03-01. A study of symplectic integrators for planetary system problems: error analysis and comparisons. https://doi.org/10.1093/mnras%2Fstx547

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↗