Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1511.07476

Fast and reliable symplectic integration for planetary system $N$-body problems

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

Abstract

We apply one of the exactly symplectic integrators, that we call HB15, of \cite{HB15}, along with the Kepler problem solver of \cite{WH15}, to solve planetary system $N$-body problems. We compare the method to Wisdom-Holman methods (WH) in the \texttt{MERCURY} software package, the \texttt{MERCURY} switching integrator, and others and find HB15 to be the most efficient method or tied for the most efficient method in many cases. Unlike WH, HB15 solved $N$-body problems exhibiting close encounters with small, acceptable error, although frequent encounters slowed the code. Switching maps like \texttt{MERCURY} change between two methods and are not exactly symplectic. We carry out careful tests on their properties and suggest they must be used with caution. We then use different integrators to solve a 3-body problem consisting of a binary planet orbiting a star. For all tested tolerances and time steps, \texttt{MERCURY} unbinds the binary after 0 to 25 years. However, in the solutions of HB15, a time-symmetric Hermite code, and a symplectic Yoshida method, the binary remains bound for $>1000$ years. The methods' solutions are qualitatively different, despite small errors in the first integrals in most cases. Several checks suggest the qualitative binary behavior of HB15's solution is correct. The Bulirsch-Stoer and Radau methods in the \texttt{MERCURY} package also unbind the binary before a time of 50 years, suggesting this dynamical error is due to a \texttt{MERCURY} bug.

Explore related subjects

astro-ph.EPastro-ph.IM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

David M. Hernandez. 2016-03-08. Fast and reliable symplectic integration for planetary system $N$-body problems. https://doi.org/10.1093/mnras%2Fstw569

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

KEEP EXPLORING

Related papers

arXiv2026

Volcanic Satellites and Ion Escape in the Magnetospheres of Ultra-Cool and Brown Dwarf Stars

Radio emissions at $\sim$ GHz frequencies of ultra-cool dwarf and brown dwarf stars suggest the presence of radiation belts not unlike Jupiter's. We investigate the possibility the inferred magnetospheric plasma at the primary star is sourced by an active planet or via ion escape modeled as a weak ionospheric outflow. We consider indirect methods to estimate the magnetospheric plasma mass flow from auroral radio emission and apply them to the ultra-cool dwarf LSR J1835+3259. We find that an ionospheric outflow is a viable source of the order of $10^{5}$ kg s$^{-1}$, if the ionospheric effective Pedersen conductance is lower than $\sim 0.02$ mho. On the other hand, a tidally-heated volcanic satellite with the same mass and radius as Io and an orbit with a semimajor axis lower than about $10$ stellar radii, whose eccentricity ($e \sim 10^{-3}$) is maintained by perturbations by other planets in the system, is found to be a viable source of magnetospheric plasma without strong limitations on the ionospheric conductance. The volcanic satellite scenario is also naturally in sync with the recent finding that ultra-cool dwarfs with distant substellar or stellar companions are remarkably more likely to be detected as radio emitters.

astro-ph.EP↗
arXiv2026

Tidal Demise: The Evolution and Fate of a Hypothetical Venus Moon

Venus possesses no natural satellite, raising the question whether a formed moon could have survived. We explore the tidal evolution of a Venus-moon system, coupling Venus's spin to the satellite's orbit under tides from the moon and Sun. We survey spin period ($P_0 = 5$--100~hr), moon mass ($M_m = 0.01$--$10~M_{\rm Moon}$), eccentricity, quality factor, and initial semi-major axis under both constant-$Q$ and constant time lag models. Survival depends on competition between outward migration ($\propto M_m$) and synchronous radius expansion ($\propto M_m^2$): for circular orbits around rapidly spinning Venus ($P_0 \lesssim 12$~hr), a lunar-mass satellite survives the age of the Solar System in both models. For $P_0 \lesssim 10$~hr, eccentricity pumping can destabilize low-mass satellites, while for $P_0 \gtrsim 15$~hr or $M_m \gtrsim 2~M_{\rm Moon}$ the synchronous radius overtakes the orbit and drives Roche destruction within $\sim$0.03--1.7~Gyr in the constant-$Q$ model. The constant time lag model instead permits quasi-synchronous survival for massive moons at fast spin. Explaining Venus's present state requires satisfying two constraints simultaneously: loss of the satellite and despinning of an initially rapid rotator. Both are met only within a restricted region of parameter space, favoring moderate post-impact spin periods and lunar-to-super-lunar masses. Giant impact simulations predict spin periods $\gtrsim$12~hr for Venus's present rotation, placing a lunar-mass satellite at the survival boundary. For last-impact conditions within this region, the present absence of a Venusian satellite arises through tidal evolution alone; a subsequent catastrophic stripping event, while capable of removing a moon, is not required.

astro-ph.EP↗
arXiv2026

Evidence for an Extended Hydrogen Outflow on WASP-12 b

Recent observations of atmospheric escape from planets orbiting early-type stars indicate that planets with higher Roche filling factors have significantly higher mass loss rates. For three of these planets, full-orbit observations have revealed the presence of large leading and trailing tails of escaping planetary material. These 3D outflow geometries encode information about the underlying outflow physics, and can also be used to constrain their stellar wind properties and to predict their long-term orbital evolution. We present new evidence for extended H$α$ and H$β$ absorption from escaping hydrogen for a fourth planet, WASP-12 b. We observed WASP-12 b with the Keck Planet Finder on Keck I over a period of approximately eight hours centered on the transit. We find a H$α$ and H$β$ absorption signal in the stellar rest frame that is strongest during the transit (H$α$ amplitude: $2.66\pm0.25\%$, H$β$ amplitude: $2.88\pm0.43\%$), with evidence of both pre- and post-transit absorption. This measurement is consistent with outflow models where the escaping gas overflows the planet's Roche lobe and is advected into the stellar rest frame before being tidally sheared into extended tails. This outflow behavior is qualitatively similar to previous H$α$ observations of this planet as well as observations of extended outflows from other gas giants orbiting early-type stars.

astro-ph.EP↗