Skip to content
Science Journaling Club

Volume 3, Issue 1September 2026

Fall 2026

Numerical integrators that quietly lie about a planet's orbit and the two Lagrange points that are stable for a genuinely strange reason, next to a moth that steers by the Milky Way, a journal-editor fraud ring caught by its own citation pattern, and a cat-sleeping-position claim that didn't survive a second look.

This issueSJC 3.1
Published
September 2026
Articles
8
Research
3
Field notes
5
With code
4

Contents

8 articles, in the order the club meant them to be read.

  1. ResearchMethods

    How to Lose a Planet by Choosing the Wrong Integration Method

    Simulating gravity is one equation applied over and over: acceleration equals minus GMGM times the position vector, divided by the cube of the distance. We integrated a single two-body Kepler orbit (eccentricity 0.6, one hundred steps per orbit, a resolution that looks perfectly reasonable) with three standard stepping rules, forward Euler, velocity Verlet and fourth-order Runge-Kutta (RK4), and checked every trajectory against the exact solution of Kepler's equation rather than against each other. At that resolution, Euler's energy flips sign within the first orbit (from −0.500 to +0.083) and never recovers. Velocity Verlet's energy error oscillates in a bounded band between roughly 0% and 2.99% for the full 300 orbits we ran, with no measurable trend (slope consistent with zero at 0.0 of its own standard error), exactly as symplectic theory predicts, and its angular momentum is conserved to 2.4×10−142.4\times10^{-14} relative error, 107 machine epsilons, indistinguishable from pure floating-point roundoff. RK4 drifts too, just far more slowly and in the opposite direction: it crosses 1% energy loss only after 47.6 orbits and 5% after 234.2 orbits, a real secular trend (21,915 standard errors from zero) that quietly contracts the orbit rather than expanding it. Fitting the measured convergence order across a range of timesteps gives 0.952 for Euler, 1.998 for Verlet and 4.166 for RK4 against textbook values of 1, 2 and 4; repeating the fit across 40 Monte Carlo trials at random eccentricities between 0.10 and 0.60 gives 0.987 ± 0.002, 2.0015 ± 0.0002 and 4.118 ± 0.005, each a small, real, explainable disagreement with the textbook exponent that we report rather than round away. Giving Euler four times the timestep resolution of RK4, so both cost the same number of force evaluations per orbit, does not rescue it: at eccentricity 0.6 it still loses 1% of the orbital energy within about a thousandth of an orbit, a failure of stability, not merely of accuracy, that a bigger budget cannot buy back. We also flag one place our own title oversells the result: at this configuration Euler's planet does not fall into the sun. It gains energy and flies apart, the better-documented and opposite failure mode; the "spiral into the sun" image turns out to describe RK4's slow contraction far better than it describes Euler's fast escape. Master seed 20260901. Total run time 65.0 seconds.

    Fall 2026Read 24 minSections 12

  2. ResearchOriginal Research

    Five Places to Park a Spacecraft, Two of Which Are Stable for a Strange Reason

    Two bodies orbit their common centre of mass in a circle. In the frame that rotates with them there are exactly five points where a third, massless body can sit still: three on the line through the two masses (L1, L2, L3), and two forming equilateral triangles with them (L4, L5). We located all five numerically for five mass ratios μ spanning five orders of magnitude, from Sun-Earth (μ = 3.00×10−6) to an illustrative equal-mass pair (μ = 0.5), by two independent numerical methods that agree with each other to machine precision (2.2×10−16) and with the classical small-μ series for the collinear points to four or more significant figures, and by exact algebra for the triangular ones (residual <4×10−16). Eigenvalues of the linearised equations of motion show L1, L2 and L3 unstable at every mass ratio tried, and show L4/L5 stable only below a critical mass ratio that our own numerical bisection places at μcrit = 0.03852085, against the classical Gascheau (1843) / Routh (1875) value of 0.03852090, a difference of 4.4×10−8 consistent with the square-root ill-conditioning of an eigenvalue problem at a genuine matrix degeneracy, not a bug. Direct integration of test particles (fixed fourth-order Runge-Kutta, Jacobi constant conserved to <4×10−13 relative up to first escape in every run) shows the same particle, same perturbation, same code, staying within 1000 times its starting displacement for the whole run at Earth-Moon's L4 and leaving it by t=15.0 at Pluto-Charon's L4, whose mass ratio (0.1087, 2.82× the critical value) exceeds threshold. A Monte Carlo experiment of 1,500 randomly directed perturbations per mass ratio, seeded at 20260914, put the escape probability at L4 at 0% ± 0% at 0.95×μcrit, 18.8% ± 1.0% at 0.98×μcrit, and 100% ± 0% by 1.20×μcrit, with the running estimate visibly converged by a few hundred trials. The stability of L4/L5 has nothing to do with sitting in a potential well: they sit on a hill of the effective potential at every mass ratio, stable or not, and what changes at μcrit is purely how the Coriolis force, which does no work and appears in no potential, organises the motion around that hill.

    Fall 2026Read 31 minSections 12

  3. ResearchOriginal Research

    Measuring Exactly How Unpredictable Three Gravitating Bodies Are

    Three point masses under Newtonian gravity are the textbook example of chaos, and the claim is usually left at that: asserted, not measured. We built a 4th-order symplectic integrator (Yoshida's composition of velocity-Verlet leapfrog steps [7]), validated it against the analytic two-body Kepler orbit to 5.1×10−12 relative error and against the published figure-eight periodic solution [3][4] to a residual of 1.4×10−4 after one full period, then measured the largest Lyapunov exponent of three configurations by Benettin's two-trajectory renormalisation method [11]. The exact figure-eight choreography is almost not chaotic at all: λ = 0.0374 ± 0.0014, a Lyapunov time of nearly 27 time units, over four full periods. The 1913 Pythagorean three-body problem [5][6], famous for a violent triple encounter, gives λ = 0.472 ± 0.007, a Lyapunov time under three time units, but only once we replaced a fixed integration step with one tied to the local free-fall time: the fixed step we tried first reported an energy that had grown by a factor of 350, a failure this article reports rather than hides. Forty randomly drawn bound triangles gave a heavy-tailed spread of exponents, median 1.326, mean pulled up to 2.545 by rare close encounters, translating to a prediction horizon of about 10.4 time units before a one-part-in-a-million initial uncertainty grows to the size of the system. Across 1,020 Monte Carlo trials at six initial energies, the fraction of triples that ejected a body within 20 time units rose from roughly 15–26% for bound systems to 62% near the escape threshold and 81% for unbound ones, with standard errors from the trial counts and a convergence plot showing the estimate settling as trials accumulate. A step-size sensitivity check moved the headline ejection fraction from 0.22 to as high as 0.34 under a four-times-coarser step, the single largest source of uncertainty in this study, reported plainly rather than tuned away. Seed 20260914.

    Fall 2026Read 26 minSections 12

  4. Field noteExplainer

    Neptune's Missing Aurora Was Hiding in the Tropics

    Jupiter, Saturn and Uranus have all been watched for decades in the infrared light of a small molecular ion called H3+, which glows wherever a giant planet's magnetic field funnels charged particles into its upper atmosphere. Neptune refused to show it. In March 2025 a team led by Henrik Melin reported that JWST had finally caught the ion, and caught with it the first clear infrared aurora at Neptune, sitting between 30 and 60 degrees south rather than over a pole [1]. The same spectrum reads the upper atmosphere at 358 ± 8 K. Voyager 2 measured 750 ± 150 K there in 1989, roughly twice as hot. We rebuild the geometry ourselves. A tilted dipole traced by hand puts the auroral oval at 56°S to 30°S, which is 86% of the observed band and misses its centre by 2.6 degrees, and a Boltzmann calculation of the ion's emission says the glow at 358 K is 0.51% of what it was at 750 K, a factor of 198. Sections 4 through 7 hold the club's own simplified model rather than the paper's analysis. Section 9 says where it breaks.

    Planetary AstronomyRead 33 minSections 12

  5. Field notePaper Analysis

    Forty-Five Editors, Thirty Percent of the Retractions

    In August 2025 a team from Northwestern, Sydney, and the PNAS editorial board published something closer to a forensic audit than a research finding: a statistical trawl through who handled which manuscript at several journals, cross-referenced against which of those manuscripts were later retracted or flagged on PubPeer [1]. Nothing in the method involves reading anyone's mind or finding a confession. At PLOS ONE alone, of 18,329 editors who have ever accepted a submission, a Poisson-binomial enrichment test flags 45, a mere 0.25%, who together handled 1.3% of the journal's 276,956 articles but sit behind 30.2% of its 702 retractions. More than half of them, 25 of 45, also authored papers that PLOS ONE retracted. A tight cluster of them, spanning four countries, sent most of their submissions to each other rather than to the journal's other 18,284 editors. The same signature, self-referential acceptance, batched retractions, and a shared trail of duplicated images, reappears at Hindawi and across IEEE conference proceedings. This Field Note walks through exactly how the authors caught it, why a coordinated ring is a fundamentally harder catch than a single fabricated paper, and what the whole exercise implies, and does not imply, about trusting the other 99.75% of editors doing the job honestly. We do our own arithmetic on the paper's numbers throughout, clearly marked as ours; the club ran no experiment and analyzed no new data of its own.

    MetascienceRead 24 minSections 14

  6. Field notePaper Analysis

    The Moth That Reads the Milky Way

    Once a year, an Australian moth with a brain you could lose in a poppy seed flies up to 1,000 km to a handful of alpine caves it has never seen, packs in among roughly 16,000 other moths per square metre of cave wall for the summer, and then flies the whole distance back to breed and die. In 2025 a team led by David Dreyer and Eric Warrant tethered these moths inside a 50 cm planetarium, projected a real, moonless star field over their heads, and switched the Earth's magnetic field off with a bank of Helmholtz coils — nulled below 100 nanotesla, a reduction our own back-of-envelope arithmetic puts at somewhere north of 250-fold. The moths kept flying the correct seasonal bearing anyway. Rotate the projected sky 180° and the moths turn with it, in both directions, in both seasons (six trials, n from 49 to 70 each). Scramble the same stars into random positions and the moths go nowhere in particular. Recordings from the moths' own brains turned up 28 neurons, out of 79 sampled, tuned to the rotating sky, almost all of them firing hardest when the moth faced within a few degrees of due south — in spring and in autumn alike, headed toward the caves or away from them. This is, by the authors' own account, the first invertebrate ever shown to steer by the stars. We think that is a bigger deal than it sounds, and this note is our attempt to say exactly why, using nothing but the numbers in the paper and a calculator.

    Animal NavigationRead 20 minSections 13

  7. Field notePaper Analysis

    The Six-Decade Blind Spot Above the Ozone Layer

    Since Christian Junge found a persistent haze of sub-micron particles in the lower stratosphere with balloon-borne counters in 1961 [2], the layer has been treated as a sulfate story: droplets of sulfuric acid and water, replenished by volcanoes, sitting well inside the size range that satellites and balloon-borne optical particle counters can actually see. In April 2026, a team flying NASA's WB-57 high-altitude aircraft during the SABRE mission in February 2023 reported something that sulfate-only bookkeeping had never counted: a persistent mode of organic-rich particles, present below 19 km wherever the air still carries a nitrous oxide signature above 270 parts per billion, with a number-weighted mean diameter of only 0.03 to 0.11 µm [1]. Weighted by the surface area that actually does the chemistry, the same population runs 0.08 to 0.2 µm; weighted by volume, or mass, it runs 0.11 to 0.3 µm — three different "sizes" for one population, depending entirely on what you ask the size to explain. What it explains, per the paper's own accompanying institutional release, is up to 90% of the surface area available in the lower stratosphere for heterogeneous chemical reactions and for condensing trace gases, dwarfing the classic sulfate mode in the one property that actually drives ozone chemistry and particle growth. It went undetected for as long as it did because most satellite retrievals only resolve particles above roughly 0.2 µm, and balloon-borne optical counters generally start around 0.15 to 0.3 µm — both comfortably above where this mode's number distribution actually sits. A global chemistry-climate model run against the same data could not reproduce the population's properties, which the authors read as a warning for anyone using such models to project ozone recovery or to evaluate stratospheric geoengineering proposals that were designed, implicitly, around the sulfate picture alone. This Field Note works through why stratospheric surface area matters at all, does two pieces of arithmetic of our own directly on the paper's three reported size numbers, and asks plainly what changes and what does not.

    Atmospheric ChemistryRead 20 minSections 14

  8. Field noteExplainer

    Two-Thirds of Cats Sleep on Their Left Side, Until Somebody Rechecked

    In June 2025 a thirteen-author team led by Sevim Isparta coded 301 YouTube videos of sleeping cats and reported, in a two-page item in Current Biology, that 63.8% slept with their left side down — a population-level bias, they argued, that lines up with the right hemisphere's job of watching for threats through the left eye [1]. Eight months later, in a paper posted online in February 2026, one researcher working alone, Andrew Cooke of the University of Lincoln, ran the same question on three independent platforms and found nothing distinguishable from a coin flip anywhere: 51.2% left among 123 YouTube cats, 48.4% among 494 on Reddit, 48.8% average among 60 Instagram accounts [3]. Sitting between the two papers, easy to miss, is a formal correction: in October 2025 the original authors published an erratum removing 107 videos with data-quality problems, prompted, Cooke says, by concerns he had raised — and the corrected number came out exactly where it started [2]. This field note is about the pair, not either paper alone. It walks through what a “population-level bias” is actually claiming, why that is not the same statistical object as an individual “preference” the way pawedness is, how three sampling frames disagree with each other more informatively than any one of them disagrees with chance, and why a claim, a self-correction and a failed replication landing inside eleven months is what a functioning literature looks like doing its job. Every comparison across the two papers below — the pooled sample sizes, the percentage-point gaps, the chance expectations — is the club's own arithmetic on their published numbers, marked inline as ours.

    MetascienceRead 18 minSections 13