| UT TIME | MAG | DEPTH km | PLACE | LAT | LON | Dn km | NEAREST NODE | SOURCE |
|---|---|---|---|---|---|---|---|---|
| Set the range and click FETCH FROM USGS — or the current globe window loads here automatically | ||||||||
Honest note: the rings, circles and nodal points are constructions — nothing here is measured at those places. Earthquakes can be shown alongside for context (off by default). The three lightning centres are representative points inside broad tropical regions (±10°); moving a centre by 10° moves the nodal points by a comparable amount. Marker sizes are display aids; positions are true. This is a learning and exploration tool — it shows real data and real computed numbers.
LAYERS
| LAYER | TYPE | SOURCE | VALIDITY | ACCURACY | CHECK |
|---|---|---|---|---|---|
| Earthquakes | FACT | USGS ANSS ComCat via FDSN event service & GeoJSON summary feeds (earthquake.usgs.gov) | 1900–present; treat before 1973 (NEIC PDE) as incomplete | as stated by USGS per event (location ±km, magnitude ±0.1–0.3) | source ⧉ |
| Kp (top bar / readout) | FACT | NOAA SWPC estimated planetary K-index (nowcast, 3-h); definitive Kp: GFZ Potsdam | live (last 7 days) | SWPC estimate; GFZ definitive value may differ by ⅓ unit | SWPC ⧉ GFZ ⧉ |
| Sub-solar point · terminator | FACT | Sun from JPL Keplerian elements (Standish & Williams) via the shared Almanac core; apparent place (Meeus ch. 21/22/25); GAST Meeus 12.4 | 1600–2100 verified; 3000 BC–3000 AD elements | lon ±0.01°, lat ±0.003° (vs JPL Horizons, 1600–2100) | ✓ VERIFY |
| Sub-lunar point · Moon distance/phase | FACT | Meeus Astronomical Algorithms ch. 47 (full 60+60 term series) + ch. 48 (phase); shared Almanac core | 1600–2100 verified | RA/Dec ≤ 15″ (≤ 0.005°), distance ±50 km, illumination ±0.05 % (vs Horizons) | ✓ VERIFY |
| Geomagnetic observatories | FACT | INTERMAGNET observatory list, BGS Geomagnetic Information Node (GIN) — 45 of 154 IMOs shown, official coordinates | list fetched 2026-08-18 | as published (0.001°) | GIN ⧉ |
| Schumann / ELF stations | FACT | Published station sites (citations below); solid markers = coordinates from the INTERMAGNET list, hollow = site coordinates transcribed from the cited papers | sites reported 1993–present; status varies | solid 0.001°; hollow ±0.5° (site-level) | see citations |
| Lightning centres · activity bars | HISTORY | Regional lightning maxima: Christian et al. 2003 (OTD), Williams & Sátori 2004; UT activity shape: Whipple 1929, Harrison 2013 (Carnegie curve) — schematic | climatology (multi-year mean) | centres ±10°; bars are a schematic shape, not a measurement | — |
| Quarter-wave rings 7.83 / 11.78 Hz | MODEL | TeslaQuake construction (U.S. provisional 63/973,214, claim 15): λ/4 = c/(4f) — the quarter-wave relation and 0.08484 s period are quoted from Tesla, US 787,412 (1905); 7.83 Hz = nominal Schumann fundamental | — | exact geometry on a 6371.0088 km sphere; not a measurement | ◇ NODE TABLE |
| Wave field (cavity modes n=1–3) | MODEL | Textbook: vertical E-field of Earth–ionosphere cavity mode n around a point source ∝ Pn(cos θ); three lightning chimneys added with UT-dependent weights (schematic Whipple/Carnegie curve); nodal lines = zero contours of the sum | Nickolaenko & Hayakawa 2002; Christian et al. 2003; Whipple 1929 | ideal lossless cavity, point sources at ±10° centres; real nodes are minima (Q ≈ 4–6); grid 0.5° | ✓ VERIFY |
| Mode nodes (n=1 ∩ n=2) | MODEL | Crossings of the n=1 and n=2 nodal lines for the same chimney weights — both mode fields vanish there; they move with universal time | — | located on the 0.5° grid (≈ ±30 km); listed in the NODE TABLE | ◇ NODE TABLE |
| Tesla 1905 picture | HISTORY | One transmitter at Colorado Springs; Tesla's stated mean velocity 471,240 km/s and period 0.08484 s → λ = 39,980 km ≈ Earth's circumference: node at the transmitter, maximum on the 90° circle, node near the antipode | US 787,412 | his numbers, drawn literally (his "velocity" is 1.57 c — a phase velocity along the surface) | — |
| Nodal points (20) | MODEL | Exact intersections of a 7.83 Hz ring with an 11.78 Hz ring from a different centre (closed-form small-circle intersection) | — | residual on both rings < 1 m; not a measurement | ◇ NODE TABLE |
| Cavity-mode nodal circles | MODEL | Textbook: vertical E-field of Schumann mode n from a point source ∝ Pn(cos θ); nodal circles at the zeros of Pn (Schumann 1952; Nickolaenko & Hayakawa 2002) | — | exact angles; the point-source and single-centre assumptions are simplifications | — |
| Tide zero circles | MODEL | Equilibrium tide potential ∝ (3cos²ψ − 1)/2 · M/d³, zero at ψ = arccos(1/√3) = 54.7356° (Melchior 1983; Agnew 2007) | — | exact angle for the equilibrium theory; real ocean tides differ | — |
ACCURACY & SOURCES — VERIFICATION RUN
This build was checked against NASA/JPL Horizons (DE441) on 2026-08-18 at 14 epochs from 1600 to 2500 (harness in the delivered zip). Largest differences: Sun RA 28″, Sun Dec 10″, sidereal time 0.36 s (UT1−UTC), sub-solar longitude 0.008°, Moon RA 14″, Moon Dec 2″, Moon distance 47 km, illumination 0.00 % for 1600–2050; the Moon-based quantities grow to 932″ RA by 2500 (Meeus theory limits), the sub-solar point stays within 0.021°.
The Sun/Moon core is the Almanac's window.TQ_ASTRO — one truth for both apps. Civil time is treated as UT1 (the ≤ 0.9 s UT1−UTC difference is ≤ 0.004° of longitude). Sub-solar/sub-lunar points are defined as the place where the body is at the zenith at that instant (geodetic latitude = apparent declination); JPL's "sub-observer point seen from the Sun" is defined with light travel time and reads about 2° further east — the ✓ VERIFY panel therefore compares RA/Dec and sidereal time, the inputs to the point.
| QUANTITY | MAX Δ 1600–2050 | MAX Δ 2100 · 2200 · 2500 | REFERENCE |
|---|---|---|---|
| Sun apparent RA | 28 ″ | 77 ″ | JPL Horizons, apparent RA (a-app), airless |
| Sun apparent Dec | 10 ″ | 11 ″ | JPL Horizons, apparent Dec |
| Greenwich apparent sidereal time | 0.360 s | 0.105 s | Horizons L_Ap_Sid_Time at 0°E · residual = UT1−UTC (app treats civil time as UT1) |
| Sub-solar longitude | 0.0076 ° | 0.0210 ° | RA − GAST from the two Horizons columns |
| Sub-solar latitude | 0.0027 ° | 0.0029 ° | = apparent declination |
| Moon apparent RA | 14 ″ | 932 ″ | JPL Horizons, geocentric apparent RA |
| Moon apparent Dec | 2 ″ | 39 ″ | JPL Horizons, geocentric apparent Dec |
| Moon distance | 47 km | 30 km | Horizons delta (geocentric) |
| Moon elongation | 27 ″ | 724 ″ | Horizons S-O-T |
| Moon illuminated fraction | 0.00 % | 0.04 % | Horizons Illu% |
THE GEOMETRY, EXACTLY
Sphere. Mean Earth radius R = 6371.0088 km (IUGG R1); 1° of arc = 111.195 km. All rings are true small circles: the set of points at a fixed great-circle distance from a centre. Nodal points are the closed-form intersections of two small circles (unit vectors a, b of the centres; cos-radii ca, cb; solve x·a + y·b ± z·(a×b)); every nodal point lies on both of its rings to better than 1 m.
Quarter-wave rings (TeslaQuake). λ/4 = c/(4f) with c = 299,792.458 km/s. f = 7.83 Hz → 9,571.9 km (rings at 1× and 2×); f = 11.78 Hz → 6,362.3 km (rings at 1×, 2×, 3×), each drawn around the three lightning centres AF (0°, 25°E), AS (0°, 110°E), AM (0°, 75°W). 11.78 Hz is the reciprocal of the period Tesla states in US 787,412 — "not less than one-twelfth or probably 0.08484 of a second" — 1/0.08484 s = 11.787 Hz. The mapping of that period and of Tesla's quarter-wave relation onto surface rings around lightning centres is TeslaQuake's construction (MODEL).
Cavity-mode circles (textbook). In the Earth–ionosphere cavity a point source excites modes whose vertical electric field varies with angular distance θ as the Legendre polynomial Pn(cos θ); the field is zero on the circles θ = 90° (n = 1, ~7.8 Hz), 54.74° and 125.26° (n = 2, ~14.1 Hz), 39.23°, 90° and 140.77° (n = 3, ~20.3 Hz). Real sources are distributed and the modes are damped, so these are ideal reference circles, not measurements.
Wave field (cavity-mode standing wave). A standing wave keeps its shape while its amplitude oscillates, so its nodal lines are fixed curves for a fixed set of sources. In the Earth–ionosphere cavity a vertical point source excites mode n with vertical electric field ∝ Pn(cos θ), θ = angular distance from the source; the zeros of Pn are the cavity-mode circles above. The WAVE FIELD layer goes one step further than a single source: the three tropical lightning chimneys are treated as three simultaneous sources and their mode-n fields are added, ψn = Σc wc(t)·Pn(cos θc) / Σc wc(t), with each chimney weighted by its activity at the selected universal time (the schematic Africa 14 UT / Asia 08 UT / Americas 20 UT curve shown in the LIGHTNING CENTRES panel). The white nodal lines are the zero contours of that sum, found on a 0.5° grid; because the weights change through the day, the nodal lines drift — Tesla's 1899 observation that nodal points "may be produced and caused to shift slowly" here has a concrete mechanism: several sources of different strength. MODE NODES mark where the n=1 and n=2 nodal lines cross, so both fields vanish there. Amplitude breathing is slowed ≈ 31× (0.25 cycle/s for 7.8 Hz; higher modes keep their true ratio). Limits: ideal lossless cavity (the real cavity has Q ≈ 4–6, so measured nodes are shallow minima, not zeros), point sources at representative centres (±10°), schematic weights, no day/night ionosphere asymmetry. Scrubbing the date moves the weights by universal time only. TESLA 1905 draws Tesla's own one-transmitter picture from Colorado Springs with the velocity and period stated in US 787,412. None of this is a measurement.
Equilibrium tide. The lunar tidal potential on a rigid Earth is ∝ (3cos²ψ − 1)/2 · M/d³, ψ = angular distance from the sub-lunar point; it is zero on the two circles at ψ = 54.74° and its sign changes across them. The TIDAL ALIGNMENT readout is cos 2D · (d̄/d)³ (D = Moon–Sun elongation, d = Moon distance): +1 at new/full Moon and mean distance, −1 at the quarters — a spring/neap alignment index, not a force and not a forecast.
WHAT WOULD BE NEEDED TO TEST THE GEOMETRY AGAINST SEISMICITY
This app does not test it. For the record: a fair test keeps the earthquake catalogue fixed, generates many random rigid rotations of the nodal geometry on the sphere, computes the same distance statistic for each rotation, and compares the observed value with that distribution — a uniform-random baseline (or a fixed "expected 33 %") is not valid because seismicity is clustered on plate boundaries. Any such analysis belongs in a separate, documented study, not on this page.
NODAL POINT TABLE
| ID | LAT | LON | 7.83 Hz RING | 11.78 Hz RING |
|---|
CITATIONS
Cavity resonances. W.O. Schumann (1952), Z. Naturforsch. 7a, 149–154 · M. Balser & C.A. Wagner (1960), Nature 188, 638–641 (first observation) · A.P. Nickolaenko & M. Hayakawa (2002), Resonances in the Earth-Ionosphere Cavity, Kluwer · D.D. Sentman (1995), in Handbook of Atmospheric Electrodynamics vol. 1.
Lightning climatology. H.J. Christian et al. (2003), Global frequency and distribution of lightning as observed from space by the OTD, J. Geophys. Res. 108, 4005 · E.R. Williams & G. Sátori (2004), J. Atmos. Sol.-Terr. Phys. 66, 1213 · F.J.W. Whipple (1929), Q. J. R. Meteorol. Soc. 55, 1 · R.G. Harrison (2013), The Carnegie Curve, Surv. Geophys. 34, 209.
Tides. P. Melchior (1983), The Tides of the Planet Earth, 2nd ed., Pergamon · D.C. Agnew (2007), Earth Tides, in Treatise on Geophysics vol. 3.
Sun, Moon, time. E.M. Standish & J.G. Williams, Keplerian Elements for Approximate Positions of the Major Planets, JPL SSD · J. Meeus (1998), Astronomical Algorithms, 2nd ed., ch. 12, 21, 22, 25, 47, 48 · F. Espenak & J. Meeus (2006), ΔT polynomials · NASA/JPL Horizons (DE441) — independent check.
Stations & data. INTERMAGNET / BGS Geomagnetic Information Node (observatory list, live minute data) · G. Sátori, J. Szendrői & J. Verő (1996), Monitoring Schumann resonances — I. Methodology, J. Atmos. Terr. Phys. 58, 1475 (Nagycenk) · A. Kułak et al. (2014), ELF electromagnetic field measurements at the Hylaty station, Radio Sci. 49, 361 · C. Price & A. Melnikov (2004), J. Atmos. Sol.-Terr. Phys. 66, 1179 (Mitzpe Ramon) · M. Hayakawa & A.P. Nickolaenko (Moshiri) · A. Ondrášková et al. (Modra) · S. Toledo-Redondo / A. Salinas et al. (Sierra Nevada) · Ukrainian Antarctic Station Akademik Vernadsky ELF · HeartMath Institute Global Coherence Monitoring System (Boulder Creek, Hofuf, Baisogala) · USGS Earthquake Hazards Program (ComCat, FDSN) · NOAA Space Weather Prediction Center · GFZ German Research Centre for Geosciences (Kp) · Natural Earth 110 m coastline (public domain) · NASA Earth Observatory night-lights imagery via three-globe examples.
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