TKS Ephemeris · प्रयोगशाला · पात (node) व ग्रहण-ऋतु

Sun–Earth–Moon — the Moon's tilted orbit, the pāta (node) line and the eclipse seasons

The Moon does not travel on the ecliptic: its orbit is tilted by i ≈ 5.145° and crosses the ecliptic at two points — Rāhu (ascending pāta) and Ketu (descending pāta). A solar eclipse needs the new moon near that line, a lunar eclipse needs the full moon near it; the months in which the Sun itself is close to the node are the eclipse seasons. This page measures all of it from the engine's own state: Ω and i from h = r × v, every node crossing (draconic month), every perigee/apogee (anomalistic month), the real latitude β☾ of every syzygy, and the windows of the span — each window cross-checked against the real eclipses from the catalogue. Data: /v1/tks/moon-nodes (one request for the whole span, computed in-process) · /v1/tks/ephemeris (instant) · /v1/tks/eclipses (cross-check).

Date (UTC) Time (UTC) Span (days) Place Lat Lon TZ (h) Orbit tilt × labels

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Live real values (this instant)

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पात (nodes) & apsides — real events

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Eclipse seasons & the real eclipses inside them

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Cross-check (measured vs classical)

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Eclipse seasons through the span

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The curve is the Sun's real angular distance from the nearer node, day by day (from the engine). The two shaded bands are the classical limits: a solar eclipse is possible while the Sun is inside ≈15.4° (extreme 18.4°) of a node, a lunar eclipse inside ≈9.5° (extreme 12.2°). Circles = new moons, filled dots = full moons, from the same engine data; ▲ = a real eclipse from the catalogue.

One nodal month — the real ecliptic latitude β☾

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The Moon's real ecliptic latitude through the current draconic month: it is zero exactly at the two pāta crossings (marked with their real instants) and reaches ±i in between — the reason a syzygy near the middle of this curve cannot eclipse.

Math & honesty

Node and inclination. The orbit plane is measured from the engine's own apparent geocentric state: position r and a central-difference velocity v (step ≈ 14 min) give the orbit normal h = r × v in the true ecliptic of date, hence i = arccos(h_z/|h|) and Ω = atan2(h_x, −h_y). These are osculating, apparent-frame elements: they wobble slightly around the classical means (i ≈ 5.145°, dΩ/dt ≈ −0.0529 °/day, nodal period 18.6 yr), and both are printed side by side instead of hiding the difference.
Node crossings & apsides. Every β☾ = 0 crossing (Rāhu/Ketu) and every extremum of the geocentric distance (perigee/apogee) inside the span is bracketed on the daily engine states and then bisected, so the instants are exact to seconds. The mean spacing of consecutive same-kind events is the draconic (≈27.212 d) and the anomalistic (≈27.555 d) month measured from data — and individual months really do vary (perigee–perigee from ≈24 to ≈29 d), which is why the measured mean of a span is not forced to equal the classical mean.
Eclipse seasons. A solar eclipse needs the Sun within ≈15.4° of a node (18.4° in the extreme case), a lunar eclipse within ≈9.5° (12.2°). The windows shown are exactly that test applied to the engine's real λ☉ and Ω day by day; the eclipse list used for the cross-check comes from a different endpoint (/v1/tks/eclipses: catalogue + Besselian machinery), so the two agree only if the geometry is right — that is the point of showing both.
One request. Ω, i, every node crossing, every apsis, the latitude of every syzygy and the season windows all come from one call to /v1/tks/moon-nodes, computed in-process from the DE kernels. Intermediate instants are linear interpolations between daily engine states (error ≤ 0.05° in λ☾, ≤ 0.01° in β☾) — never invented values, and playing the animation generates no extra HTTP traffic.
Drawing conventions. Only one thing is exaggerated: the drawn orbit tilt (×N, default ×5), because the real 5.145° plane is almost the ecliptic itself. Every number in the tables, canvas captions and counts is the real one.