TKS Ephemeris · research · long-term stellar motion
Vyādha (Sirius) — ecliptic-crossing, past & future
Vyādha = Sirius (α CMa). Its proper motion ~1.34″/yr carries it ~90° across the sky in 250,000 years. This page
propagates its position from the measured proper motion + radial velocity + parallax, evaluates the
ecliptic latitude β(t) against the J2000 ecliptic, and reports the β = 0 crossings (ecliptic-crossings) —
past and future. Everything is computed from the engine's own proper-motion + geometry (no external library), with an explicit
uncertainty section at the end.
β(t) — ecliptic latitude
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x: year (BCE ← → CE) · y: ecliptic latitude β (deg, J2000 ecliptic). Dashed = β=0 (ecliptic). Each β=0 crossing is circled.
Ecliptic-crossings
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… computing …
Position each epoch (relative data)
RA · Dec · λ · β
… computing …
The star's great-circle path
J2000 equatorial
Sirius's positions under proper motion (dots) — over long spans this traces an almost straight line on a great circle; β(t) is its separation from the ecliptic plane.
Inputs (measured)
Hipparcos / GAIA
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Sirius is a binary (A+B); systemic (barycentre) values are used here — the RV of A itself oscillates over its ~50-yr orbit.
Ecliptic of date: "crossing the ecliptic" depends on which ecliptic — the J2000 plane (used here; fixed & reproducible) vs the ecliptic-of-date (Earth's orbital plane at that epoch, which itself moves by planetary precession). A correct of-date comparison needs the long-term precession model (Vondrák 2011); the short IAU-2006 form extrapolates unreliably at ±100 kyr, so it is not shown.
Yeh is an estimate, not a validated ephemeris. Sirf tārā (deterministic motion) — planets/Moon intentionally omitted (their phase is lost over such spans). Crossing-date uncertainty ≈ position-error(″) ÷ dβ/dt(″/yr) → ~decades–centuries.