Astronomy Mode — Positional Precision

How CuriousPilot places celestial objects and satellites on the sky, the accuracy of each, and how to read a comparison against a real photograph.

Summary. In Astronomy Mode the sky is built as two independent halves. Stars and planets use the full IAU apparent-place reduction and match professional references (astropy) to < 0.01″ — effectively an absolute, observer-independent reference grid. Satellites are propagated from their orbital element set with SGP4; their apparent-position error is dominated, in order, by time ≫ element epoch ≫ observer position ≫ altitude. Because the star grid is exact and position-independent, any star-vs-satellite mismatch isolates cleanly to the satellite side.

1. Celestial objects — the apparent-place pipeline

A star’s catalog position (ICRS / J2000) is not where it appears in the sky at the moment of observation. CuriousPilot applies the complete IAU reduction, in the standard order, to turn the catalog position into the apparent, of-date direction an observer actually sees. Each layer and its typical magnitude:

Layer	What it corrects	Typical size
Proper motion	The star’s own motion across the sky since the catalog epoch (J2000)	up to ~arcsec/yr
Annual parallax	Shift from Earth’s position in its orbit (nearest stars only)	≤ 0.77″
Gravitational light deflection	Bending of starlight by the Sun’s gravity	≤ 1.75″ near Sun; < 0.01″ at night
Annual aberration	Apparent tilt of starlight from Earth’s orbital velocity	≤ 20.5″
Diurnal aberration	Same, from Earth’s rotation at the observer	≤ 0.32″
Precession (IAU 2006)	Slow wobble of Earth’s axis since J2000	~50″/yr → ~0.3–1° over decades
Nutation (IAU 2000B)	Shorter-period nodding of the axis	≤ 17″
Frame bias	ICRS → mean equator/equinox of J2000	~0.02″
Sidereal (GAST) rotation	Earth’s rotation, to horizontal Az/El	per-frame

The precession–nutation step uses the exact IAU 2006 precession (Fukushima–Williams angles) and IAU 2000B nutation (77-term luni-solar series), not an approximation. Proper motion, parallax and radial velocity come from the HYG catalog (Hipparcos-derived). Planets, the Sun and the Moon use the same of-date apparent frame.

Validated. The pipeline is checked term-by-term against astropy’s TETE frame (itself an ERFA / IAU implementation) across many stars, dates and observer positions, agreeing to < 0.01″. In practice this has been confirmed against catalog positions in real photographs — e.g. the star Jishui (ο Gem) matched its SIMBAD J2000 position to sub-arcsecond.

The accuracy floor: Earth-orientation parameters

The one thing the model cannot predict is the unpredictable part of Earth’s orientation — polar motion (~0.4″) and the UT1−UTC clock difference (~0.2″). These are measured after the fact and published by the IERS. Two properties make them harmless here:

They only affect the absolute Az/El pointing, not the relative geometry between objects.
They are common-mode: they shift stars and satellites together, so they cancel when you compare a satellite against the background stars — exactly the measurement that matters.

2. Satellites — SGP4 and observer geometry

Satellites are not modeled from first principles; they are propagated from a published orbital element set using SGP4, then placed on the sky from the observer’s position. Their apparent-position accuracy depends on:

The element set itself — its intrinsic accuracy and how it was generated.
Epoch age — SGP4 error grows with the time between the element epoch and the simulated instant; a freshly-launched, still-maneuvering satellite degrades fastest.
Observer position (latitude, longitude, altitude) — parallax against a nearby (hundreds-of-km) object.
Time — a low-Earth-orbit satellite sweeps the sky quickly, so the clock matters more than anything else (below).

3. Interpreting a comparison: the error budget

When you overlay the simulation on a real photograph, it helps to know which term dominates. The total error splits into the two halves, and the satellite half is strongly ordered.

The satellite budget, largest first

Sensitivities below use a fresh, low (~300 km) Starlink train at slant range ρ ≈ 700 km; they scale with 1/ρ, so a higher or more distant object is less sensitive.

Term	Sensitivity	Rough size
Time	θ̇ ≈ v⊥/ρ ≈ 7 km/s ÷ 700 km ≈ 0.5°/s	1 s → ~30′
Element epoch / SGP4	grows with age from epoch	hours of drift → arcmin+
Observer lat/lon	parallax ∝ baseline / ρ	arcmin → degree
Altitude (barometric vs geometric)	Δelev ≈ Δh·cos E / ρ	~1–3′ (negligible)
Stars (any observer change)	objects at infinity	~0″

Two consequences worth internalizing:

Time is the master lever. At ~0.5°/s, a one-second clock error moves a low-orbit train ~half a degree along its track — larger than the entire altitude budget and ~30× the barometric-vs-geometric correction. Get the timestamp right to a fraction of a second before worrying about anything else.
A residual converts to a distance. Because 1′ ≈ ρ · Δθ ≈ 700 km × 3×10⁻⁴ ≈ 200 m, a small angular offset between the simulated satellite and the stars reads directly as a ~few-hundred-meter difference in the satellite’s 3-D position — a useful cross-check of the element set, not a repositioning error.

Why the star grid is the reference

Stars are at infinity, so the observer’s position and altitude cannot move them — the star field is the same rigid grid of directions no matter where the observer is. That, plus the sub-arcsecond modeling, is what lets you treat the stars as ground truth and read any star-vs-satellite mismatch as a satellite-side effect.† The order to check: the clock first, then the element epoch, then observer position, and altitude last.

4. Choosing the displayed coordinate frame

RA/Dec readouts (the aim boxes and the hover popups) can be shown in either frame, and the choice applies consistently everywhere so the two can never disagree:

J2000 catalog — the fixed epoch-2000.0 (ICRS) reference position that every modern catalog, finding chart, and paper uses. Astronomy Mode’s default, because it is the frame astronomers read and cross-reference.
Apparent (of-date) — where the object actually appears at the simulated instant, with the full pipeline above applied — what a telescope mount is pointed with. One toggle away.

The toggle is under Settings → Astronomy — Celestial Coordinates → Star & planet RA/Dec frame. Fractional seconds are shown to two decimals everywhere (RA to 0.01^s ≈ 0.15″, Dec to 0.01″).

References

IAU 2006 precession — Capitaine, Wallace & Chapront (2003, 2005), “Expressions for IAU 2000 precession quantities” (P03), Astronomy & Astrophysics.
IAU 2000A / 2000B nutation — Mathews, Herring & Buffett (2002); the truncated 2000B model, McCarthy & Luzum (2003).
IERS Conventions (2010) — Petit & Luzum (eds.), IERS Technical Note No. 36 (Earth-orientation parameters: precession/nutation, polar motion, UT1).
SOFA / ERFA — IAU Standards of Fundamental Astronomy library and its ERFA (Essential Routines for Fundamental Astronomy) derivative; aberration follows SOFA iauAb. iausofa.org
astropy — validation reference for the apparent-place pipeline (TETE / AltAz frames). astropy.org
HYG star catalog — Astronexus, compiled from Hipparcos, Yale Bright Star, and Gliese catalogs (positions, proper motion, parallax, magnitude). astronexus.com/hyg
SGP4 satellite propagation — Vallado, Crawford, Hujsak & Kelso (2006), “Revisiting Spacetrack Report #3”; original Hoots & Roehrich (1980).

† If the observer’s own position was fitted to a photograph (e.g. an aircraft with no ADS-B, solved backward from the image), only the star-field agreement is independent; the satellite match is then a consistency check, not a prediction.