A telescope never sees an orbit from above — it sees one number per epoch: the star's tiny angular position on the sky. That raw position is a mix of three motions layered on top of each other: the star's proper motion (a steady drift as it moves through the galaxy relative to us), the Earth's own annual parallax (a yearly loop caused by our vantage point orbiting the Sun), and — if a planet is present — the star's reflex wobble around the system barycenter. Real astrometric pipelines like Gaia's fit and subtract the first two, linear-in-time proper motion and one-year parallax, leaving a residual. If anything periodic survives in that residual at the planet's orbital period, that's the discovery.
Barycenter balance: M★ · a★ = Mₚ · aₚ
Star's true orbit: a★ = a · Mₚ / (M★ + Mₚ)
Angular amplitude: α [arcsec] = a★ [AU] / d [pc]
Kepler's 3rd law: P² [yr] = a³ [AU] / (M★ + Mₚ) [M☉]
Parallax: π [arcsec] = 1 / d [pc]
Raw track: pos(t) = μ·t + π·(cos 2πt, sin 2πt) + α·(cos 2πt/P, sin 2πt/P) + noise
Residual: pos(t) − μ·t − π·(cos 2πt, sin 2πt) = α·(cos 2πt/P, sin 2πt/P) + noise
- The left panel plots the raw apparent sky position over a rolling few-year window — this is what a telescope's astrometric catalogue actually records, epoch by epoch. Proper motion and parallax are almost always far larger than any planetary wobble, so the left panel looks like a drifting loop with no visible planet signature — exactly what real archival data looks like before reduction.
- The right panel subtracts the known proper-motion drift and the one-year parallax loop, leaving only the planet's reflex ellipse (plus whatever measurement noise is left over). Its axes are in microarcseconds — a thousand times finer than the left panel's milliarcsecond scale — because that's genuinely how small the surviving signal is.
- Per-epoch measurement noise sets how much scatter each simulated observation carries, mimicking real instrument precision (Gaia's best single-epoch astrometric precision for bright stars is roughly 20–40 μas). Raise it and the reflex ellipse dissolves into scatter; lower it and the ellipse becomes crisp — the same information Gaia's real pipeline uses to certify a detection.
- Unlike the transit method, astrometry works at any orbital inclination — it is most sensitive to planets on wide orbits around nearby, low-mass stars, exactly the systems transits and radial velocity struggle with.