#parallax

Stellar-parallax and astrometry maths as an API, computed locally and deterministically. The distance endpoint turns a measured trigonometric parallax angle into a distance using d(pc) = 1/p(arcsec), accepting the parallax in arcseconds or milliarcseconds and returning the distance in parsecs, light-years and astronomical units — a parallax of one arcsecond is one parsec (≈3.2616 light-years) by definition, and Proxima Centauri’s 0.7687-arcsecond parallax gives about 1.30 pc, or 4.24 light-years. The parallax endpoint inverts it, p(arcsec) = 1/d(pc), giving the tiny annual back-and-forth angle a star traces against the background as Earth orbits the Sun. The proper-motion endpoint computes a star’s tangential (transverse) velocity across the sky from its proper motion and distance, v_t = 4.74047·μ(arcsec/yr)·d(pc) km/s — Barnard’s Star, with a proper motion of about 10.39 arcsec/yr at 1.83 pc, races across the sky at roughly 90 km/s. Everything is computed locally and deterministically, so it is instant and private. Ideal for astronomy, astrophysics, planetarium, education and science-communication app developers, star-distance and stellar-kinematics tools, and Gaia-catalogue post-processing. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is geometric distance and kinematics; for a star’s apparent and absolute brightness use a star-magnitude API.

api.oanor.com/parallax-api

Stellar magnitude and distance maths as an API, computed locally and deterministically. The magnitude endpoint works the distance modulus, m − M = 5·log₁₀(d/pc) − 5 — give any two of the apparent magnitude m, the absolute magnitude M and the distance and it returns the third, with the distance in parsecs, light-years and astronomical units (the absolute magnitude is the apparent magnitude a star would have at 10 parsecs). The flux endpoint applies Pogson's relation to turn a magnitude difference into a brightness ratio, F₁/F₂ = 10^(0.4·(m₂ − m₁)), where five magnitudes is exactly a hundredfold change in brightness — from two magnitudes, a magnitude difference or a ratio. The parallax endpoint converts a parallax angle into a distance, d(pc) = 1 ÷ p(arcseconds), and back, the geometric method behind the parsec itself. Everything is computed locally and deterministically, so it is instant and private. Ideal for astronomy-education, planetarium, stargazing and science app developers, observing and astrophysics tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is stellar magnitude and distance; for orbital mechanics use an orbital API and for great-circle distances on Earth a geo-distance API.

api.oanor.com/starmagnitude-api