Built by Claude Opus 4.8 · an AI model from Anthropic

First-Principles Planetarium

Claude Opus 4.8 — an AI model — designed and coded this entire planetarium from a single prompt. Every Sun, Moon, and planet position is computed live from Keplerian orbital elements and spherical astronomy, not looked up. No libraries, no data files. Works for any place and moment from 1900 to 2100.

Date (local at location)

Time (local clock at location)

Location

Sky size Planet size Stars Names

Tap or hover any body — in the sky chart or the table — to see its live coordinates here.

Geocentric apparent coordinates & local horizon position. Azimuth from true North, clockwise (N 0°, E 90°). Altitude is geometric — atmospheric refraction is ignored.
Body	RA	Dec	Azimuth	Altitude	Status

Self-Testrunning…

Test	Expected	Computed	Diff	Result

Methods & simplifications (so results can be verified)

Planets (Mercury–Saturn): heliocentric positions from J2000 mean Keplerian elements with secular (linear) rates — JPL "Keplerian Elements for Approximate Positions" (1800–2050 set) — then differenced against the Earth–Moon barycentre and rotated to the J2000 equatorial frame (obliquity 23.43928°). Most accurate ~1900–2050; accuracy degrades modestly toward 2100 (Saturn most).
Sun: low-precision series from the Astronomical Almanac (mean longitude + equation of centre), good to ≈0.01°.
Moon: Schlyter's truncated series. Principal perturbations included — evection −1.274° sin(M−2D), variation +0.658° sin 2D, annual equation −0.186° sin M☉, parallactic equation −0.035° sin D, plus 8 further longitude terms, 5 latitude terms and 2 distance terms. Omitted: the full ELP-2000 series (hundreds of terms) and most planetary perturbations on the Moon. Topocentric parallax applied as a first-order altitude correction −HP·cos(alt).
Neglected throughout: atmospheric refraction (altitudes are geometric), nutation & aberration (each ≲0.02°), light-time, and ΔT = TT−UT (TT≈UT; sub-degree across the range). Azimuth parallax is also neglected.
Time zones & DST: the modern U.S. daylight-saving rule (2nd Sunday of March → 1st Sunday of November) is applied to every year in range. Arizona and Hawaii are treated as no-DST.
Stars & rendering: the ~48 brightest stars are plotted from catalogue J2000 positions with first-order precession to the date. Planet, Sun, and Moon discs are illustrative (textures and relative sizes are not to physical scale), though the Moon's lit fraction and the orientation of its bright limb toward the Sun are computed.

Model: Claude Opus 4.8

Generated: June 11, 2026 · last revised in this session

Version: 1.12 — iteratively refined across this conversation (no longer a single-prompt build)

Purpose: started from a single prompt to test whether an AI can compute the real sky from first principles, then extended through a series of user requests.