NavList:

Hi Frank,

>Ian, but because of Grok's failure to show its work.

My bad; I failed to point Grok at your OP thread and I should of posted the work and source URL.  Here is my latest GOOD Grok AI:

Approximately 40°N, 87°W (near the Illinois/Indiana border in the US Midwest, e.g., around Champaign-Urbana, IL area).

This is a clever "wrist-sized celestial navigation problem" from Frank Reed on NavList (May 2026), based on a commercial astro-jewelry bracelet ad showing a star chart customized for a specific date/time/location (here, Christmas = 25 Dec 2026 at 0400 UT). The chart's constellation lines, declination circles, and horizon frame encode the local sky view, which uniquely (enough) determines the observer's position on Earth.

Key assumptions from the source (valid per the puzzle setup):

• The framed sky view ≈ observer's visible sky down to the (local) horizon.
• Constellation lines are standard/accurate.
• Declination circles shown at roughly 85°, 55°, 25°, -5°, -35° (30° spacing offset by ~5° from NCP).
• Two marked "corner" points on/near the horizon for easy solving:
  • Point x: Dec +25°, SHA 180°.
  • Point y: Dec -35°, SHA 240°.
• These are treated as exactly (or very near) altitude 0°.
• GHA of Aries (from almanac/date-time) ≈ 154° (confirmed via sidereal time calc: ~153.7°).

Step-by-step solution (the "two-body fix" with alts=0°):

Use the altitude formula for a celestial body (spherical trig, law of cosines for the navigational triangle):

sin(alt) = sin(Lat) ⋅ sin(Dec) + cos(Lat) ⋅ cos(Dec) ⋅ cos(LHA)

For alt = 0° → sin(alt) = 0, so:

sin(Lat) ⋅ sin(Dec) + cos(Lat) ⋅ cos(Dec) ⋅ cos(LHA) = 0

LHA = GHA_body − Lon (Lon east-positive convention here; adjust mod 360° as needed). GHA_body = GHA_Aries + SHA.

This yields two equations (one per point) in two unknowns (Lat, Lon). Solving analytically or numerically:

• For the given points and GHA_Aries ≈ 154° → Lat ≈ 40°N, Lon ≈ 87°W (SHAmer ≈ 293°).

This matches independent estimates from participants (e.g., ~45°N 85°W via Polaris + Aldebaran meridian; or fine-tuning in Stellarium). Small projection/distortion effects in the bracelet graphic explain minor variances (± a few degrees, as Frank noted; don't over-precisify).

Extra credit (alts ≈ +3° instead of 0°):

Slightly shifts the fix (horizon a bit inside the frame), but it remains in the same general area—still ~40°N 87°W within the puzzle's tolerance. The main solution holds.

Why this works (and why it's "verbose" celestial nav fun):

• At any instant, the sky is a unique "fingerprint" of time + position (local hour angles/altitudes shift with Lon/Lat; polar distance with Lat).
• Horizon-limited view + coordinate grid pins it down like a traditional two-star (or more) sight reduction, but here the "sights" are implicit in the graphic.
• Real products use astronomy software (e.g., similar to the armchairastronautics skymap tool Frank referenced) to generate custom charts.

Bottom line: On Christmas 2026 at 0400 UT, "you" (per the bracelet) were at ~40°N, 87°W—central US, winter sky with prominent northern/winter constellations framed as shown. Great puzzle! If you have the actual bracelet image or more details, I can refine further.

Source:
https://grok.com/c/90d2e92f-b092-4c82-a227-9da2d1e58641 

Note 1: This from the latest version of Grok is Grok 4.3, which was released on April 17, 2026.

Note 2: “Grok means to understand so thoroughly that the observer becomes a part of the observed—to merge, blend, intermarry, lose identity in group experience.” Robert A. Heinlein in his 1961 science fiction novel Stranger in a Strange Land

Have fun!
--
Ian Gifford 42° 38' N, 71° 24' W