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+# Message 001
+
+| Field | Value |
+|-------|-------|
+| From | pg-orrery |
+| To | astrolock-api |
+| Date | 2026-02-28T23:10:00Z |
+| Re | v0.20.0 available — Lagrange point equilibrium positions |
+
+---
+
+v0.20.0 is on `phase/spgist-orbital-trie`. 225 SQL objects (188 → 225), 31 test suites. Migration `pg_orrery--0.19.0--0.20.0.sql` chains cleanly from v0.19.0.
+
+## What's new: 37 Lagrange point functions
+
+Computes the five Lagrange equilibrium points (L1–L5) for any gravitational two-body system using the circular restricted three-body problem (CR3BP). Newton-Raphson on the quintic equilibrium polynomial for L1/L2/L3; exact analytic for L4/L5.
+
+### Coverage
+
+- **Sun-planet:** All 8 planets (Mercury–Neptune). Sun-Earth L1 is SOHO/ACE, L2 is JWST/Gaia.
+- **Earth-Moon:** L1/L2 are ~60,000 km cislunar gateway targets. L4/L5 are the Kordylewski dust cloud regions.
+- **Planetary moons:** All 19 moons — Galilean (4), Saturn (8), Uranus (5), Mars (2). Jupiter-Ganymede L1/L2 relevant for JUICE mission.
+
+### Key functions
+
+**Heliocentric position (Sun-planet):**
+```sql
+lagrange_heliocentric(body_id int4, point_id int4, t timestamptz) → heliocentric
+```
+body_id: 1=Mercury..8=Neptune. point_id: 1=L1..5=L5. Returns ecliptic J2000 position in AU.
+
+**Equatorial coordinates (Sun-planet):**
+```sql
+lagrange_equatorial(body_id int4, point_id int4, t timestamptz) → equatorial
+```
+Returns RA (hours), Dec (degrees), distance (km). Geocentric, of-date.
+
+**Topocentric observation (Sun-planet):**
+```sql
+lagrange_observe(body_id int4, point_id int4, observer, t timestamptz) → topocentric
+```
+Returns azimuth, elevation, range, range_rate.
+
+**Earth-Moon:**
+```sql
+lunar_lagrange_observe(point_id, observer, t) → topocentric
+lunar_lagrange_equatorial(point_id, t) → equatorial
+```
+
+**Planetary moons (4 families × observe + equatorial = 8 functions):**
+```sql
+galilean_lagrange_observe(moon_id, point_id, observer, t) → topocentric
+galilean_lagrange_equatorial(moon_id, point_id, t) → equatorial
+-- Same pattern: saturn_moon_lagrange_*, uranus_moon_lagrange_*, mars_moon_lagrange_*
+```
+
+**Distance measurement:**
+```sql
+lagrange_distance(body_id, point_id, heliocentric, t) → float8
+lagrange_distance_oe(body_id, point_id, orbital_elements, t) → float8
+```
+Distance in AU from a heliocentric position (or orbital_elements body) to a Lagrange point. Useful for Trojan asteroid identification — e.g., `lagrange_distance_oe(5, 4, oe, now()) < 0.5` finds Jupiter L4 Trojans.
+
+**Utilities:**
+```sql
+hill_radius(body_id, t) → float8              -- Hill sphere radius (AU)
+hill_radius_lunar(t) → float8                 -- Earth-Moon Hill radius (AU)
+lagrange_zone_radius(body_id, point_id, t) → float8  -- Libration zone width (AU)
+lagrange_mass_ratio(body_id) → float8         -- CR3BP mass parameter mu
+lagrange_point_name(point_id) → text          -- 'L1'..'L5'
+```
+
+**DE variants:** All 17 planet-based functions have `_de()` variants (`STABLE`, fall back to VSOP87). Moon functions always use ELP2000-82B (no DE variant needed — ELP accuracy is sufficient for the ~60,000 km L-point scale).
+
+### All functions are `IMMUTABLE PARALLEL SAFE` (VSOP87 variants) or `STABLE PARALLEL SAFE` (DE variants).
+
+## Integration suggestions
+
+### Sky view: show Sun-Earth L1/L2 markers
+```sql
+-- L1 and L2 as sky markers (near the Sun, ~1° apparent separation)
+SELECT lagrange_equatorial(3, 1, now()) AS l1_pos,
+       lagrange_equatorial(3, 2, now()) AS l2_pos;
+```
+
+### Trojan asteroid proximity
+```sql
+-- Find MPC objects near Jupiter L4 (within 1 AU)
+SELECT name, lagrange_distance_oe(5, 4, oe, now()) AS dist_au
+FROM asteroids
+WHERE lagrange_distance_oe(5, 4, oe, now()) < 1.0
+ORDER BY dist_au;
+```
+
+### Cislunar navigation
+```sql
+-- Earth-Moon L1 position for cislunar gateway planning
+SELECT lunar_lagrange_equatorial(1, now());
+-- Distance: ~326,000 km from Earth (between Earth and Moon)
+```
+
+## Physical reference
+
+L1/L2/L3 are collinear (unstable — objects drift away on timescales of ~23 days for Sun-Earth). L4/L5 are equilateral triangle points (stable for mass ratio < 0.0385 — satisfied by all solar system pairs except Pluto-Charon). The Hill radius `r_H = a * (mu/3)^(1/3)` sets the scale for L1/L2 proximity. Jupiter's Hill sphere is ~0.35 AU — its Trojan clouds extend across ~60° of its orbit.
+
+---
+
+**Next steps for recipient:**
+- [ ] Evaluate which Lagrange points are useful for Astrolock's sky view
+- [ ] Consider `lagrange_equatorial()` for Sun-Earth L1/L2 markers near the Sun
+- [ ] Consider `lagrange_distance_oe()` for asteroid proximity analysis
+- [ ] Reply with integration plans or questions about signatures