Ryan Malloy
024c0c1e0c
Add positive-gamma clamp in L1/L2/L3 Newton-Raphson iterations to prevent divergence on extreme mass ratios. Add missing CREATE EXTENSION, tighter L1/L2 precision checks (4 decimal places), lagrange_distance_oe test with Ceres, L1-Earth-L2 ordering verification, and DE fallback tests for planetary moon Lagrange functions.
267 lines
9.8 KiB
SQL
267 lines
9.8 KiB
SQL
-- v020_features: Lagrange point support
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-- Tests Sun-planet, Earth-Moon, planetary moon Lagrange points,
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-- Hill radius, zone radius, DE fallback, and input validation.
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CREATE EXTENSION IF NOT EXISTS pg_orrery;
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-- Reference observer: Greenwich, UK
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\set obs '''(51.4769,-0.0005,0)'''
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-- Reference time: J2000 epoch (2000-01-01 12:00:00 UTC)
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\set t '''2000-01-01 12:00:00+00'''
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-- ============================================================
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-- Sun-Earth L1/L2: should be ~0.01 AU from Earth (~1.5 million km)
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-- SOHO is at L1, JWST at L2.
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-- ============================================================
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-- L1 heliocentric: should be close to Earth's heliocentric (~1 AU from Sun)
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SELECT
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round(helio_distance(lagrange_heliocentric(3, 1, :t ::timestamptz))::numeric, 2) AS sun_dist_au;
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-- L2 heliocentric: also ~1 AU from Sun, slightly further than L1
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SELECT
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round(helio_distance(lagrange_heliocentric(3, 2, :t ::timestamptz))::numeric, 2) AS sun_dist_au;
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-- L1 between Sun and Earth (closer to Sun than L2)
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SELECT
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helio_distance(lagrange_heliocentric(3, 1, :t ::timestamptz))
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<
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helio_distance(lagrange_heliocentric(3, 2, :t ::timestamptz))
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AS l1_closer_than_l2;
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-- ============================================================
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-- Sun-Jupiter L4/L5: ~60 degrees from Jupiter, ~5.2 AU from Sun
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-- These are the Trojan asteroid zones.
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-- ============================================================
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-- L4/L5 should be ~5.2 AU from Sun
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SELECT
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round(helio_distance(lagrange_heliocentric(5, 4, :t ::timestamptz))::numeric, 1) AS l4_sun_dist;
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SELECT
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round(helio_distance(lagrange_heliocentric(5, 5, :t ::timestamptz))::numeric, 1) AS l5_sun_dist;
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-- L4 and L5 equidistant from Sun (within 0.001 AU)
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SELECT
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abs(
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helio_distance(lagrange_heliocentric(5, 4, :t ::timestamptz))
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-
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helio_distance(lagrange_heliocentric(5, 5, :t ::timestamptz))
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) < 0.001 AS l4_l5_equidistant;
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-- ============================================================
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-- Earth-Moon L1: ~326,000 km from Earth
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-- ============================================================
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-- lunar_lagrange_equatorial returns distance in km
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SELECT
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round(eq_distance(lunar_lagrange_equatorial(1, :t ::timestamptz))::numeric, -3)
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BETWEEN 300000 AND 360000 AS em_l1_in_range;
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-- ============================================================
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-- lagrange_observe returns valid az/el
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-- ============================================================
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SELECT
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topo_elevation(lagrange_observe(3, 2, :obs ::observer, :t ::timestamptz))
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BETWEEN -90 AND 90 AS valid_elevation;
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-- lagrange_equatorial returns valid RA/Dec
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SELECT
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eq_ra(lagrange_equatorial(3, 1, :t ::timestamptz)) BETWEEN 0 AND 24 AS valid_ra,
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eq_dec(lagrange_equatorial(3, 1, :t ::timestamptz)) BETWEEN -90 AND 90 AS valid_dec;
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-- ============================================================
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-- lagrange_distance self-test: L-point distance to itself ≈ 0
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-- ============================================================
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SELECT
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round(lagrange_distance(
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5, 4,
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lagrange_heliocentric(5, 4, :t ::timestamptz),
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:t ::timestamptz
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)::numeric, 10) AS self_distance;
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-- ============================================================
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-- Hill radius
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-- ============================================================
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-- Jupiter Hill radius ~0.35 AU
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SELECT
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round(hill_radius(5, :t ::timestamptz)::numeric, 2)
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BETWEEN 0.30 AND 0.40 AS jupiter_hill_ok;
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-- Earth Hill radius ~0.01 AU
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SELECT
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round(hill_radius(3, :t ::timestamptz)::numeric, 3)
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BETWEEN 0.008 AND 0.012 AS earth_hill_ok;
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-- Lunar Hill radius (much smaller, AU)
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SELECT
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hill_radius_lunar(:t ::timestamptz) > 0 AS lunar_hill_positive;
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-- ============================================================
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-- Zone radius
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-- ============================================================
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SELECT
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lagrange_zone_radius(5, 4, :t ::timestamptz) > 0 AS jup_l4_zone_positive;
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SELECT
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lagrange_zone_radius(5, 1, :t ::timestamptz) > 0 AS jup_l1_zone_positive;
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-- ============================================================
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-- Convenience functions
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-- ============================================================
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-- lagrange_mass_ratio returns small positive number
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SELECT
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lagrange_mass_ratio(5) > 0 AND lagrange_mass_ratio(5) < 0.01 AS jupiter_mu_ok;
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SELECT
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lagrange_mass_ratio(3) > 0 AND lagrange_mass_ratio(3) < 0.001 AS earth_mu_ok;
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-- lagrange_point_name
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SELECT lagrange_point_name(1) AS l1_name;
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SELECT lagrange_point_name(5) AS l5_name;
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-- ============================================================
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-- All planets produce valid results
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-- ============================================================
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SELECT body_id,
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round(helio_distance(lagrange_heliocentric(body_id, 1, :t ::timestamptz))::numeric, 2) AS sun_dist_au
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FROM generate_series(1, 8) AS body_id
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ORDER BY body_id;
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-- ============================================================
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-- Planetary moon Lagrange points
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-- ============================================================
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-- Galilean: Io L4 (body=0, point=4)
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SELECT
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eq_ra(galilean_lagrange_equatorial(0, 4, :t ::timestamptz)) BETWEEN 0 AND 24
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AS io_l4_valid_ra;
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-- Saturn: Titan L1 (body=5, point=1)
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SELECT
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eq_ra(saturn_moon_lagrange_equatorial(5, 1, :t ::timestamptz)) BETWEEN 0 AND 24
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AS titan_l1_valid_ra;
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-- Uranus: Titania L2 (body=3, point=2)
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SELECT
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eq_ra(uranus_moon_lagrange_equatorial(3, 2, :t ::timestamptz)) BETWEEN 0 AND 24
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AS titania_l2_valid_ra;
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-- Mars: Phobos L5 (body=0, point=5)
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SELECT
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eq_ra(mars_moon_lagrange_equatorial(0, 5, :t ::timestamptz)) BETWEEN 0 AND 24
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AS phobos_l5_valid_ra;
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-- Galilean observe returns valid topocentric
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SELECT
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topo_elevation(galilean_lagrange_observe(2, 3, :obs ::observer, :t ::timestamptz))
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BETWEEN -90 AND 90 AS ganymede_l3_valid_el;
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-- ============================================================
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-- DE fallback (no DE loaded, should produce same results as VSOP87)
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-- ============================================================
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SELECT
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round(helio_distance(lagrange_heliocentric_de(3, 1, :t ::timestamptz))::numeric, 4) AS de_l1_dist;
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SELECT
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round(helio_distance(lagrange_heliocentric(3, 1, :t ::timestamptz))::numeric, 4) AS vsop_l1_dist;
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-- DE hill_radius fallback
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SELECT
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round(hill_radius_de(5, :t ::timestamptz)::numeric, 4) =
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round(hill_radius(5, :t ::timestamptz)::numeric, 4)
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AS hill_de_matches_vsop;
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-- ============================================================
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-- Tighter L1/L2 precision (4 decimal places)
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-- ============================================================
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SELECT
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round(helio_distance(lagrange_heliocentric(3, 1, :t ::timestamptz))::numeric, 4) AS earth_l1_dist;
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SELECT
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round(helio_distance(lagrange_heliocentric(3, 2, :t ::timestamptz))::numeric, 4) AS earth_l2_dist;
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-- L1 and L2 bracket Earth's heliocentric distance
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SELECT
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helio_distance(lagrange_heliocentric(3, 1, :t ::timestamptz))
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<
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helio_distance(planet_heliocentric(3, :t ::timestamptz))
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AND
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helio_distance(planet_heliocentric(3, :t ::timestamptz))
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<
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helio_distance(lagrange_heliocentric(3, 2, :t ::timestamptz))
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AS l1_earth_l2_ordering;
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-- ============================================================
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-- lagrange_distance_oe — Ceres distance from Jupiter L4
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-- Ceres orbits at ~2.77 AU, Jupiter L4 at ~5.2 AU, so distance > 2 AU
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-- ============================================================
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SELECT
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round(lagrange_distance_oe(
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5, 4,
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oe_from_mpc('00001 3.33 0.12 K24AM 60.07966 73.42937 80.26860 10.58664 0.0789126 0.21406048 2.7660961 0 MPO838504 8738 115 1801-2024 0.65 M-v 30k MPCLINUX 0000 (1) Ceres 20240825'),
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:t ::timestamptz
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)::numeric, 2) AS ceres_jup_l4_dist;
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-- Distance should be positive and > 2 AU (main belt vs Trojan zone)
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SELECT
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lagrange_distance_oe(
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5, 4,
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oe_from_mpc('00001 3.33 0.12 K24AM 60.07966 73.42937 80.26860 10.58664 0.0789126 0.21406048 2.7660961 0 MPO838504 8738 115 1801-2024 0.65 M-v 30k MPCLINUX 0000 (1) Ceres 20240825'),
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:t ::timestamptz
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) > 2.0 AS ceres_far_from_trojan;
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-- ============================================================
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-- DE fallback for planetary moon Lagrange functions
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-- ============================================================
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SELECT
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round(eq_ra(galilean_lagrange_equatorial_de(0, 4, :t ::timestamptz))::numeric, 4) =
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round(eq_ra(galilean_lagrange_equatorial(0, 4, :t ::timestamptz))::numeric, 4)
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AS galilean_de_fallback_matches;
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SELECT
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round(eq_ra(saturn_moon_lagrange_equatorial_de(5, 1, :t ::timestamptz))::numeric, 4) =
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round(eq_ra(saturn_moon_lagrange_equatorial(5, 1, :t ::timestamptz))::numeric, 4)
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AS saturn_de_fallback_matches;
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-- ============================================================
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-- Input validation
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-- ============================================================
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-- Bad body_id
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SELECT lagrange_heliocentric(0, 1, :t ::timestamptz); -- Sun not valid
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SELECT lagrange_heliocentric(9, 1, :t ::timestamptz); -- body 9 invalid
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-- Bad point_id
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SELECT lagrange_heliocentric(3, 0, :t ::timestamptz); -- point 0 invalid
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SELECT lagrange_heliocentric(3, 6, :t ::timestamptz); -- point 6 invalid
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-- Bad lunar point_id
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SELECT lunar_lagrange_equatorial(0, :t ::timestamptz); -- point 0 invalid
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SELECT lunar_lagrange_equatorial(6, :t ::timestamptz); -- point 6 invalid
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-- Bad planetary moon body_id
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SELECT galilean_lagrange_equatorial(4, 1, :t ::timestamptz); -- Galilean 4 invalid
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SELECT saturn_moon_lagrange_equatorial(8, 1, :t ::timestamptz); -- Saturn 8 invalid
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SELECT uranus_moon_lagrange_equatorial(5, 1, :t ::timestamptz); -- Uranus 5 invalid
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SELECT mars_moon_lagrange_equatorial(2, 1, :t ::timestamptz); -- Mars 2 invalid
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-- lagrange_mass_ratio bad body
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SELECT lagrange_mass_ratio(0);
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SELECT lagrange_mass_ratio(9);
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-- lagrange_point_name bad id
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SELECT lagrange_point_name(0);
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SELECT lagrange_point_name(6);
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