-- kepler_comet regression tests
--
-- Tests Keplerian propagation and comet observation.
-- Verifies Kepler equation solver for elliptic, parabolic,
-- and hyperbolic orbits.

\set boulder '''40.015N 105.270W 1655m'''::observer

-- ============================================================
-- Test 1: Circular orbit (e=0) at 1 AU
-- A body in a circular orbit at 1 AU with i=0, omega=0, Omega=0,
-- perihelion at J2000.0 should complete one orbit in ~365.25 days.
-- At T=0 (perihelion), position should be (1, 0, 0).
-- ============================================================
SELECT 'circular_t0' AS test,
       round(helio_x(kepler_propagate(1.0, 0.0, 0.0, 0.0, 0.0,
             2451545.0, '2000-01-01 12:00:00+00'))::numeric, 6) AS x,
       round(helio_y(kepler_propagate(1.0, 0.0, 0.0, 0.0, 0.0,
             2451545.0, '2000-01-01 12:00:00+00'))::numeric, 6) AS y,
       round(helio_z(kepler_propagate(1.0, 0.0, 0.0, 0.0, 0.0,
             2451545.0, '2000-01-01 12:00:00+00'))::numeric, 6) AS z;

-- ============================================================
-- Test 2: Circular orbit at 1 AU, quarter orbit (~91.3 days)
-- Should be at approximately (0, 1, 0) for i=0 prograde orbit.
-- ============================================================
SELECT 'circular_quarter' AS test,
       round(helio_x(kepler_propagate(1.0, 0.0, 0.0, 0.0, 0.0,
             2451545.0, '2000-04-01 18:00:00+00'))::numeric, 1) AS x_approx,
       round(helio_y(kepler_propagate(1.0, 0.0, 0.0, 0.0, 0.0,
             2451545.0, '2000-04-01 18:00:00+00'))::numeric, 1) AS y_approx;

-- ============================================================
-- Test 3: Eccentric elliptic orbit (e=0.5)
-- q=0.5 AU, e=0.5 -> a=1.0 AU, same period as Earth.
-- At perihelion (t=0), position should be (0.5, 0, 0).
-- ============================================================
SELECT 'eccentric_t0' AS test,
       round(helio_x(kepler_propagate(0.5, 0.5, 0.0, 0.0, 0.0,
             2451545.0, '2000-01-01 12:00:00+00'))::numeric, 6) AS x,
       round(helio_y(kepler_propagate(0.5, 0.5, 0.0, 0.0, 0.0,
             2451545.0, '2000-01-01 12:00:00+00'))::numeric, 6) AS y;

-- ============================================================
-- Test 4: Inclined orbit (i=90 deg)
-- With i=90, the orbit is polar. At perihelion the position
-- is still in the orbital plane but rotated by inclination.
-- q=1.0 AU, e=0, i=90, omega=0, Omega=0 at t=0:
-- position should be (1, 0, 0) regardless of inclination
-- (perihelion direction is in the node line).
-- ============================================================
SELECT 'inclined_t0' AS test,
       round(helio_x(kepler_propagate(1.0, 0.0, 90.0, 0.0, 0.0,
             2451545.0, '2000-01-01 12:00:00+00'))::numeric, 6) AS x,
       round(helio_z(kepler_propagate(1.0, 0.0, 90.0, 0.0, 0.0,
             2451545.0, '2000-01-01 12:00:00+00'))::numeric, 6) AS z;

-- ============================================================
-- Test 5: Heliocentric distance conservation for circular orbit
-- Distance should remain ~1.0 AU at all times.
-- ============================================================
SELECT 'distance_conservation' AS test,
       round(helio_distance(kepler_propagate(1.0, 0.0, 0.0, 0.0, 0.0,
             2451545.0, '2000-07-01 12:00:00+00'))::numeric, 6) AS dist_au;

-- ============================================================
-- Test 6: Hyperbolic orbit (e=1.5)
-- q=1.0 AU, e=1.5, i=0, omega=0, Omega=0
-- At perihelion, position = (1, 0, 0). Should propagate without error.
-- ============================================================
SELECT 'hyperbolic_t0' AS test,
       round(helio_x(kepler_propagate(1.0, 1.5, 0.0, 0.0, 0.0,
             2451545.0, '2000-01-01 12:00:00+00'))::numeric, 6) AS x,
       round(helio_distance(kepler_propagate(1.0, 1.5, 0.0, 0.0, 0.0,
             2451545.0, '2000-07-01 12:00:00+00'))::numeric, 2) AS dist_later;

-- ============================================================
-- Test 7: Near-parabolic orbit (e=1.0)
-- Comet on parabolic trajectory, q=1.0 AU.
-- At perihelion, position = (1, 0, 0).
-- ============================================================
SELECT 'parabolic_t0' AS test,
       round(helio_x(kepler_propagate(1.0, 1.0, 0.0, 0.0, 0.0,
             2451545.0, '2000-01-01 12:00:00+00'))::numeric, 6) AS x;

-- ============================================================
-- Test 8: Comet observation with known Earth position
-- Place a "comet" at (2, 0, 0) AU heliocentric ecliptic.
-- Earth at (1, 0, 0) AU. Geocentric comet is at (1, 0, 0) AU,
-- which in equatorial J2000 is RA=0h, Dec=0 (on ecliptic plane
-- after rotation, dec ~ -obliquity... actually RA=0, Dec=0
-- because ecliptic-to-equatorial of (1,0,0) = (1,0,0)).
-- Geocentric distance should be 1 AU = 149597870.7 km.
-- ============================================================
SELECT 'comet_obs_range' AS test,
       round(topo_range(comet_observe(
           2.0, 0.0, 0.0, 0.0, 0.0, 2451545.0,
           1.0, 0.0, 0.0,
           :boulder, '2000-01-01 12:00:00+00'))::numeric, 0) AS range_km;

-- ============================================================
-- Test 9: Input validation
-- ============================================================
SELECT 'negative_q' AS test, kepler_propagate(-1.0, 0.5, 0.0, 0.0, 0.0, 2451545.0, now());