Coordinate and astrometric transforms

Coordinate and astrometric transforms¶

Coordinate singular-domain exclusions¶

Status: verified

Coordinate functions expose physically undefined bases and angular singularities instead of inventing finite surrogate gradients.

Scope¶

Cartesian origin, coincident observer/star geometry, spherical poles, and zenith/nadir/horizon observing geometry documented by public transforms.

Conventions¶

• AD-vs-FD contracts apply to interior regular-domain probes

• non-finite derivatives at undefined geometries are explicit exclusions

• forward values alone are not evidence of a valid inference gradient

Sources¶

• source — the nine interior gradient contracts and enumerated singular exclusions. Locator: Confirmed findings A-006 and A-007; Tests and reproductions

Code & validation¶

• code: src/jaxstro/coords.py::cartesian_to_spherical

• code: src/jaxstro/coords.py::compute_parallax

• code: src/jaxstro/coords.py::zenith_parallactic

• validation: tests/unit/test_coords.py::TestSingularDomainContracts::test_cartesian_spherical_origin_has_no_finite_angular_jacobian

• validation: tests/unit/test_coords.py::TestSingularDomainContracts::test_coincident_star_has_no_finite_parallax_gradient

• validation: tests/validation/test_coords_grad_audit.py::test_public_coordinate_gradient_contract

IAU 1958 Galactic coordinates expressed in ICRS¶

Status: verified

A fixed orthogonal rotation maps IAU 1958 Galactic directions to ICRS and its transpose supplies the inverse transformation.

Scope¶

The Galactic/ICRS rotation coefficients and the public galactic_to_equatorial and equatorial_to_galactic functions.

Conventions¶

• the Galactic system is IAU 1958; ICRS is the equatorial realization

• public spherical inputs and outputs are degrees

• longitude derivatives at a coordinate pole are not physical tangent-plane derivatives

Sources¶

• source — the IAU 1958 to ICRS convention and rotation coefficients. Locator: SOFA routine iauG2icrs and Galactic-coordinate-system notes

Code & validation¶

• code: src/jaxstro/coords.py::_GALACTIC_TO_ICRS

• code: src/jaxstro/coords.py::galactic_to_equatorial

• code: src/jaxstro/coords.py::equatorial_to_galactic

• validation: tests/unit/test_coords.py::TestGalacticEquatorial::test_galactic_center

• validation: tests/unit/test_coords.py::TestGalacticEquatorial::test_north_galactic_pole

• validation: tests/unit/test_coords.py::TestGalacticEquatorial::test_roundtrip_galactic_equatorial

• validation: tests/validation/test_coords_grad_audit.py::test_public_coordinate_gradient_contract

Explicit sky-tangent and proper-motion frames¶

Status: verified

Cluster-frame positions and velocities are rotated through an explicit ICRS tangent center and projected onto each star’s local RA-star/Dec basis.

Scope¶

sky_tangent and compute_proper_motions on their documented regular domains.

Conventions¶

• positions are parsecs and velocities are kilometres per second

• sky centers and roll angle are explicit degrees

• proper motions are milliarcseconds per Julian year

• the old implicit global x/y-as-RA/Dec interpretation is retired

Sources¶

• source — the verified frame-ownership correction and eager wide-field warning contract. Locator: Confirmed findings A-002 and A-003

Code & validation¶

• code: src/jaxstro/coords.py::sky_tangent

• code: src/jaxstro/coords.py::compute_proper_motions

• code: src/jaxstro/astrometry.py::K_PROPER_MOTION

• validation: tests/unit/test_coords.py::TestSkyTangent::test_large_field_warns_eagerly

• validation: tests/unit/test_coords.py::TestProperMotions::test_off_axis_uses_local_equatorial_basis

• validation: tests/unit/test_astrometry.py::TestProperMotionConstant::test_k_proper_motion_derivation

• validation: tests/validation/test_coords_grad_audit.py::test_public_coordinate_gradient_contract