Model the Shapiro delay in radar residuals

[matthewholman]

Radar signals pass through the Sun's gravitational potential on both legs, and that delay was not modelled. For a leg between A and B,

dt = (2 GM / c^3) ln[(r_A + r_B + rho) / (r_A + r_B - rho)]

with r_A and r_B heliocentric distances. It is one to two microseconds at the geometries these observations are made, which sounds negligible until you notice that radar delay uncertainties in the JPL database run 0.2 to 4 microseconds, and are 0.30 for Golevka at Arecibo. Leaving it out biases every radar observation by several sigma.

Validated against real Apophis radar, on the epochs near the reference orbit where propagation error is negligible: the delay residual falls from 2.16 sigma to 0.312 sigma, and Doppler is unchanged at 0.28 sigma. The comparison is against an independent Python implementation of the same formula (ISSUE_146_shapiro_validation.py), so it checks the physics rather than this code. That confirms the conjecture recorded when the two-leg model was written, which attributed its residual to exactly this term. It also bears on the Apophis covariance work, where the unmodelled term was running at a median 8.5 sigma.

Two things came with it:

• The ephemeris is passed into compute_radar_residuals rather than read from r->extras. The simulation used for residuals has no assist_extras attached, so that pointer is NULL there.
• The radar test fixtures carry the term now. radar_synthetic.json was generated with delay = 2 rho/c and no Shapiro, so once the fitter modelled it the truth was inconsistent by 19.2 us per observation. There were two stale generators: the fixture script, and a second copy inlined in test_radar_end_to_end. Fixing both made the end-to-end tests pass with no tolerance touched.

test_radar_validation's chi-square bound did move, and the reason is in the test: the fixture now comes from an independent implementation, which agrees with the C++ to about 0.3 ns per observation rather than exactly. That is 3e-4 of the fixture's own stated uncertainty. The old 1e-6 bound was achievable only while fixture and fitter shared a formula. State tolerances are tightened rather than relaxed, 10x on position and 100x on velocity, since those carry the physics.

The partials are left alone: the Jacobian is already a single-leg approximation by design, and a microsecond-scale slowly varying term does not change the step direction.

Suite: 536 passed, 1 skipped on all four CI legs. Related: #528.

Reviewing this branch requires rebuilding the C++ extension. orbit_fit.cpp and radar_synthetic.json change together, so an older binary gets scored against a fixture that now carries the Shapiro term. The fit still converges and absorbs most of the 19.2 us into the orbit, which makes the failure look like a physics error rather than a stale build: test_radar_validation reports chi-square 0.0104 against its 1e-4 bound, and the end-to-end test a 3.7e-6 velocity drift. After pip install -e . all five radar tests pass.

[kjnapier]

Very impressive