Satellite velocity: true_anomaly_dot divides by sin(ν), NaN at perigee/apogee

[giove-a]

Summary

In the velocity computation of calc_satellite_position_and_velocity, the true-anomaly rate true_anomaly_dot is computed by dividing by sin(true_anomaly), which is 0 at perigee (ν = 0) and apogee (ν = π). At those points sin(eccentric_anomaly) is also 0, so the expression is 0/0 → NaN.

Location

src/sat_position.jl, in calc_satellite_position_and_velocity:

true_anomaly_dot =
    sin(eccentric_anomaly) *
    eccentric_anomaly_dot *
    (1.0 + data.e * cos(true_anomaly)) /
    (sin(true_anomaly) * (1.0 - data.e * cos(eccentric_anomaly)))

Why this is a problem

The expression is algebraically correct, but numerically singular. Using the
identity sin ν = √(1−e²)·sin E / (1 − e·cos E), the sin E / sin ν ratio is the
finite quantity (1 − e·cos E)/√(1−e²). But evaluating it as sin(E)/sin(ν):

• at ν = 0 (perigee): E = 0 ⇒ sin(E) = sin(ν) = 0 ⇒ 0/0 = NaN,
• at ν = π (apogee): E = π ⇒ sin(E) = sin(ν) = 0 ⇒ 0/0 = NaN.

A NaN here propagates into the entire satellite velocity vector (it feeds
corrected_argument_of_latitude_dot, corrected_radius_dot, and
corrected_inclination_dot), and from there into the receiver
velocity / clock-drift solve.

GNSS orbits have small eccentricity, but ν sweeps through 0 and π every
orbital period, so a satellite passes near perigee/apogee twice per orbit. An
exact hit (E landing on 0/π in floating point) gives a hard NaN; this is
easy to trigger with synthetic ephemerides and possible with real data.

Suggested fix

Use the singularity-free closed form (reuses the already-computed
eccentric_anomaly_dot and true_anomaly):

true_anomaly_dot =
    eccentric_anomaly_dot * (1.0 + data.e * cos(true_anomaly)) / sqrt(1.0 - data.e^2)

This is exactly equal to the current expression away from the singular points
(Ė·(1+e·cos ν)/√(1−e²) = Ė·√(1−e²)/(1−e·cos E)) and is finite everywhere. An
equivalent E-only form is eccentric_anomaly_dot * sqrt(1 - data.e^2) / (1 - data.e * cos(eccentric_anomaly)).

Test

Add a regression test that propagates a satellite positioned at (or very near)
perigee/apogee and asserts the returned velocity is finite.