Numerical conventions

Unless an API states otherwise:

• scalar computations use IEEE-754 binary64 (f64);
• position is in metres and velocity is in metres per second;
• gravitational parameters are in cubic metres per square second;
• durations are in seconds, while Julian-date conversions operate in days;
• angles are in radians;
• scalar ephemeris epochs use MJD2000;
• Cartesian state ordering is [x, y, z, vx, vy, vz];
• classical element ordering is [a, e, i, Ω, ω, ν];
• modified equinoctial ordering is [p, f, g, h, k, L];
• matrices use row-major nested arrays in Rust and C-contiguous row-major arrays at the Python boundary;
• public functions reject NaN and positive or negative infinity;
• deterministic batch APIs preserve input order; workers=0 uses Rayon’s shared pool, workers=1 is serial, and workers=N uses a cached pool with exactly N workers.

Some upstream functions propagate non-finite values or use them as invalid domain sentinels. The Rust API reports explicit errors instead. Algorithm guides document any narrower valid domain and all intentional deviations.

Classical conversion reports circular and equatorial states as singular because their node/periapsis angles are undefined. Modified equinoctial elements cover those states: choose the prograde convention except at inclination π, and the retrograde convention except at inclination zero. Element Jacobians are 6 × 6, with output components as rows and input components as columns.

Two-body propagation accepts any caller-consistent position, velocity, time, and gravitational-parameter units. Negative durations propagate backward. Time grids are relative to their first entry. State-transition matrices use ∂state_final/∂state_initial, with output components as rows.

Lambert solutions are ordered deterministically: the zero-revolution solution first, then left and right solutions for each increasing revolution count. clockwise = false selects prograde motion as viewed from positive z; collinear endpoints are rejected because that automatic direction convention is undefined.

Ephemeris scalar epochs use MJD2000 days. Returned states use SI units for built-in Solar System providers and caller-consistent units for constructed Keplerian providers. Provider metadata uses Option rather than upstream negative sentinels, and hyperbolic periods are None.