solve_kepler_equation
このコンテンツはまだ日本語訳がありません。
Defined in: kepler.rs:70
fn solve_kepler_equation(mean_anomaly: f64, eccentricity: f64) -> f64
Solve Kepler’s equation M = E - e·sin(E) for eccentric anomaly E.
Newton-Raphson, kept inside a bracket that contains the root: at high
eccentricity f' = 1 - e·cos(E) falls to 1 - e at periapsis, and near
there an unguarded Newton step from E₀ = M is long enough to leave the
interval and not come back. At e = 0.995, M = 0.4 the step is 4.64 rad,
landing at E = 5.04 outside the bracket [-0.595, 1.395]. Bisecting
instead of taking such a step converges for every eccentricity the
signature accepts.
Arguments
Section titled “Arguments”mean_anomaly- Mean anomaly M [rad]eccentricity- Orbital eccentricity (0 ≤ e < 1)
Returns
Section titled “Returns”Eccentric anomaly E [rad], within e of the reduced M.
The residual is evaluated at the periapsis nearest E, so how accurately it
can be computed is set by its own magnitude rather than by the size of E.
What that leaves is the spacing of f64 itself, which grows with E: a
root just below 2π is placed to ulp(2π) = 8.9e-16, one just above zero
to far finer.