astrodynx.solve_kepler_hypb

astrodynx.solve_kepler_hypb#

astrodynx.solve_kepler_hypb(N, e, tol=1e-06, max_iter=50)[source]#

Returns the hyperbolic eccentric anomaly for a hyperbolic orbit.

Parameters:

  • N (DTypeLike) – Hyperbolic mean anomaly.

  • e (DTypeLike) – Eccentricity of the orbit, e > 1.

  • tol (DTypeLike) – (optional) Tolerance for convergence.

  • max_iter (int) – (optional) Maximum number of iterations.

Return type:

Array

Returns:

The hyperbolic eccentric anomaly for a hyperbolic orbit.

Notes

The hyperbolic eccentric anomaly is calculated by solving Kepler’s equation for hyperbolic orbits:

\[ e \sinh H - H = N \]
where \(H\) is the hyperbolic eccentric anomaly, \(e\) is the eccentricity, and \(N\) is the hyperbolic mean anomaly.

References

Battin, 1999, pp.168.

Examples

A simple example:

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> e = 2.7696
>>> N = 40.69
>>> adx.solve_kepler_hypb(N,e)
Array(3.463..., dtype=float32, weak_type=True)