astrodynx.kepler_equ_hypb

astrodynx.kepler_equ_hypb#

astrodynx.kepler_equ_hypb(H, e, N=0)[source]#

Returns the Kepler’s equation for hyperbolic orbits in the form f(H) = 0.

Parameters:

  • H (ArrayLike) – Hyperbolic eccentric anomaly.

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

  • N (ArrayLike) – (optional) Hyperbolic mean anomaly.

Returns:

e*sinh(H) - H - N.

Return type:

Array

Notes

Kepler’s equation for hyperbolic orbits relates the hyperbolic eccentric anomaly H to the hyperbolic mean anomaly N:

\[ e \sinh H - H = N \]
This function returns the equation in the form f(H) = 0, which is useful for root-finding algorithms.

References

Battin, 1999, pp.168.

Examples

A simple example:

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> H = 1.0
>>> e = 1.5
>>> N = 1.0
>>> adx.kepler_equ_hypb(H, e, N)
Array(-0.2371..., dtype=float32, weak_type=True)

With broadcasting, you can calculate the Kepler’s equation for multiple hyperbolic eccentric anomalies, eccentricities, and hyperbolic mean anomalies:

>>> H = jnp.array([1.0, 2.0])
>>> e = jnp.array([1.5, 1.5])
>>> N = jnp.array([1.0, 1.0])
>>> adx.kepler_equ_hypb(H, e, N)
Array([-0.2371...,  2.4402...], dtype=float32)