:mod:`lamberthub.utils.kepler`
==============================

.. py:module:: lamberthub.utils.kepler
   :noindex:

.. autoapi-nested-parse::

   This module holds the so-called Kepler equations for each one of the particular
   orbit shapes, that is elliptical, parabolic and hyperbolic.

   The required formulas are found to be within Vallado's[1] manual.

   .. rubric:: References

   [1] Vallado, D. A. (2001). Fundamentals of astrodynamics and applications
       (Vol. 12). Springer Science & Business Media.



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::


   lamberthub.utils.kepler.kepler_elliptic


   lamberthub.utils.kepler.kepler_parabolic


   lamberthub.utils.kepler.kepler_hyperbolic


   lamberthub.utils.kepler.kepler_from_nu



.. py:function:: kepler_elliptic(E, ecc)

   Computes the time of flight since perigee passage at particular eccentric
   anomaly for elliptical orbit.

   :param E: Eccentric anomaly.
   :type E: float
   :param ecc: Eccentricity of the orbit. Must be between (0,1).
   :type ecc: float

   :returns: **M** -- Time since perigee passage.
   :rtype: float


.. py:function:: kepler_parabolic(B)

   Computes the time of flight since perigee passage at particular eccentric
   anomaly for paraboliparabolic orbit.

   :param B: Parabolic anomaly.
   :type B: float

   :returns: **Mp** -- Parabolic mean motion
   :rtype: float


.. py:function:: kepler_hyperbolic(H, ecc)

   Computes the time of flight since perigee passage at particular eccentric
   anomaly for hyperbolic orbit.

   :param H: Hyperbolic anomaly.
   :type H: float
   :param ecc: Eccentricity of the orbit.

   :returns: **Mh** -- Hyperbolic mean motion
   :rtype: float


.. py:function:: kepler_from_nu(nu, ecc)

   Compute the mean anomaly depending on the particular orbit shape, that is
   elliptical, parabolic or hyperbolic.

   :param nu: True anomaly.
   :type nu: float
   :param ecc: Orbit's eccentricity.
   :type ecc: float

   :returns: **M** -- Mean anomaly.
   :rtype: float