boinor.threebody.restricted
===========================

.. py:module:: boinor.threebody.restricted

.. autoapi-nested-parse::

   Circular Restricted 3-Body Problem (CR3BP).

   Includes the computation of Lagrange points



Functions
---------

.. autoapisummary::

   boinor.threebody.restricted.lagrange_points
   boinor.threebody.restricted.lagrange_points_vec


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

.. py:function:: lagrange_points(r12, m1, m2)

   Computes the Lagrangian points of CR3BP.

   Computes the Lagrangian points of CR3BP given the distance between two
   bodies and their masses.
   It uses the formulation found in Eq. (2.204) of Curtis, Howard. 'Orbital
   mechanics for engineering students'. Elsevier, 3rd Edition.

   :param r12: Distance between the two bodies
   :type r12: ~astropy.units.Quantity
   :param m1: Mass of the main body
   :type m1: ~astropy.units.Quantity
   :param m2: Mass of the secondary body
   :type m2: ~astropy.units.Quantity

   :returns: Distance of the Lagrangian points to the main body,
             projected on the axis main body - secondary body
   :rtype: ~astropy.units.Quantity


.. py:function:: lagrange_points_vec(m1, r1, m2, r2, n)

   Computes the five Lagrange points in the CR3BP.

   Returns the positions in the same frame of reference as `r1` and `r2`
   for the five Lagrangian points.

   :param m1: Mass of the main body. This body is the one with the biggest mass.
   :type m1: ~astropy.units.Quantity
   :param r1: Position of the main body.
   :type r1: ~astropy.units.Quantity
   :param m2: Mass of the secondary body.
   :type m2: ~astropy.units.Quantity
   :param r2: Position of the secondary body.
   :type r2: ~astropy.units.Quantity
   :param n: Normal vector to the orbital plane.
   :type n: ~astropy.units.Quantity

   :returns: Position of the Lagrange points: [L1, L2, L3, L4, L5]
             The positions are of type ~astropy.units.Quantity
   :rtype: list