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 :cite:t:`Curtis2013`, 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