.. GREOPy documentation master file, created by
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Welcome to GREOPy's documentation
=================================

**General Relativistic Emitter-Observer problem Python Algorithm** or *GREOPy* is a Python library for calculating relativistic light rays sent by an emitter to a receiver in the presence of a gravitational field.

The basic setup involves two objects :math:`O_{1, 2}` moving along two curves :math:`C_{1, 2}` in a gravitational field caused by some central mass :math:`M`.
One object successively emits light signals :math:`\gamma_i` that the other object receives at some *event* (time and spatial position).
An example could be a ground station :math:`O_1` rotating with the Earth :math:`M` sending out light signals to a satellite :math:`O_2` orbiting the Earth, or vice versa.

.. figure:: images/doc_index.png
   :figwidth: 100 %

   A light signal (yellow) is emitted at an event along the red curve on the surface of a central mass and received at an event along the blue curve.

Two factors play an important role in this scenario:

* During the propagation of a light signal between ground station and satellite, the receiver moves along its own curve.
* The presence of Earth's gravitational field bends light signals.

Therefore once a light signal is emitted (fixed emission event), the reception event (signal reaches the receiver) is initially unknown and depends solely on the signal's initial direction relative to some reference.

*GREOPy* solves for these :math:`\gamma_i` for arbitrary curves :math:`C_{1, 2}` and some rotating, non-accelerating central mass.

Please refer to the following table of contents for more information about the theoretical background, installation and usage of the package.

.. toctree::
   :maxdepth: 1
   :caption: Contents:

   about/index.rst
   installation.rst
   quickstart.rst
   usage/index.rst
   auto_tutorials/index.rst
   function_documentation/index.rst