Radius of geostationary orbit
=============================

A geostationary orbit is a circular orbit located above the Earth's equator (0° latitude),
where an artificial satellite orbits the planet with an angular velocity equal to the
angular speed of the Earth's rotation around its axis.

**Notation:**

#. :math:`G` (:code:`G`) is :attr:`~symplyphysics.quantities.gravitational_constant`.

**Links:**

#. `Wikipedia, possible formula derivable from here <https://en.wikipedia.org/wiki/Geostationary_orbit#Derivation>`__.

..
    TODO: find link with exact formula

.. py:currentmodule:: symplyphysics.laws.gravity.radius_of_geostationary_orbit

.. py:data:: orbital_radius

    :attr:`~symplyphysics.symbols.classical_mechanics.radius` of the satellite's geostationary orbit.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: planet_mass

    :attr:`~symplyphysics.symbols.basic.mass` of the attracting body (planet).

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: satellite_angular_speed

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_speed` of the satellite's rotation.

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: law

    :code:`r = (G * m / w^2)^(1/3)`


    Latex:
        .. math::
            r = \sqrt[3]{\frac{G m}{\omega^{2}}}