Orbital speed from semimajor axis and planet mass
=================================================

The orbital speed of a body is the speed at which it rotates around the barycenter of the
system, usually around a more massive body. It can be calculated from the mass of the
planet and the orbit configuration parameters.

**Notation:**

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

**Conditions:**

#. The distance to the barycenter :math:`r` must not exceed the length :math:`a` of the
   semi-major axis of the orbit.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Orbital_speed#Instantaneous_orbital_speed>`__.

.. py:currentmodule:: symplyphysics.laws.gravity.orbital_velocity_from_length_of_large_half_axis_and_planet_mass

.. py:data:: orbital_speed

    Orbital :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the satellite.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: distance

    :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance` at which the speed is calculated.

Symbol:
    :code:`d`

Latex:
    :math:`d`

Dimension:
    :code:`length`


.. py:data:: semimajor_axis

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

Symbol:
    :code:`a`

Latex:
    :math:`a`

Dimension:
    :code:`length`


.. py:data:: planet_mass

    :attr:`~symplyphysics.symbols.basic.mass` of the planet.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: law

    :code:`v = sqrt(G * m * (2 / d - 1 / a))`


    Latex:
        .. math::
            v = \sqrt{G m \left(\frac{2}{d} - \frac{1}{a}\right)}