First escape speed
==================

**First escape speed** is the minimum speed needed for an object to escape from contact with or orbit of a primary body.

**Notation:**

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

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Escape_velocity#From_an_orbiting_body>`__.

..
    TODO rename file

.. py:currentmodule:: symplyphysics.laws.gravity.escape_velocity

.. py:data:: speed

    Escape :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the body.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: radius

    :attr:`~symplyphysics.symbols.classical_mechanics.radius` of the planet.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: height

    Elevation (:attr:`~symplyphysics.symbols.classical_mechanics.height`) of the body from the surface of the planet

Symbol:
    :code:`h`

Latex:
    :math:`h`

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 / (r + h))`


    Latex:
        .. math::
            v = \sqrt{\frac{G m}{r + h}}