Second escape velocity
======================

The second cosmic velocity is the lowest velocity that must be given to an object starting from the surface of
a celestial body, the mass of which is negligible compared to the mass of a celestial body, in order to overcome
the gravitational attraction of this celestial body and leave a closed orbit around it.

**Notation:**

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

**Links:**

#. `Physics LibreTexts. Conservation of Energy, Escape velocity (13.4.10) <https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/13%3A_Gravitation/13.04%3A_Gravitational_Potential_Energy_and_Total_Energy>`__.

.. py:currentmodule:: symplyphysics.laws.gravity.second_escape_velocity

.. py:data:: speed

    Second escape :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: planet_mass

    Planetary :attr:`~symplyphysics.symbols.basic.mass`.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: planet_radius

    Planetary :attr:`~symplyphysics.symbols.classical_mechanics.radius`.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: height

    Elevation (see :attr:`~symplyphysics.symbols.classical_mechanics.height`) of the body above the planet's surface.

Symbol:
    :code:`h`

Latex:
    :math:`h`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`v = sqrt(2 * G * m / (r + h))`


    Latex:
        .. math::
            v = \sqrt{\frac{2 G m}{r + h}}