Gravitational potential energy
==============================

The **gravitational potential energy** of a system of two particles is the negative of the work
that would be done by the gravitational force of either particle acting on the other if the
particles were brought together from infinity to the given distance.

**Notation:**

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

**Links:**

#. `Physics LibreTexts. Gravitational Potential Energy beyond Earth (13.4.6) <https://phys.libretexts.org/Workbench/PH_245_Textbook_V2/13%3A_Gravitation/13.04%3A_Gravitational_Potential_Energy_and_Total_Energy>`__.

.. py:currentmodule:: symplyphysics.laws.gravity.gravitational_potential_energy

.. py:data:: gravitational_potential_energy

    Gravitational :attr:`~symplyphysics.symbols.classical_mechanics.potential_energy`.

Symbol:
    :code:`U`

Latex:
    :math:`U`

Dimension:
    :code:`energy`


.. py:data:: first_mass

    :attr:`~symplyphysics.symbols.basic.mass` of the first particle.

Symbol:
    :code:`m_1`

Latex:
    :math:`m_{1}`

Dimension:
    :code:`mass`


.. py:data:: second_mass

    :attr:`~symplyphysics.symbols.basic.mass` of the second particle.

Symbol:
    :code:`m_2`

Latex:
    :math:`m_{2}`

Dimension:
    :code:`mass`


.. py:data:: distance_between_mass_centers

    :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance` between mass centers of the particles.

Symbol:
    :code:`d`

Latex:
    :math:`d`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`U = -G * m_1 * m_2 / d`


    Latex:
        .. math::
            U = - \frac{G m_{1} m_{2}}{d}