Potential energy of radial planetary motion
===========================================

The total mechanical energy of the planet can be viewed as the sum of the kinetic and potential energy.
The potential energy is in turn the sum of the potential energy due to the gravitational interaction
between the planet and the Sun, and the the energy of the tangential motion, which depends on the
planet's angular momentum.

**Links:**

#. Sivukhin, D.V. (1979). *Obshchiy kurs fiziki* [General course of Physics], vol. 1, p. 315.

.. py:currentmodule:: symplyphysics.laws.gravity.radial_motion.potential_energy_of_planetary_motion

.. py:data:: total_potential_energy

    The total :attr:`~symplyphysics.symbols.classical_mechanics.potential_energy` of the planet.

Symbol:
    :code:`U_tot`

Latex:
    :math:`U_\text{tot}`

Dimension:
    :code:`energy`


.. py:data:: gravitational_potential_energy

    The :attr:`~symplyphysics.symbols.classical_mechanics.potential_energy` of the planet due to the gravitational interaction of the planet and the star.

Symbol:
    :code:`U_gr`

Latex:
    :math:`U_\text{gr}`

Dimension:
    :code:`energy`


.. py:data:: angular_momentum

    The :attr:`~symplyphysics.symbols.classical_mechanics.angular_momentum` of the planet.

Symbol:
    :code:`L`

Latex:
    :math:`L`

Dimension:
    :code:`length**2*mass/time`


.. py:data:: planetary_mass

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

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: distance

    The :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance` between the star and the planet.

Symbol:
    :code:`d`

Latex:
    :math:`d`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`U_tot = U_gr + L^2 / (2 * m * d^2)`


    Latex:
        .. math::
            U_\text{tot} = U_\text{gr} + \frac{L^{2}}{2 m d^{2}}