Average potential energy via average kinetic energy
===================================================

The average potential energy of an orbiting planet is directly proportional to its average
kinetic energy. The average of both energies is taken w.r.t. time.

**Conditions:**

#. Works for elliptical orbits, in which case the total energy :math:`E` of the planet is negative.

**Links:**

#. `Physics LibreTexts. Energy in Circular Orbits <https://phys.libretexts.org/Workbench/PH_245_Textbook_V2/13%3A_Gravitation/13.05%3A_Satellite_Orbits_and_Energy>`__.

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

.. py:data:: average_potential_energy

    The :attr:`~symplyphysics.symbols.classical_mechanics.potential_energy` of the planet averaged over :attr:`~symplyphysics.symbols.basic.time`.

Symbol:
    :code:`avg(U)`

Latex:
    :math:`\langle U \rangle`

Dimension:
    :code:`energy`


.. py:data:: average_kinetic_energy

    The :attr:`~symplyphysics.symbols.classical_mechanics.kinetic_energy` of the planet averaged over :attr:`~symplyphysics.symbols.basic.time`.

Symbol:
    :code:`avg(K)`

Latex:
    :math:`\langle K \rangle`

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`avg(U) = -2 * avg(K)`


    Latex:
        .. math::
            \langle U \rangle = - 2 \langle K \rangle