Radial kinetic energy plus potential energy is constant
=======================================================

The total energy of the planet is composed of its radial kinetic energy and potential
energy. Note that the sign of the total energy determines the type of the planet's orbit:

#. If :math:`E < 0`, the orbit is elliptical.
#. If :math:`E = 0`, the orbit is parabolical.
#. If :math:`E > 0`, the orbit is hyperbolical.

**Links:**

#. `Physics LibreTexts <https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Dourmashkin)/25%3A_Celestial_Mechanics/25.03%3A_Energy_and_Angular_Momentum_Constants_of_the_Motion>`__.

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

.. py:data:: planetary_mass

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

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: radial_speed

    The projection of the velocity vector in the radial direction. See :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v_r`

Latex:
    :math:`v_{r}`

Dimension:
    :code:`velocity`


.. py:data:: potential_energy

    The :doc:`potential energy <laws.gravity.radial_motion.potential_energy_of_planetary_motion>` of the planet.
    See :attr:`~symplyphysics.symbols.classical_mechanics.potential_energy`.

Symbol:
    :code:`U`

Latex:
    :math:`U`

Dimension:
    :code:`energy`


.. py:data:: total_mechanical_energy

    Total :attr:`~symplyphysics.symbols.classical_mechanics.mechanical_energy` of the planet, assumed to be constant.

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`m * v_r^2 / 2 + U = E`


    Latex:
        .. math::
            \frac{m v_{r}^{2}}{2} + U = E