Planet period squared is proportional to cube of semimajor axis
===============================================================

Also known as **Kepler's third law** of planetary motion, the law of periods relates
the period of rotation of any planet to the semi-major axis of its orbit.

**Links:**

#. `Physics LibreTexts. Kepler's Third Law, Derivation of Kepler's Third Law (5.6.23) <https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/5%3A_Uniform_Circular_Motion_and_Gravitation/5.6%3A_Keplers_Laws>`__.

.. py:currentmodule:: symplyphysics.laws.gravity.planet_period_squared_is_proportional_to_cube_of_semimajor_axis

.. py:data:: rotation_period

    The planet's :attr:`~symplyphysics.symbols.basic.period` of rotation.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`time`


.. py:data:: attracting_mass

    :attr:`~symplyphysics.symbols.basic.mass` of the attracting body, e.g. the Sun in case of the solar system.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: semimajor_axis

    :attr:`~symplyphysics.symbols.classical_mechanics.semimajor_axis` of the planet's orbit. It is equal to the :attr:`~symplyphysics.symbols.classical_mechanics.radius` in case of
    a round orbit.

Symbol:
    :code:`a`

Latex:
    :math:`a`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`T^2 = 4 * pi^2 / (G * m) * a^3`


    Latex:
        .. math::
            T^{2} = \frac{4 \pi^{2}}{G m} a^{3}