Radius of planetary orbits from number
======================================

The Titius—Bode rule is an empirical formula that roughly describes the distances between the planets of the
Solar System and the Sun (the average radii of the orbits).

**Notes:**

#. This rule fails to predict the correct value of the Neptune's orbit radius.

**Links:**

#. `Wikipedia, third formula <https://en.wikipedia.org/wiki/Titius%E2%80%93Bode_law#Original_formulation>`__.

.. py:currentmodule:: symplyphysics.laws.astronomy.radius_of_planets_orbit_from_its_number

.. py:data:: orbit_radius

    :attr:`~symplyphysics.symbols.classical_mechanics.radius` of the planet's orbit.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: planet_number

    The value :math:`-\infty` corresponts to Mercury, :math:`0` to Venus, :math:`1` to
    Earth, :math:`2` to Mars, :math:`3` to Ceres, :math:`4` to Jupyter, :math:`5` to Saturn,
    :math:`6` to Uranus, and :math:`7` to Pluto.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: first_constant

    A quantity which is the free term in the formula.

Symbol:
    :code:`a`

Latex:
    :math:`a`

Dimension:
    :code:`length`


.. py:data:: second_constant

    A quantity which is the factor before the exponent.

Symbol:
    :code:`b`

Latex:
    :math:`b`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`r = a + b * 2^N`


    Latex:
        .. math::
            r = a + b 2^{N}