Relative rocket speed from mass change and effective exhaust speed
==================================================================

The Tsiolkovsky formula determines the speed that an aircraft develops due to the
constant-direction thrust of the rocket engine in the absence of other forces. The generalized
Tsiolkovsky formula is valid for a rocket flying at a speed close to the speed of light.

**Notation:**

#. :math:`c` (:code:`c`) is :attr:`~symplyphysics.quantities.speed_of_light`.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation#Special_relativity>`__.

.. py:currentmodule:: symplyphysics.laws.astronomy.relativistic.relative_rocket_speed_from_mass_change_and_effective_exhaust_speed

.. py:data:: speed

    Final :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the rocket in the inertial reference frame where the rocket started at
    rest.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: effective_exhaust_speed

    Effective exhaust :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the rocket engine.

Symbol:
    :code:`v_e`

Latex:
    :math:`v_\text{e}`

Dimension:
    :code:`velocity`


.. py:data:: initial_mass

    Initial :attr:`~symplyphysics.symbols.basic.mass` of the rocket.

Symbol:
    :code:`m_0`

Latex:
    :math:`m_{0}`

Dimension:
    :code:`mass`


.. py:data:: final_mass

    Final :attr:`~symplyphysics.symbols.basic.mass` of the rocket.

Symbol:
    :code:`m_1`

Latex:
    :math:`m_{1}`

Dimension:
    :code:`mass`


.. py:data:: law

    :code:`m_1 / m_0 = ((1 - v / c) / (1 + v / c))^(c / (2 * v_e))`


    Latex:
        .. math::
            \frac{m_{1}}{m_{0}} = \left(\frac{1 - \frac{v}{c}}{1 + \frac{v}{c}}\right)^{\frac{c}{2 v_\text{e}}}