Rocket thrust is rocket mass times acceleration
===============================================

Assuming we are at rest relative to an inertial reference frame, we observe a rocket
through space with no gravitational or atmospheric drag forces acting on it.
The mass of the rocket changes as it burns fuel and releases the products of burning,
the total mass of the system does not change.

**Conditions:**

#. The fuel consumption rate is constant.
#. The velocities are non-relativistic.

**Notes:**

#. The quantity :math:`R v_\text{rel}` is called the **thrust of rocket engine**.

    .. _rate_note:

#. The rate :math:`R` of fuel consumption is defined as
    .. math::

        R = - \frac{d m}{d t}

    where :math:`m` is the :ref:`rocket mass <rocket_mass_definition>`.

**Links:**

#. Equation 9-87 on p. 242 of "Fundamentals of Physics" by David Halladay et al., 10th Ed.

.. py:currentmodule:: symplyphysics.laws.dynamics.rocket_thrust_is_rocket_mass_times_acceleration

.. py:data:: fuel_consumption_rate

    The rate of fuel consumption, or :attr:`~symplyphysics.symbols.classical_mechanics.mass_flow_rate` of exhaust. See :ref:`Note <rate_note>`
    for the definition.

Symbol:
    :code:`R`

Latex:
    :math:`R`

Dimension:
    :code:`mass/time`


.. py:data:: relative_speed

    The :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the rocket relative to its products.

Symbol:
    :code:`v_rel`

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

Dimension:
    :code:`velocity`


.. py:data:: acceleration

    The :attr:`~symplyphysics.symbols.classical_mechanics.acceleration` of the rocket.

Symbol:
    :code:`a`

Latex:
    :math:`a`

Dimension:
    :code:`acceleration`


.. py:data:: mass

    .. _rocket_mass_definition:

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

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: law

    :code:`R * v_rel = m * a`


    Latex:
        .. math::
            R v_\text{rel} = m a