Celestial dynamics
--------------------

    * **Topic:** dynamics, conservation laws 
    * **Task A:** 
        1. Run the simulation (a planet orbiting a star) using the Euler algorithm.
           Study the trajectory. Is the orbit stable? 
           Does changing the time step :math:`\Delta t` affect this?
        2. Study the momentum and energy during the run. Are they conserved?
    * **Task B:** 
        1. Implement the leapforg or standard velocity Verlet algorithm.
        2. Run the simulation with Verlet using different :math:`\Delta t`.
           Compare the results to Euler.
    * **Template:** `dynamics.py <http://users.utu.fi/tejohy/teaching/simu/templates/dynamics.py>`_
    * **Data:** `orbit.txt <http://users.utu.fi/tejohy/teaching/simu/templates/orbit.txt>`_
    * **Further reading:** 
        - https://en.wikipedia.org/wiki/Verlet_integration
        - https://en.wikipedia.org/wiki/Leapfrog_integration
        - https://en.wikipedia.org/wiki/Molecular_dynamics


dynamics.py
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.. automodule:: dynamics
    :members:
    :undoc-members: