===========
Formalities
===========

The projects should be performed 
by the same groups handing in the
exercises.

The results of the project should
be handed in as files
- A pdf-report of maximal 10 pages containing 
  an introduction to the subject and to the 
  numerical methods used, a description of the 
  programming effort (structure, and important, nontrivial 
  code snippets, but not all the code), and the presentation
  of the results. For the presentation of the
  results we expect both figures of simulated data
  and a stastitical evaluation of any
  reasonable property that you choose.
- The documented code
- Additional media files (optional) referred-to
  in the report. Hint: you can also generate 
  gif files from series of images to visualize 
  the dynamics.

The date to hand-in is: Januar 13, 2017.

=======
Remarks
=======

(a) Do NOT use any other libraries or sample
codes except for those used and presented in the
lecture or the lecture script. We expect you to
write the code simple and efficient on your own.

(b) For all projects that involve simulation of a
planetary system, assume that the planets move on
circles (instead of elipses), and that all planets are
in one plane (to make it a two dimensional problem).

(c) In order to check the validity of your calculation,
track the momentum, angular momentum and energy of the
whole system simulated and compare it to analytic
results (conservation laws) where possible. (This is 
not neccessary for Project (B) -- Roche stability)

(d) Consider rescaling the important quantities, e.g. 
masses by the mass of Jupiter or distances by astronomic
units (only where applicable and reasonable).

(e) Assume all objects for which the spacial extension
is not a property of interest as point masses.
But mind to include a realisitic object radius for the
gravitational potential.


========
Projects
========

Here a list of proposals involving the numerical 
simulation, f.i. by Runge-Kutta, of planetary 
dynamical systems (Newton mechanics).
Additionally, everybody is welcome to propose 
their own project to their tutor from the field 
of celestrial mechanics.

(A) Two colliding solar systems
-------------------------------

Extract the orbital parameters of one or more
multi-planetary extrasolar systems. Simulate
the collision of an extrasolar and the solar system. 
Consider initial conditions for which both
suns pass within a finite but close distance.
What happens?

(B) Roche instability
---------------------

Form a gravitational bound asteroid out of
N (~100) rocks. For this consider initially
an additional (to the Newton equations of
motions) damping term poportional to the
negative speed, and a short-distance
repulsion. The overall mass and density
should correspond to a real asteroid.

Once the asteroid is formed, let it pass
close to a planet, like Earth or Jupiter.
What happens, if the the asteroid passes
within the Roche radius?

(C) Saturn rings
----------------

Throw a large number of small objects into
random orbits around Saturn. See, whether 
they tend to self-organize into rings. You
may add a shepherd moon.

(D) Double stars
----------------

Consider the stability of exoplanets
around double stars. Are slingshot orbits
involving both stars possible? If yes, find 
one and examine the stability of their trajectory.

(E) Hill instability
--------------------

Simulate a known exoplanetary system. Put
an additional Jupiter-size planet close to
one of the exoplanets. When does the orbit of the
exoplanet become unstable?
Find the analytic estimate and compare it
to your result.

(F) Solar system with motion of the Sun
---------------------------------------

Simulate the solar system with all planets
and the Sun, using exact parameters
(mass, distance to Sun, etc.).
Does the motion of the planets influence the
position of the Sun?

(G) Slingshot to Jupiter
-------------------------

Simulate the journey of a space orbiter from
Earth to Jupiter on a slingshot trajectory
via Venus and Mars.
Therefore implement the planets and try to find
such a trajectory by sampling over different
initial conditions (i.e. positions of the planets
and speed/direction of the orbiter).