Solar System model.
•The Solar system is a familiar model and a useful test
bed for evaluating integrators.
•The eccentricity for Mercury is sufficient to produce
improvements in efficiency of around
1.8 when using a variable stepsize method based on the Sun-Mercury distance. The function used was,
•The MO method lends itself to this model as a second
order approximation to the re-parameterisation
is sufficiently accurate. A graph of the efficiency of the method compared to the fixed step method is given below.
•Simulations of over 1 Billion years
have been done with this
method.
•The Hamiltonian equation used, where
mi is the mass of
the ith planet and G is
the gravitational
constant is,
