chosing a CAS



I cannot afford the price of Mathematica for my hobby, even les as an
European customer (3185€ vs 2495$).
I am interrested in celestial mechanics and want to develop
perturbation calculations using Lagrange or Poisson brackets.
As a hobbyist, I also don't have too much time to develop the basis
for such calculations fully by myself.
I would prefer to re-use some existing package.

Therefore, I would like to know which free (or cheap) CAS software
would offer me the fastest way to start on my celestial mechanics
calculations.

Thanks
.



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