Celestial mechanics with the celmech code

I will introduce “celmech”, a new publicly available open-source python package for performing celestial mechanics calculations by constructing, manipulating, and integrating perturbative models for planetary systems’ dynamics. While direct numerical integrations with modern computers have largely replaced the need for highly precise perturbative calculations, classical perturbation theory still plays an important role in modern planetary dynamics by providing simplified models for a variety of complex phenomena including mean motion resonances, secular evolution, and dynamical chaos. Classical perturbation theories in planetary dynamics can be elegantly formulated using a Hamiltonian framework, but non-experts (and experts alike) can quickly get mired in the complexities of computing disturbing function expansions and Laplace coefficients. The celmech code automatically computes and evaluates disturbing function coefficients, allowing users to quickly and easily construct Hamiltonian models by adding disturbing function terms with any desired cosine arguments. The code also interfaces closely with the popular REBOUND N-body integrator so that users can easily compare perturbative models against direct N-body integrations. I will give an overview of the code and highlight some example applications. The code can be downloaded at github.com/shadden/celmech.