Heterogeneous multiscale methods for orbital dynamics

The Heterogeneous Multiscale Method (HMM) is a general framework to deal with problems having multiple scales (in time or in a space). In the context of oscillatory ordinary differential equations with disparate timescales, the HMM scheme exploits the scale separation to build an approximate, on the fly, of an effective system. The effective system obtained by a mollification, supposed to encapsulate the essential degree of freedom, can then be integrated numerically at a cheaper cost. In this contribution, after reviewing the components of the averaging theory and the formalism of the HHM scheme, we deploy it towards the deterministic equations of Earth satellites. This scheme could inspire the design of a single, monolithic and hierarchical orbital integrator suited for short or longer arc computations.