The expansion separates naturally into three timescales:

* A <short-period orbital perturbation> contains rapidly varying <mean longitudes>. It describes individual conjunction kicks and usually averages to zero away from a commensurability.
* A <resonant orbital perturbation> has a nearly stationary integer combination of mean longitudes near a <mean-motion resonance>. Successive conjunctions then occur at correlated phases, so their effects accumulate and the <resonant argument> may librate.
* A <secular perturbation> survives averaging over both mean longitudes. It drives slow <apsidal precession>, <nodal precession>, and exchange of <orbital eccentricity> or <orbital inclination> over many orbital periods.

Short-period terms matter for instantaneous osculating elements and encounters, resonant terms near period commensurabilities, and secular terms for long-term evolution away from strong resonance.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 316 / 4 / iii / Solution

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Apsidal precession is the gradual rotation of an orbit's line of apsides, equivalently a change in its <longitude of periapsis>.

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 Incoming links: Apsidal precession