English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Since the original work of Hansen and Tisserand in the XIXth century, therehave been many variations in the analytical expansion of the three-bodydisturbing function in series of the semi-major axis ratio. With the increasingnumber of planetary systems of large eccentricity, these expansions are evenmore interesting as they allow us to obtain for the secular systems finiteexpressions that are valid for all eccentricities and inclinations. Werevisited the derivation of the disturbing function in Legendre polynomial,with a special focus on the secular system. We provide here expressions of thedisturbing function for the planar and spatial case at any order with respectto the ratio of the semi-major axes. Moreover, for orders in the ratio ofsemi-major axis up to ten in the planar case and five in the spatial case, weprovide explicit expansions of the secular system, and simple algorithms withminimal computation to extend this to higher order, as well as the algorithmsfor the computation of non secular terms.

Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations