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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

When a test particle moves about an oblate spheroid, it is acted upon, amongother things, by two standard perturbing accelerations. One, of Newtonianorigin, is due to the quadrupole mass moment $J_2$ of the orbited body. Theother one, of the order of $\mathcal{O}\left(1/c^2\right)$, is caused by thestatic, post-Newtonian field arising solely from the mass of the centralobject. Both of them concur to induce \textrm{indirect}, \textrm{mixed} orbitaleffects of the order of $\mathcal{O}\left(J_2/c^2\right)$. They are of the sameorder of magnitude of the \textrm{direct} ones induced by the post-Newtonianacceleration arising in presence of an oblate source, not treated here. Wecalculate these less known features of motion in their full generality in termsof the osculating Keplerian orbital elements. Subtleties pertaining the correctcalculation of their mixed net \textrm{precessions} per orbit to the full orderof $\mathcal{O}\left(J_2/c^2\right)$ are elucidated. The obtained results holdfor arbitrary orbital geometries and for any orientation of the body's spinaxis $\mathbf{\hat{k}}$ in space. The method presented is completely general,and can be extended to any pair of post-Keplerian accelerations entering theequations of motion of the satellite, irrespectively of their physical nature.

general relativity and gravitation

The post-Newtonian motion around an oblate spheroid: the mixed orbital  effects due to the Newtonian oblateness and the post-Newtonian mass monopole  accelerations