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

This paper investigates the coplanar and circular three-body problem in theparametrized post-Newtonian (PPN) formalism, for which we focus on a class offully conservative theories characterized by the Eddington-Robertson parameters$\beta$ and $\gamma$. It is shown that there can still exist a collinearequilibrium configuration and a triangular one, each of which is ageneralization of the post-Newtonian equilibrium configuration in generalrelativity. The collinear configuration can exist for arbitrary mass ratio,$\beta$, and $\gamma$. On the other hand, the PPN triangular configurationdepends on the nonlinearity parameter $\beta$ but not on $\gamma$. For anyvalue of $\beta$, the equilateral configuration is possible, if and only ifthree finite masses are equal or two test masses orbit around one finite mass.For general mass cases, the PPN triangle is not equilateral as in thepost-Newtonian case. It is shown also that the PPN displacements from theLagrange points in the Newtonian gravity $L_1$, $L_2$ and $L_3$ depend on$\beta$ and $\gamma$, whereas those to $L_4$ and $L_5$ rely only on $\beta$.

Collinear and triangular solutions to the coplanar and circular three-body problem in the parametrized post-Newtonian formalism