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/

Zendy Plus

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

Zendy Tools

Zendy Open

Embedding diagrams prove to be quite useful when learning general relativityas they offer a way of visualizing spacetime curvature through warped twodimensional (2D) surfaces. In this manuscript we present a different 2Dconstruct that also serves as a useful conceptual tool for gaining insight intogravitation, in particular, orbital dynamics - namely the cylindricallysymmetric surfaces that generate Newtonian and general relativistic orbits withsmall eccentricities. Although we first show that no such surface exists thatcan exactly reproduce the arbitrary bound orbits of Newtonian gravitation or ofgeneral relativity (or, more generally, of any spherically symmetricpotential), surfaces do exist that closely approximate the resulting orbitalmotion for small eccentricities; exactly the regime that describes the motionof the solar system planets. These surfaces help to illustrate thesimilarities, as well as the differences, between the two theories ofgravitation (i.e. stationary elliptical orbits in Newtonian gravitation andprecessing elliptical-like orbits in general relativity) and offer, in this ageof 3D printing, an opportunity for students and instructors to experimentallyexplore the predictions made by each.

The 2D surfaces that generate Newtonian and general relativistic orbits with small eccentricities