Elliptical-like orbits on a warped spandex fabric: A theoretical/experimental undergraduate research project

TL;DR

This paper combines theoretical and experimental approaches to analyze elliptical-like orbits of a marble on a warped spandex fabric, revealing how the angular separation varies with surface slope and central mass, and comparing to relativistic orbits.

Contribution

It provides a novel analytical expression for orbital angular separation on a warped fabric, validated through experiments, and draws parallels with general relativity.

Findings

Minimal angular separation of ~197 degrees without central mass.

Angular separation exceeds 360 degrees with large central mass.

Theoretical predictions align with experimental results.

Abstract

We present a theoretical and experimental analysis of the elliptical-like orbits of a marble rolling on a warped spandex fabric. We arrive at an expression describing the angular separation between successive apocenters, or equivalently successive pericenters, in both the small and large slope regimes. We find that a minimal angular separation of approximately 197 degrees is predicted for orbits with small radial distances when the surface is void of a central mass. We then show that for small radii and large central masses, when the orbiting marble is deep within the well, the angular separation between successive apocenters transitions to values greater than 360 degrees. We lastly compare these expressions to those describing elliptical-like orbits about a static, spherically symmetric massive object in the presence of a constant vacuum energy, as described by general relativity.