Eur. Phys. J. C (2018) 78: 843
https://doi.org/10.1140/epjc/s10052-018-6341-8

Regular Article - Theoretical Physics

Non-geodesic circular motion of massive spinning test bodies around a Schwarzschild field in the Lagrangian theory

¹ Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Santiago, Chile
² Centro de Investigación en Matemáticas, A.C, Unidad Mérida, Mérida, Yuc, Mexico
³ Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
⁴ Centro de Recursos Educativos Avanzados, CREA, Santiago, Chile
⁵ Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile

^* e-mail: felipe.asenjo@uai.cl

Received: 13 July 2018
Accepted: 12 October 2018
Published online: 20 October 2018

Abstract

Recent interest on studying possible violations of the Equivalence Principle has led to the development of space satellite missions testing it for bodies moving on circular orbits around Earth. This experiment establishes that the validity of the equivalence principle is independent of the composition of bodies. However, the internal degrees of freedom of the bodies (such as spin) were not taken into account. In this work, it is shown exactly that the circular orbit motion of test bodies does present a departure from geodesic motion when spin effects are not negligible. Using a Lagrangian theory for spinning massive bodies, an exact solution for their circular motion is found showing that the non-geodesic behavior manifests through different tangential velocities of the test bodies, depending on the orientation of its spin with respect to the total angular momentum of the satellite. Besides, for circular orbits, spinning test bodies present no tangential acceleration. We estimate the difference of the two possible tangential velocities for the case of circular motion of spinning test bodies orbiting Earth.