CMMSE: Study of a new symmetric anomaly in the elliptic, hyperbolic and parabolic Keplerian motion

In the present work, we define a new anomaly, $\Psi$, termed semifocal anomaly. It is determined by the mean between the true anomaly, $f$, and the antifocal anomaly, $f^{\prime}$; Fukushima defined $f^{\prime}$ as the angle between the periapsis and the secondary around the empty focus. In this first part of the paper, we take an approach to the study of the semifocal anomaly in the hyperbolic motion and in the limit case correspoding to the parabolic movement. From here we find a relation beetween the semifocal anomaly and the true anomaly that holds independently of the movement type. We focus on the study of the two-body problem when this new anomaly is used as the temporal variable.\\ In the second part, we show the use of this anomaly —combined with numerical integration methods— to improve integration errors in one revolution. Finally, we analyze the errors committed in the integration process —depending on several values of the eccentricity— for the elliptic, parabolic and hyperbolic cases in the apsidal region.

Force, metric, or mass: Disambiguating causes of uniform gravity

In addition to nonzero forces and nontrivial metrics, here I show that a nonconstant Higgs expectation value, which endows elementary particles with their masses, also leads to apparent universal particle accelerations and photon frequency shifts. When effects of the Higgs is attributed to spacetime curvatures, a spurious stress-energy tensor is required in Einstein’s equation. On cosmological scales, the spurious density coincides with the observed dark energy density. On smaller scales, effects of the Standard Model Higgs gradients are unlikely observable except near compact astrophysical bodies. To estimate the experimental precision required to disambiguate causes of apparent accelerations, I compare distinct effects of the force, metric, and Higgs profiles that cause uniform acceleration of a test particle. When the acceleration is caused by a force, the motion of all particles are hyperbolic with the same acceleration. However, when the cause is a metric, only a one-parameter family of particles undergo hyperbolic motion. In comparison, when the cause is a Higgs gradient, the trajectory of all particles are hyperbolic, but the acceleration is larger when the particle’s energy is higher. The discrepancies among the three causes are minuscule on laboratory scales, which makes experimental tests very challenging.