Impact of a Pioneer/Rindler-type acceleration on the Oort cloud

TL;DR

This study examines how a Rindler-type acceleration affects Oort cloud objects, revealing significant orbital alterations that challenge the standard understanding of the cloud's stability and dynamics.

Contribution

It provides the first detailed analysis of Rindler-type acceleration effects on Oort cloud comets, highlighting radical orbital changes and implications for the cloud's structure.

Findings

Positive A_Rin leads to unbound orbits.

Negative A_Rin causes reduced distances and high-frequency oscillations.

Orbital patterns become more isotropic under Rindler acceleration.

Abstract

According to a recent modified model of gravity at large distances, a radial constant and uniform extra-acceleration A_Rin of Rindler type acts upon a test particle p in the static field of a central mass M if certain conditions are satisfied. Among other things, it was proposed as a potentially viable explanation of a part of the Pioneer anomaly. We study the impact that an anomalous Rindler-type term as large as |A_Rin| \sim 10^-10 m s^-2 may have on the the orbital dynamics of a typical object of the Oort cloud whose self-energy is quite smaller than its putative Rindler energy. By taking a typical comet moving along a highly eccentric and inclined orbit throughout the expected entire extension of the Oort cloud (0.02 pc-1 pc), it turns out that the addition of an outward Rindler-like acceleration, i.e. for A_Rin > 0, does not allow bound orbits. Instead, if A_Rin < 0, the resulting numerically integrated trajectory is limited in space, but it radically differs from the standard Keplerian ellipse. In particular, the heliocentric distance of the comet gets markedly reduced and experiences high frequency oscillations, its speed is increased, and the overall pattern of the trajectory is quite isotropic. As a consequence, the standard picture of the Oort cloud is radically altered since its modified orbits are much less sensitive to the disturbing actions of the Galactic tide and nearby passing stars whose effects, in the standard scenario, are responsible for the phenomenology on which our confidence in the existence of the cloud itself is based. The present analysis may be supplemented in future by further statistical Monte Carlo-type investigations by randomly varying the initial conditions of the comets.