Testing quasilinear modified Newtonian dynamics in the Solar System

Abstract

A unique signature of the modified Newtonian dynamics (MOND) paradigm is its peculiar behavior in the vicinity of the points where the total Newtonian acceleration exactly cancels. In the Solar System, these are the saddle points of the gravitational potential near the planets. Typically, such points are embedded into low-acceleration bubbles where modified gravity theoriesà la MOND predict significant deviations from Newton's laws. As has been pointed out recently, the Earth-Sun bubble may be visited by the LISA Pathfinder spacecraft in the near future, providing a unique occasion to put these theories to a direct test. In this work, we present a high-precision model of the Solar System's gravitational potential to determine accurate positions and motions of these saddle points and study the predicted dynamical anomalies within the framework of quasi-linear MOND. Considering the expected sensitivity of the LISA Pathfinder probe, we argue that interpolation functions which exhibit a "faster" transition between the two dynamical regimes have a good chance of surviving a null result. An example of such a function is the QMOND analog of the so-called simple interpolating function which agrees well with much of the extragalactic phenomenology. We have also discovered that several of Saturn's outermost satellites periodically intersect the SaturnSun bubble, providing the first example of Solar System objects that regularly undergo the MOND regime.PACS numbers: 98.10.+z, 95.35.+d, 98.62.Dm, 95.30.Sf

Reconciliation of modified Newtonian dynamics and dark matter theory

“…Therefore, the apparent sucess of MOND may be just a coincidence. However, apart from the context of dark matter, MOND also predicts that some strange effects may be observable in the Solar system [47]. For example, around each equinox date, 2 spots emerge on the Earth where static bodies experience spontneous acceleration due to the possible violation of Newton's second law [48].…”

Tests of modified gravity theories in the Solar System

“…Their complexity and differences arise from the requirement that they should explain relativistic phenomena (such as lensing and structure formation) without appealing to dark matter, whilst in the nonrelativistic regime have some Newtonian and other modified limit. The manner in which such effects are manifest may however vary widely and there have been many previous studies as to the phenomenology of these ideas, particularly in this non-relativistic regime [7,9,35,40,41]. We will briefly outline some of these here, with the caveat that this list is neither exhaustive, nor represents the final story on gravity theories at the time of writing and for a more in depth look at gravity theories, we point the reader towards [18].…”

“…We will only consider type IIB theories here, the IIA case has been considered separately [40], which suggested such theories represent poor targets for an LPF test. In these theories, we have the driven Poisson equation…”

Lunar System Constraints on the Modified Theories of Gravity

“…Ref. [12] reports that the size of MOND window at the gravitational saddle points of the Moon and the Earth is about few centimeters. However, identifying the exact time and place of the Earth-Moon system requires taking into account the higher gravitational moments of the Earth and Moon [13,14].…”