The Impact of the External Field Effect in the MOdified Newtonian Dynamics on Solar System's Orbits

TL;DR

This study investigates how the External Field Effect in Modified Newtonian Dynamics influences the orbits of objects in the Solar System's distant regions, revealing significant deviations from classical predictions.

Contribution

It provides a detailed analysis of the EFE impact on Solar System orbits within the deep MOND regime using various interpolating functions and Galactic parameters.

Findings

EFE causes strong distortions of Newtonian elliptical orbits.

Orbital paths become more complex and less extended due to EFE.

Results depend on the Galactic velocity and interpolating function used.

Abstract

We looked at the orbital motions of test particles according to the External Field Effect (EFE) predicted by the MOdified Newtonian Dynamics (MOND) in the Oort cloud which falls in the deep MONDian regime (r\approx 50-150 kAU). Concerning the interpolating function \mu(x), we extensively used the forms \mu_1=1/(1+x),\mu_2=x/(1+x^2)^1/2,\mu_3/2=x/(1+x^3/2)^2/3. We integrated both the MOND and the Newtonian equations of motion in Cartesian coordinates sharing the same initial conditions. We considered both ecliptic and nearly polar trajectories, all with high eccentricities (e>0.1). In order to evaluate the characteristic MOND parameters \mu_g and L_g entering the problem, we used two different values (V=220 km s^-1 and V=254 km s^-1) of the circular speed of the solar system's motion through the Galaxy; $V$ allows to evaluate the Milky Way's gravitational field at the Sun's location. It turns out that EFE induces strong distortions of the Newtonian ellipses, especially in the ecliptic plane yielding more involved paths which span less extended spatial regions.