Constraints on a MOND effect for isolated aspherical systems in deep Newtonian regime from orbital motions

Understand

Non-spherical systems described by MOND theories of modified gravity arising from generalizations of the Poisson equations are affected by a MONDian extra-quadrupolar potential \phi_M even if they are isolated and they are in deep Newtonian regime.

• In general MOND theories quickly approaching Newtonian dynamics for accelerations beyond A_0, \phi_M is proportional to a multiplicative scaling coefficient \alpha \sim 1, while in MOND models becoming Newtonian beyond \kappa A_0, \kappa >> 1, it is enhanced by \kappa^2.
• We analytically work out some orbital effects due to \phi_M in the framework of QUMOND, and compare them with the latest observational determinations of Solar System's planetary dynamics, exoplanets and double lined spectroscopic binary stars.
• The current admissible range for the anomalous perihelion precession of Saturn yields |\kappa| <= 3.5 x 10^3, while the radial velocity of \alpha Cen AB allows to infer |\kappa|<= 6.2 x 10^4 (A) and |\kappa|<= 4.2 x 10^4 (B).