Galactic orbital motions in the dark matter, modified Newtonian dynamics and modified gravity scenarios

We simultaneously integrate in a numerical way the equations of motion of both the Magellanic Clouds (MCs) in the MOdified Newtonian Dynamics (MOND), MOdified Gravity (MOG) and cold dark matter (CDM) frameworks for -1 <= t <= 1 Gyr in order to see if, at least in principle, it is possible to discriminate between them. Since the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) are at distances of approximately 50-60 kpc from the centre of the Milky Way ( MW), they are ideal candidates for investigating the deep MOND regime occurring when the characteristic MOND acceleration A(0) = 1.2 x 10(-10) m s(-2) is larger than the internal acceleration A of the system considered; indeed, the Newtonian baryonic accelerations A(N) involved are about 0.02-0.03 A(0) for them. It turns out that CDM, MOND and MOG yield, in fact, different trajectories. In MOND the external field effect A(ext) must, in principle, also be considered. Since for the MW A(ext) approximate to 0.01 A(0), with a lingering uncertainty, we consider both the cases A(ext) < A(N), A(ext) << A(0) and A(ext) = A(N), A(ext) << A(0). We also investigate the impact of the current uncertainties in the velocity components of MCs on their motions in the theories considered. In modelling the mutual interaction between the clouds and the dynamical friction ( in CDM and MOND) we use for the masses of MCs the total (baryonic + dark matter) values, dynamically inferred, in CDM, and the smaller ones ( baryonic), coming from direct detection of visible stars and neutral gas, in MOND and MOG.