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 \leq t \leq 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 center of the Milky Way ( MW ) , they are ideal candidates to investigate the deep MOND regime occurring when the characteristic MOND acceleration A _ { 0 } = 1.2 \times 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 also the External Field Effect ( EFE ) A _ { ext } must , in principle , be considered .
Since for MW A _ { ext } \approx 0.01 A _ { 0 } , with a lingering uncertainty , we consider both the cases A _ { ext } \ll A _ { N } ,A _ { ext } \ll A _ { 0 } and A _ { ext } = A _ { N } ,A _ { ext } \ll 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 modeling 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 .