The Large and Small Magellanic clouds (LMC and SMC) are galaxies just outside the Milky Way, named after the explorer Magellan. These minor galaxies appear to be gravitationally bound to our Milky Way galaxy because they have left a trail of debris behind them, called the Magellanic stream, that curves around in a way that seems to show that they are orbiting our galaxy, see the schematic below:
However, as for almost every orbit on a cosmic scale (galaxy clusters, disc galaxies, dwarf galaxies, globular clusters, Proxima Centauri) the observed orbital velocity is so high that the orbiting mass should break free and zoom off to infinity. The observed orbital velocity of the LMC around the Milky Way is 378 km/s (Kallivayalil, 2013). If we assume Newtonian physics and that the Milky Way has only baryonic (normal) matter, this predicts an orbital speed v = sqrt(GM/r), where G is Newton's gravitational constant, M is the Milky Way's mass and r is the radial distance. This predicts that the maximum orbital velocity that the LMC can have without breaking away is 75 km/s. Oops. So, the LMC should have broken away, but the Magellanic stream suggests it hasn't.
If we assume the usual amount of dark matter in the galaxy, so boost the galactic mass by a factor of ten by adding an invisible and unexplained new kind of matter, then this predicts a maximum orbital velocity before breakaway of 237 km/s, so the LMC should still break away in contradiction to the Magellanic Stream.
MiHsC says that because of its low acceleration outside the galaxy, the LMC has lost some inertial mass and it predicts the following orbital speed, the second term being due to MiHsC:
v = sqrt(GM/r + 2c^2r/Theta)
where c is the speed of light and Theta is the Hubble scale. The MiHsC maximum speed for LMC boundedness is
v = 967 km/s
The observed orbital velocity of the LMC is 378 km/s, so from these examples you can see that MiHsC predicts that the LMC is bound to the Milky Way and is consistent with the observation of the Magellanic Stream that seems to show a bound past trajectory for it. Of course, you can mess around with dark matter arbitrarily till you get the answer you want, but that arbitrariness is deeply abhorrent.
Kallivayalil et al., 2013. http://arxiv.org/abs/1301.0832
McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophys. Space Sci., 342, 575-578. http://arxiv.org/abs/1207.7007