  The works in this portfolio test the hypothesis that it is not possible to
extrapolate the Newtonian inverse square law of gravity from Solar System to
galaxy scales. In particular, I look into various tests of Modified Newtonian
Dynamics (MOND), which posits a modification below a very low acceleration
threshold. Although discrepancies with Newtonian dynamics are indeed observed,
they can usually be explained by invoking an appropriate distribution of
invisible mass known as dark matter (DM). This leads to the standard
cosmological paradigm, $\Lambda$CDM. I consider how it may be distinguished
from MOND using collision velocities of galaxy clusters, which should sometimes
be much faster in MOND. I focus on measuring these velocities more accurately
and conclude that this test ought to be feasible in the near future.
  For the time being, I look at the much nearer and more accurately observed
Local Group (LG) of galaxies. Its main constituents $-$ the Milky Way (MW) and
Andromeda (M31) $-$ should have undergone a past close flyby in MOND but not in
$\Lambda$CDM. The fast MW-M31 relative motion around the time of their flyby
would have allowed them to gravitationally slingshot any passing LG dwarf
galaxies out at high speed. I consider whether there is any evidence for such
high-velocity galaxies (HVGs). Several candidates are found in two different
$\Lambda$CDM models of the LG, one written by a founding figure of the
paradigm. The properties of these HVGs are similar to what might be expected in
MOND, especially their tendency to lie close to a plane. Being more confident
of its validity, I then used MOND to determine the escape velocity curve of the
MW over the distance range 8$-$50 kpc, finding reasonable agreement with the
latest observations. I finish by discussing possible future directions for MOND
research.
