  Recent studies have shown that velocity differences of very wide binary
stars, measured to high precision with GAIA, can provide an interesting test
for modified-gravity theories which emulate dark matter; in essence, MOND-like
theories (with external field effect included) predict that wide binaries
(wider than ~ 7 kAU) should orbit ~ 15% faster than Newtonian for similar
orbits; such a shift is readily detectable in principle in the sample of 9,000
candidate systems selected from GAIA EDR3 by Pittordis and Sutherland (2022;
PS22). However, the main obstacle at present is the observed "fat tail" of
candidate wide-binary systems with velocity differences at ~1.5 - 6x circular
velocity; this tail cannot be bound pure binary systems, but a possible
explanation of the tail is triple or quadruple systems with unresolved or
undetected additional star(s). While this tail can be modelled and
statistically subtracted, obtaining an accurate model for the triple population
is crucial for a robust test for modified gravity. In this paper we explore
prospects for observationally constraining the triple population: we simulate a
population of hierarchical triple systems "observed" as in PS22 at random
epochs and viewing angles; for each simulated system we evaluate various
possible methods for detecting the third star, including GAIA astrometry,
radial velocity drift, and several imaging methods from direct Rubin images,
speckle imaging and coronagraphic imaging. Results are generally encouraging,
in that typically 90% of the triple systems in the key regions of parameter
space are detectable; there is a moderate "dead zone" of cool brown-dwarf
companions at ~ 25-100 AU separation which are not detectable with any of our
baseline methods. A large but feasible observing campaign can greatly clarify
the effect of the triple/quadruple population and make the gravity test
decisive.
