  The Event Horizon Telescope (EHT) has imaged the shadow of the supermassive
black hole in M87. A library of general relativistic magnetohydrodynamics
(GMRHD) models was fit to the observational data, providing constraints on
black hole parameters. We investigate how much better future experiments can
realistically constrain these parameters and test theories of gravity. We
generate realistic synthetic 230 GHz data from representative input models
taken from a GRMHD image library for M87, using the 2017, 2021, and an expanded
EHT array. The synthetic data are run through a data reduction pipeline used by
the EHT. Additionally, we simulate observations at 230, 557, and 690 GHz with
the Event Horizon Imager (EHI) Space VLBI concept. Using one of the EHT
parameter estimation pipelines, we fit the GRMHD library images to the
synthetic data and investigate how the black hole parameter estimations are
affected by different arrays and repeated observations. Repeated observations
play an important role in constraining black hole and accretion parameters as
the varying source structure is averaged out. A modest expansion of the EHT
already leads to stronger parameter constraints. High-frequency observations
from space rule out all but ~15% of the GRMHD models in our library, strongly
constraining the magnetic flux and black hole spin. The 1$\sigma$ constraints
on the black hole mass improve by a factor of five with repeated high-frequency
space array observations as compared to observations with the current ground
array. If the black hole spin, magnetization, and electron temperature
distribution can be independently constrained, the shadow size for a given
black hole mass can be tested to ~0.5% with the EHI, which allows tests of
deviations from general relativity. High-precision tests of the Kerr metric
become within reach from observations of the Galactic Center black hole
Sagittarius A*.
