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*.
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