  The concept of a new space very long baseline interferometry system named the
Event Horizon Imager (EHI) has been proposed to dramatically improve black hole
imaging and provide precise tests of the theory of general relativity. We
investigate the ability to make high-resolution movies of the black hole shadow
and jet launching region around the supermassive black hole M87* and other
black hole jets with a three-satellite EHI configuration. We aim to identify
orbital configurations to optimize the uv-coverage to image variable sources.
Observations of general relativistic magnetohydrodynamics models were simulated
for the configuration, consisting of three satellites in circular medium earth
orbits with an orbital plane perpendicular to the line of sight. The expected
noise was based on preliminary system parameters. Movie frames, for which a
part of the uv-coverage may be excessively sparse, were reconstructed with
algorithms that recover missing information from other frames. Averaging
visibilities accumulated over multiple epochs of observations with an
appropriate orbital configuration then improves the image quality. With an
enhanced signal-to-noise ratio (S/N), timescales of observed variability were
decreased. Our simulations show that the EHI with standard system parameters is
capable of imaging the variability in the M87* environment on event horizon
scales with approximately a month-long temporal resolution. The EHI with more
optimistic noise parameters (enhancing S/N about 100-fold) would allow for
imaging of the variability on gravitational timescales. Observations with an
EHI setup at lower frequencies are capable of imaging the variability in
extended jets. The EHI concept can be used to image the variability in a black
hole environment and extended jets, allowing for stronger tests of gravity
theories and models of black hole accretion, plasma dynamics, and jet
launching.
