  It has been proposed that Very Long Baseline Interferometry (VLBI) at
sub-millimeter waves will allow us to image the shadow of the black hole in the
center of our Milky Way, Sagittarius A* (Sgr A*), and thereby test basic
predictions of general relativity. This paper presents imaging simulations of a
new Space VLBI mission concept. An initial design study of the concept has been
presented as the Event Horizon Imager (EHI). The EHI may be suitable for
imaging Sgr A* at high frequencies (up to ~690 GHz), which has significant
advantages over performing ground-based VLBI at 230 GHz. The concept EHI design
consists of two or three satellites in polar or equatorial circular
Medium-Earth Orbits with slightly different radii. Due to the relative drift of
the satellites along the individual orbits, this setup will result in a dense
spiral-shaped uv-coverage with long baselines (up to ~60 Glambda), allowing for
extremely high-resolution and high-fidelity imaging of radio sources. We
simulate EHI observations of general relativistic magnetohydrodynamics models
of Sgr A* and calculate the expected noise based on preliminary system
parameters. On long baselines, where the signal-to-noise ratio may be low,
fringes could be detected if the system is sufficiently phase stable and the
satellite orbits can be reconstructed with sufficient accuracy. Averaging
visibilities accumulated over multiple epochs of observations could then help
improving the image quality. With three satellites, closure phases could be
used for imaging. Our simulations show that the EHI could be capable of imaging
the black hole shadow of Sgr A* with a resolution of 4 uas (about 8% of the
shadow diameter) within several months of observing time. The EHI concept could
thus be used to measure black hole shadows much more precisely than with
ground-based VLBI, allowing for stronger tests of general relativity and
accretion models.
