  Direct imaging of extrasolar planets with future space-based coronagraphic
telescopes may provide a means of detecting companion moons at wavelengths
where the moon outshines the planet. We propose a detection strategy based on
the positional variation of the center of light with wavelength,
"spectroastrometry." This new application of this technique could be used to
detect an exomoon, to determine the exomoon's orbit and the mass of the host
exoplanet, and to disentangle of the spectra of the planet and moon. We
consider two model systems, for which we discuss the requirements for detection
of exomoons around nearby stars. We simulate the characterization of an
Earth-Moon analog system with spectroastrometry, showing that the orbit, the
planet mass, and the spectra of both bodies can be recovered. To enable the
detection and characterization of exomoons we recommend that coronagraphic
telescopes should extend in wavelength coverage to 3 micron, and should be
designed with spectroastrometric requirements in mind.
