  We perform Monte Carlo simulations of cosmic ray-induced hard X-ray radiation
from the Earth's atmosphere. We find that the shape of the spectrum emergent
from the atmosphere in the energy range 25-300 keV is mainly determined by
Compton scatterings and photoabsorption, and is almost insensitive to the
incident cosmic-ray spectrum. We provide a fitting formula for the hard X-ray
surface brightness of the atmosphere as would be measured by a satellite-born
instrument, as a function of energy, solar modulation level, geomagnetic cutoff
rigidity and zenith angle. A recent measurement by the INTEGRAL observatory of
the atmospheric hard X-ray flux during the occultation of the cosmic X-ray
background by the Earth agrees with our prediction within 10%. This suggests
that Earth observations could be used for in-orbit calibration of future hard
X-ray telescopes. We also demonstrate that the hard X-ray spectra generated by
cosmic rays in the crusts of the Moon, Mars and Mercury should be significantly
different from that emitted by the Earth's atmosphere.
