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We explore the feasibility of Auger electron spectroscopy as a remote sensing technique to map the composition of the sunlit surfaces of planetary bodies without atmospheres. Solar x rays eject photoelectrons from the planetary surface. The resulting ions relax by emission of fluorescence x rays or Auger electrons, with energies characteristic of the element which is ionized. The spectrum of Auger electrons and photoelectrons is computed for a variety of elements and for representative lunar rock types illuminated by soft x‐ray line and continuum emission typical of solar long‐lived coronal active regions. The Auger electron lines for O, Si, Mg, Al, Fe, and Ca in lunar rocks stand well above the continuum background from photoelectrons and backscattered interplanetary electrons, with typical line‐to‐continuum ratios of ∼20 to ≳103. An ideal Auger electron spectroscopy instrument to map the elemental composition of planetary surfaces should have a combination of high energy resolution (≲2 eV) and large geometric factor (≳0.1 cm2 sr). This technique could be applied to the Moon, Mercury, asteroids, comets, and perhaps the moons of outer planets.