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We have demonstrated a remote magnetometer based on sodium atoms in the Earth's mesosphere, at a 106-kilometer distance from our instrument. A 1.33-watt laser illuminated the atoms, and the magnetic field was inferred from back-scattered light collected by a telescope with a 1.55-meter-diameter aperture. The measurement sensitivity was 162 nT/$\sqrt{Hz}$. The value of magnetic field inferred from our measurement is consistent with an estimate based on the Earth's known field shape to within a fraction of a percent. Projected improvements in optics could lead to sensitivity of 20 nT/$\sqrt{Hz}$, and the use of advanced lasers or a large telescope could approach 1-nT/$\sqrt{Hz}$ sensitivity. All experimental and theoretical sensitivity values are based on a 60$^\circ$ angle between the laser beam axis and the magnetic field vector; at the optimal 90$^\circ$ angle sensitivity would be improved by about a factor of two., Comment: 15 pages, 15 figures, 4 tables

We have demonstrated a remote magnetometer based on sodium atoms in the Earth's mesosphere, at a 106-kilometer distance from our instrument. A 1.33-watt laser illuminated the atoms, and the magnetic field was inferred from back-scattered light collected by a telescope with a 1.55-meter-diameter aperture. The measurement sensitivity was 162 nT/$\sqrt{Hz}$. The value of magnetic field inferred from our measurement is consistent with an estimate based on the Earth's known field shape to within a fraction of a percent. Projected improvements in optics could lead to sensitivity of 20 nT/$\sqrt{Hz}$, and the use of advanced lasers or a large telescope could approach 1-nT/$\sqrt{Hz}$ sensitivity. All experimental and theoretical sensitivity values are based on a 60$^\circ$ angle between the laser beam axis and the magnetic field vector; at the optimal 90$^\circ$ angle sensitivity would be improved by about a factor of two., Comment: 15 pages, 15 figures, 4 tables