  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.
