Painting Asteroids for Planetary Defense

Asteroidal impact threats to the Earth will be predicted a century or more in advance. Changing an asteroid's albedo changes the force of Solar radiation on it, and hence its orbit. Albedo may be changed by applying a thin ($\sim 0.1\,\mu$) reflective coat of alkali metal, dispensed as vapor by an orbiting spacecraft. A complete coat reduces the effective Solar gravity, changing the orbital period. A Tunguska-class (50 m diameter) asteroid in a nominal orbit with perihelion 1 AU and aphelion 3 AU ($a = 2\,$AU, $e = 0.5$) may be displaced along its path by $\sim 1000\,$km in 100 years, sufficient to avoid impact in a populated area, by application of one kg of lithium or sodium metal over its entire surface. Alternatively, coating one hemisphere of an asteroid in an elliptical orbit may produce a Solar radiation torque, analogous to but distinct from the Yarkovsky effect, displacing it by an Earth radius in $\sim 200$ years. The time required scales as the square root of the asteroid's diameter (the 1/6 power of its mass) because the displacement increases quadratically with time, making it possible to prevent the catastrophic impact of a km-sized asteroid with a minimal mass.