  Cosmology experiments at mm-wavelengths can detect Planet Nine if it is the
size of Neptune, has an effective temperature of 40 K, and is 700 AU from the
Sun. It would appear as a ~30 mJy source at 1 mm with an annual parallax of ~5
arcmin. The challenge is to distinguish it from the approximately 4000
foreground asteroids brighter than 30 mJy. Fortunately, these asteroids are
known to the Minor Planet Center and can be identified because they move across
a resolution element in a matter of hours, orders of magnitude faster than
Planet Nine. If Planet Nine is smaller, colder, and/or more distant than
expected, then it could be as faint as 1 mJy at 1 mm. There are roughly $10^6$
asteroids this bright and many are unknown, making current cosmology
experiments confusion limited for moving sources. Nonetheless, it may still be
possible to find the proverbial needle in the haystack using a matched filter.
This would require mm telescopes with high angular resolution and high
sensitivity in order to alleviate confusion and to enable the identification of
moving sources with relatively short time baselines. Regardless of its mm flux
density, searching for Planet Nine would require frequent radio measurements
for large swaths of the sky, including the ecliptic and Galactic plane. Even if
Planet Nine had already been detected by other means, measuring its mm-flux
would constrain its internal energy budget, and therefore help resolve the
mystery of Uranus and Neptune, which have vastly different internal heat.
