The Kuiper Belt and Olbers Paradox

We investigate the constraints that Olbers Paradox, applied to the Zodiacal Background as measured from space, sets on outer solar system objects. If extended to very faint limits, R = 40--50 mag, the steep optical luminosity function (LF) of Kuiper Belt objects (KBOs) at R less than 26 mag implies an infinitely bright night sky. Small KBOs with radii of 1 mm to 1 km must have a size distribution n(r) proportional to r^{-a}, with a = 3.5 or smaller to satisfy the known limits on the sky-surface brightness at optical and far-infrared wavelengths. Improved limits on the measured KBO surface brightness can yield direct estimates of the albedo, temperature, and size distribution for small KBOs in the outer solar system.