Global spectra are available for topography and geoid on the earth, Venus, Mars, and the moon. If the spectral energy density has a power law dependence on wave number a fractal is defined. The topography spectrum for the earth is a well-defined fractal with D=1.5; this corresponds to Brown noise with the amplitude proportional to the wave length. Although there is more scatter for the other planetary bodies, the data for Mars and the moon correlate well with the data for the earth. Venus topography also exhibits a Brown noise behavior but with a smaller amplitude. The power law dependence of the earth's geoid is known as Kaula's law. We show that uncompensated Brown topography gives a geoid with a power law dependence that is in quite good agreement with Kaula's law. However, the required amplitude is only 8% of the observed topography. A similar result is found for the other bodies with the ratio of the amplitude of topography required to explain the geoid to the observed topography increasing to 72% for the moon. ¿ American Geophysical Union 1987