between the body and the observer is the distance between the body and the Sun is the distance between the observer and the Sun , a unit conversion factor, is the constant 1 AU, the average distance between the Earth and the Sun Approximations for phase integral The value of depends on the properties of the reflecting surface, in particular on its roughness. In practice, different approximations are used based on the known or assumed properties of the surface. The surfaces of terrestrial planets are generally more difficult to model than those of gaseous planets, the latter of which have smoother visible surfaces. Planets as diffuse spheres Planetary bodies can be approximated reasonably well as ideal diffuse reflecting spheres. Let be the phase angle in degrees, then A full-phase diffuse sphere reflects two-thirds as much light as a diffuse flat disk of the same diameter. A quarter phase () has as much light as full phase (). By contrast, a diffuse disk reflector model is simply , which isn't realistic, but it does represent the opposition surge for rough surfaces that reflect more uniform light back at low phase angles. The definition of the geometric albedo , a measure for the reflectivity of planetary surfaces, is based on the diffuse disk reflector model. The absolute magnitude , diameter (in kilometers) and geometric albedo of a body are related by Example: The Moon's absolute magnitude can be calculated from its diameter and geometric albedo : We have , At quarter phase, (according to the diffuse reflector model), this yields an apparent magnitude of The actual value is somewhat lower than that, The phase curve of the Moon is too complicated for the diffuse reflector model. A more accurate formula is given in the following section. More advanced models Because Solar System bodies are never perfect diffuse reflectors, astronomers use different models to predict apparent magnitudes based on known or assumed properties of the body. For planets, approximations for the correction term in the formula for have been derived empirically, to match observations at different phase angles. The approximations recommended by the Astronomical Almanac are (with in degrees): Here is the effective inclination of Saturn's rings (their tilt relative to the observer), which as seen from Earth varies between 0° and 27° over the course of one Saturn orbit, and is a small correction term depending on Uranus' sub-Earth and sub-solar latitudes.