Albedo used in astronomy are the (V-band) geometric albedo (measuring brightness when illumination comes from directly behind the observer) and the Bond albedo (measuring total proportion of electromagnetic energy reflected). Their values can differ significantly, which is a common source of confusion. In detailed studies, the directional reflectance properties of astronomical bodies are often expressed in terms of the five Hapke parameters which semi-empirically describe the variation of albedo with phase angle, including a characterization of the opposition effect of regolith surfaces. The correlation between astronomical (geometric) albedo, absolute magnitude and diameter is: formula_7, where formula_8 is the astronomical albedo, formula_9
Incompressible surface ∂"D". If "D" were to bound a disk inside "S" (which is always the case if "S" is incompressible, for example), then compressing "S" along "D" would result in a disjoint union of a sphere and a surface homeomorphic to "S". The resulting surface without the sphere might or might not be isotopic to "S". There is also an algebraic version of incompressibility. Suppose formula_4 is a proper embedding of a compact surface in a 3-manifold. Then "S" is "π"-injective (or algebraically incompressible) if the induced map on fundamental groups is injective. In general, every "π"-injective surface is incompressible, but