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 Incompressible surface In mathematics, an incompressible surface is a surface properly embedded in a 3-manifold, which, in intuitive terms, is a "nontrivial" surface that has been simplified as much as possible by compressing disks. They are useful for decomposition of Haken manifolds and for normal surface theory. Let "S" be a compact surface properly embedded in a smooth or PL 3-manifold "M", and suppose that there is a disk "D" embedded in "M" such that where the curve ∂"D" does not bound a disk inside of "S". Then "D" is called a compressing disk for "S", and we call "S"