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
Riemannian connection on a surface Riemannian connection on a surface embedded in Euclidean space "E" is just the pullback under the Gauss map of the Riemannian connection on "S". Using the identification of "S" with the homogeneous space SO(3)/SO(2), the connection 1-form is just a component of the Maurer–Cartan 1-form on SO(3). In other words, everything reduces to understanding the 2-sphere properly. For a surface "M" embedded in E (or more generally a higher-dimensional Euclidean space), there are several equivalent definitions of a vector field "X" on "M": The last condition means that the assignment "f" "Xf" on "C"("M") satisfies the Leibniz rule The space