This topic is central to the entire site, and will be under construction for the foreseeable future. Below is a taste of what will become available here!
An overview of what lunar libration is, why it occurs, and how it reveals slightly more than half of the Moon’s surface to Earth over time. This section introduces physical causes such as orbital eccentricity, inclination, and parallax, and explains their combined role in eclipse prediction and topographic modeling.
An interactive tool for generating Besselian eclipse elements from modern SPICE-derived Sun–Moon geometry. The calculator samples the eclipse geometry around a selected reference epoch, builds polynomial reductions for multiple choices of t0, and displays the resulting fundamental-plane motion, shadow radii, and element tables. It also supports comparison against published legacy elements, helping document how classical Besselian methods can be preserved, inspected, and modernized using contemporary ephemeris data.
The full web calculator that computes high-precision values of many positional and orientation values such as l, b, and c directly from JPL SPICE kernels (DE440/441). All results are derived from the underlying numerical ephemeris. Designed as the primary foundation for the Umbra Visualizer and future eclipse modeling tools.
Defines the Earth-centered Fundamental Plane (+x₍FP₎, +y₍FP₎, +z₍FP₎) and explains how geocentric, topocentric, and heliocentric coordinate systems interrelate. Establishes the geometric basis for all libration and eclipse calculations by fixing orientations and sign conventions used throughout the project.
Derives quaternion components directly from (l, b, C) and explains their equivalence to axis–angle and Rodrigues formulations. Demonstrates how quaternions preserve orthogonality, avoid gimbal lock, and represent lunar orientation in a compact 4-parameter form suitable for 3-D rendering and interpolation.
Explores how libration differs for observers at various locations. Derives Δl and Δb from Besselian fundamental-plane coordinates, explains fixed sign conventions, and shows how altitude and parallax shift the apparent lunar orientation during eclipses.
Introduces the *NEW* (q, θ) coordinate system developed for high-precision lunar limb modeling. Details the conversion between (q, θ) and global XYZ coordinates, the right-handed local frame orientation, and how lunar tile data and surface normals connect libration angles to measurable limb profiles.
Describes the Potree/Three.js-based visualization system used to render libration and lunar topography. Explains how quaternions drive real-time rotation, how tile datasets are positioned with orientation matrices, and how the viewer integrates into the broader Libration Station environment.
Presents the new conceptual model treating the umbra as a continuous scalar field F(x,y,z,t). Defines eclipse duration as the integral of F along the observer’s trajectory and relates its gradients to contact times, linking libration orientation directly to shadow geometry.
Traces the evolution of libration modeling from early 20th-century analytic theories to the modern hybrid numerical era. Highlights contributions by Atkinson, Chapront-Touzé, Meeus, Herald, Duncombe, Wright, Zeiler, and Quaglia, showing how their combined work led to today’s unified analytic-numerical framework.