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.
A multi-century comparison of the Chapront-Touzé analytic series with modern JPL SPICE kernels (DE440/441). Polynomial and harmonic patching methods were tested to reduce discrepancies in l, b, and c across 1900–2150, but these proved insufficient for long-term consistency. The study highlights the limits of analytic correction and motivates a transition toward fully numerical or hybrid approaches for future libration modeling.
The full web calculator that uses 13 pre-computed JSON data series to generate high-precision values of l, b, and c. It implements the aligned Chapront–SPICE model to reproduce official almanac values. Designed as a foundation for future integration into the Umbra Visualizer.
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.