SPICE-Based Lunar State and Libration Calculator

Overview

This project provides SPICE-derived lunar orientation, lunar state vector, and solar geometry quantities for a selected epoch in Terrestrial Time (TT). It is intended both as a practical calculation tool and as an educational reference for understanding how modern lunar geometry is constructed from state vectors, reference frames, and body-orientation models.

The calculator displays geocentric lunar libration quantities \(\ell\), \(b\), and \(c\), together with supporting geometric and reference quantities used in lunar and eclipse-related work.

How to Use the Calculator

Enter either:

• a TT calendar date and time, or
• a Julian Date TT.

Then press Compute.

The calculator will display:

• the interpreted epoch,
• the Julian Date TT,
• the corresponding time parameter \(t\),
• and the computed lunar and solar geometry.

The ΔT field is used for UT and sidereal-time reference quantities shown on the right side of the page. The primary SPICE geometry itself is evaluated directly for the entered TT epoch.

SPICE Values

The left side of the calculator contains the primary SPICE-derived quantities, including:

• lunar libration quantities \(\ell\), \(b\), and \(c\),
• Earth–Moon distance,
• Moon right ascension and declination,
• Moon ecliptic longitude and latitude,
• Moon position and velocity vectors,
• lunar pole and prime-meridian orientation,
• Sun geometry as seen from both Earth and Moon.

These values are computed from SPICE state vectors and reference-frame transformations using the backend API.

Other Values

The right side of the calculator contains supporting educational and reference quantities, including:

• UT,
• Greenwich Mean Sidereal Time,
• classical nutation and obliquity reference quantities,
• Delaunay arguments,
• derived fundamental elements.

These quantities provide context for the analytical lunar tradition and are included for educational and verification purposes. They are not the source of the main SPICE libration results.

Technical Documentation

For the complete technical explanation, reference frames, kernel set, vector definitions, libration construction, historical background, and references, see:

• From Lunar Tables to SPICE

For a detailed explanation of the Moon state vector and the meaning of the displayed \(x\), \(y\), \(z\), \(v_x\), \(v_y\), and \(v_z\) components, see:

• Moon State Vector

SPICE Kernels

The calculator currently uses the following kernel set:

• naif0012.tls
• pck00011.tpc
• gm_de440.tpc
• moon_080317.tf
• moon_pa_de440_200625.bpc
• de440.bsp

All SPICE kernels used by the calculator were obtained directly from the NAIF repository and verified using SHA-256 checksums.

A complete verification package containing the kernel manifest, SHA-256 hash list, and verification instructions is included with the project distribution.

Credits & Intent

This project was created to provide a single, practical source for modern lunar orientation and libration calculations while also serving as an educational and verification tool. It is intended for readers, students, eclipse observers, and researchers who want access to high-quality lunar geometry together with the mathematical and historical context behind it.

The author gratefully acknowledges Ernie Wright of NASA for recommendations, advice, and inspiration regarding the use of SPICE in lunar and eclipse geometry work.