Note on authorship: Throughout this document, the term “Chapront” is used as a shorthand reference to the collaborative analytical work of Jean Chapront and Michelle Chapront-Touzé at the Bureau des Longitudes in Paris.
No distinction is intended between their respective contributions, and all references to "Chapront", the "Chapront model" or "Chapront series" should be understood to mean the full joint authorship and analytical legacy they share.
For years, the Chapront analytical series was the gold standard for computing the Moon’s orientation and libration. It’s fast, elegant, and mathematically consistent—but when we began testing it against SPICE, NASA’s high-precision numerical ephemeris system, we discovered small but persistent drifts. At first we assumed Chapront was “good enough” and tried to patch it by adding bias, drift, and harmonic corrections. Those adjustments improved short-term agreement, but the residuals grew over longer timescales. The analytic series simply couldn’t follow SPICE perfectly through the complex long-period terms of the lunar motion.
That (and some guidance and inspiration from Ernie Wright at NASA) led us to adopt SPICE as the reference truth. Because SPICE data can’t be (easily!) computed live in the browser, we pre-ran it at 15-minute intervals and built Hermite interpolation so the web page could show accurate, continuous motion without querying SPICE directly. (The Chapront calculations are performed explicitly, without interpolation.) The result is a direct side-by-side comparison of SPICE and Chapront librations—both now expressed in the same coordinate frame—so you can see where the old analytical method still holds up and where modern numerical data has taken over. It’s a bridge between tradition and precision.
Of course, there are other models out there that can be used to calculate lunar librations, and the user is encouraged to explore these further. However, we have landed on SPICE as the final and best source of truth for modern calculations. NASA uses it to land spacecraft, so it is certainly appropriate to use for libration calculations!
When the page loads, the system will attempt to load the correct current time using your system time. You can then enter an epoch which MUST be from years 1900 through 2150. You can enter a full JD, or the date-time directly in YYYY-MM-DD hh:mm:ss(.sss) This time is in TT – NOT UTC, which means there is no need for ΔT.)
Choose Apparent vs Geometric (SPICE only):
The page updates both sides to keep frames consistent. Results will display in the panels: SPICE on the left, Chapront on the right. Values update instantly.
Two models, same sky. We compute SPICE directly, and we map Chapront from its native mean-ecliptic frame into the same “true-of-date” frame to allow direct left-right model comparison. One toggle, Apparent / Geometric - Only SPICE can show both.
We explored “patching” Chapront to better match SPICE (bias / drift / harmonic terms). That makes a neat demo, but it creates confusion:
Bottom line: Two clear options are preferred over three murky ones. The page shows the real, interpretable differences without overfitting.
SPICE: High-precision numerical ephemerides; we read Moon attitude / geometry in the true-of-date frame and compute l, b, c. Apparent mode includes light-time and aberration effects.
Chapront: Analytic series in mean-ecliptic coordinates. We apply nutation in longitude (Δψ) and obliquity (Δε), and rotate into the true-of-date frame before extracting l, b, c — yielding a fair comparison.
Patching attempt: We tested bias / drift / harmonics to reduce residuals vs SPICE. It works in limited intervals but adds a maintenance and interpretability burden, so it is not exposed in the UI.
Use: Set time in TT → toggle Apparent / Geometric → compare SPICE vs Chapront (l, b, c)
This page exists to provide a single source of usable libration calculations, but also teach and verify: it shows how an analytic tradition (Chapront) compares with a modern numerical source (SPICE) once both speak the same coordinate language. It’s a tool for readers, students, and researchers to get the data they need while developing intuition — without drowning in options.
The author graciously thanks Ernie Wright of NASA for recommendations and advice on using SPICE.