Vol. Science · Astronomy · The limbs

Libration
past the mean face

The Moon keeps the same face toward Earth, and we still see past the edge of that face. NASA Science calls the match synchronous rotation: the time to turn once equals the time to orbit once, so the same side faces our planet. On the Moon Fact Sheet the sidereal rotation period is 655.720 hours and the revolution period is 27.3217 days. Divide the hours by 24 and the result rounds to that same 27.3217 days. That is the lock. The peek has two classroom parts. Libration in longitude comes from the eccentric orbit. The fact sheet lists orbit eccentricity 0.0549, a maximum orbital speed of 1.082 km/s, and a minimum of 0.970 km/s. NASA’s Moon phases page says the closest, fastest part of the orbit shows a little more of the eastern side, and the farthest, slowest part shows a bit more of the western side. Libration in latitude comes from a tilted lunar equator. The fact sheet lists obliquity to orbit as 6.68°. NASA SVS uses that same angle: the orbit and the equator are 6.68° apart, and the nod reveals parts of the north and south poles. Over time the visible surface is more than half. A JPL lunar constants document states that the geometric librations allow 59% of the Moon’s surface to be visible from Earth. The Moon dial is the phase. This page is the peek.

Classroom schematic — a Moon globe, north up, lunar east to the right. The pale disk is the mean Earth-facing hemisphere. The dark strip is far-side terrain sliding into view. Both peeks are drawn larger than the real angles so a phone can see them. The fact sheet does not publish a libration angle in degrees. SVS and the Moon phases page describe the east–west peek without one. The 6.68° figure is the tilt between equator and orbit, and this drawing is not a 6.68° tip. A 2005 JPL note prints larger figure angles, including 8.16° and 6.87° once solar perturbations are included. The sliders do not use those degrees. Play walks two classroom cycles whose periods are the SVS round numbers, about 27.55 days east–west and about 27.12 days north–south. It is not a clock and not a date. This is not a live Moon orientation for tonight. Not an ephemeris. Not a limb finder for imaging. Not a phase calendar. Not astrology.

Literacy · the lock and the peek

Tidal locking

NASA Science: the Moon does spin. The time to rotate once equals the time to orbit once. Thanks to that synchronous rotation, the same side of the Moon always faces Earth. The Moon Fact Sheet lists a sidereal rotation period of 655.720 hours and a revolution period of 27.3217 days. 655.720 divided by 24 is 27.3217 days when rounded to four decimal places — the revolution figure on the same sheet. NASA SVS says the Moon spins at a steady rate, turning once each orbit, which is why it shows us more or less the same face. “More or less” is the rest of this page.

Libration in longitude

An east–west rock. NASA’s Moon phases page: when the Moon is closest and moving most quickly, it does not rotate quite fast enough to keep entirely the same side facing us, and we see a little more of the eastern side. When it is farthest and orbiting at its slowest, the rotation gets a little ahead, and we see a bit more of the western side. SVS calls it a slow shake of the head, “no,” revealing thin strips over the eastern and western edge, on a cycle of about 27.55 days — the anomalistic month, the average time between perigees. The fact sheet’s eccentricity is 0.0549. Its orbital speeds are 1.082 km/s at the fast end, 1.022 km/s on average, and 0.970 km/s at the slow end. Those pages do not print a longitude amplitude in degrees. This slider does not invent one.

Libration in latitude

A north–south nod. NASA SVS: mostly an effect of the tilt of the Moon’s orbit relative to its equator. The angle between those two planes is 6.68°. The fact sheet lists the same number as obliquity to orbit. The nod reveals parts of the north and south poles and repeats in about 27.12 days, the draconic month on that page. NASA’s Moon phases page tells the same nod with a round “5 degree tilt” of the orbit, and says we see slightly more of the northern or southern hemisphere. The fact sheet’s inclination to the ecliptic is 5.145°. This desk does not treat 5.145° and 6.68° as one measurement. 6.68° is the tilt. It is not a separate maximum-peek angle, and the drawing is larger than the tilt.

More than half

NASA says frequent observers catch glimpses of the farside. The percentage is on a different NASA page. Ralph Roncoli’s Lunar Constants and Models Document (JPL D-32296, 23 September 2005) states that the geometric librations allow 59% of the Moon’s surface to be visible from Earth: 41% is always visible, 41% is never visible, and 18% is alternately visible and not visible. The same section says more than 50% is visible over time. The 59% is that cumulative result. It is not a reading of one frame on this slider.

Diurnal libration

A smaller, secondary effect. The same JPL document calls it diurnal or topocentric libration: an observer on a rotating Earth sees the Moon from different angles. Its example is an observer at Earth’s equator, who over a 12-hour period can see a total of almost 2 degrees more of the Moon in longitude than at any instant during the day. This desk leaves that off the sliders. The word on the document is “almost 2 degrees.” This page does not sharpen it.

What the globe leaves out

The peek is enlarged. Full travel on the sliders is a classroom cartoon, not the JPL figure notes and not the fact sheet’s 6.68°. Those notes, in the same 2005 document, say a simple two-body ellipse is usually quoted as 6.28° of longitudinal libration, while their figure shows 8.16° once solar perturbations are included, and 6.87° of latitudinal libration against 6.69° for the equator’s inclination to the orbit. The fact sheet and SVS print 6.68°, not 6.69°. This page quotes the pair and does not blend them. The document also separates a physical libration — a real wobble of the spin, less than about 0.035° — from the geometric picture drawn here. The disk is flat-lit on purpose. Phase lives on the Moon dial. The 5.145° orbital tilt that makes eclipses rare lives on the eclipses desk. East on this drawing is to the right with north up, matching NASA’s north-up SVS animations: when the sub-Earth point moves left of the meridian, more of the western limb rotates into view, and when it moves above the equator, a bit of the far side beyond the north pole becomes visible.

Sources · public NASA pages

Classroom picture of a locked face and an optical peek. Not an ephemeris, not a limb finder, not a phase calendar, and not astrology. The globe’s travel is exaggerated. 0.0549, 655.720 hours, 27.3217 days, 6.68°, 5.145°, and the three orbital speeds are the Moon Fact Sheet. About 27.55 days and about 27.12 days are the SVS cycle lengths, used only so Play’s two motions do not share one period. 59%, 41%, 18%, “almost 2 degrees,” and the figure-note angles are the 2005 JPL document. Earthrise preview: NASA / Bill Anders (public domain).

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