Vol. Science · Astronomy · The month

Synodic
the longer month

One full trip of the Moon around Earth is not new Moon to new Moon. A sidereal month brings the Moon back to the same stars. NASA’s Moon Fact Sheet lists that revolution period as 27.3217 days. A synodic month brings the same phase back. The same sheet lists the synodic period as 29.53 days. NASA Space Place says it in round numbers: about 27.3 days for the Moon to orbit Earth, and about 29.5 days from one new moon to the next. The phase cycle is the longer one. Earth is moving too. After the Moon has returned to the same stars, the Sun has shifted on the sky, because Earth moved along its orbit. The Moon still has farther to go before it sits between Earth and the Sun again. NASA Science calls that remainder a little more than two additional days. The same catch-up, on a daily spin, is the sidereal day. A phase you can set to a clock is the Moon dial.

Classroom schematic — top-down, from the north, so both orbits run counterclockwise. The Sun sits at the center of a short arc of Earth’s orbit. The Moon’s circle is drawn large so the phase can be seen. The Moon Fact Sheet lists a semimajor axis of 0.3844 × 10⁶ km. The Earth Fact Sheet lists Earth’s semimajor axis as 149.598 × 10⁶ km. On those two numbers the Moon’s circle would be a dot. The arc itself is not enlarged: it is 360° divided by the Earth Fact Sheet’s 365.256-day sidereal orbit. The Moon Fact Sheet lists orbit eccentricity 0.0549 and an inclination to the ecliptic of 5.145°. This drawing is a flat circle and leaves both out. The distance on that sheet roughly ranges from 357,000 km to 407,000 km. This circle does not. Not an ephemeris. Not a phase calendar for observing. Not astrology. Not a tide table.

Literacy · two kinds of month

Sidereal month

One full orbit of the Moon relative to the distant stars. The Moon Fact Sheet lists the revolution period as 27.3217 days. NASA’s eclipse glossary rounds that orbit: a sidereal month is 27.32 days. Space Place says about 27.3 days. On this desk the reference star is the direction the Moon pointed at the first new Moon. The next time the Moon faces that star is one revolution later. The phase is not new yet.

Synodic month

New Moon to the next new Moon — the mean cycle of phases. The fact sheet lists the synodic period as 29.53 days. The eclipse glossary uses the same 29.53 days and calls it the time from one full moon to the next. Space Place and NASA’s Moon phases page say about 29.5 days. The Moon dial uses a finer year-2000 mean, 29.530588 days, from Fred Espenak. This slider stays on the fact sheet’s 29.53. It does not set a date.

The extra days

NASA Science: as the Moon completes each 27.3-day orbit, Earth and the Moon are moving around the Sun, so it takes a little more than two additional days before sunlight hits the Moon the way it did on day zero. At this desk’s star preset the slider is on 27.3217 days, and the next new Moon is the fact sheet’s 29.53. “Still to new Moon” at that stop is the subtraction of those two published numbers. It is not a third measurement. The Sun’s shift on the arc is 360° × the elapsed days ÷ 365.256, the Earth Fact Sheet’s sidereal orbit — the same kind of leftover as the sidereal day, stretched from one spin to one month.

Phase

How much of the lit half faces Earth. The Moon is always half-lit by the Sun. NASA lists eight phases: new, waxing crescent, first quarter, waxing gibbous, full, waning gibbous, third quarter, and waning crescent. The name on this page comes from the Earth–Moon–Sun angle on the sketch. The lit percent is that angle turned into a disk: (1 − cos φ) / 2. It is not a measured brightness. In the northern-hemisphere picture, waxing light sits on the right.

What the circle leaves out

Eccentricity 0.0549, so the real distance changes. The fact sheet says the Moon ranges roughly from 357,000 km to 407,000 km. Inclination 5.145° to the ecliptic, which is why a new or full Moon usually misses Earth’s shadow — that is the eclipses desk, not this one. NASA’s Moon phases page also gives an average distance of 238,855 miles (384,399 km), beside the fact sheet’s semimajor axis of 0.3844 × 10⁶ km. This page prints both and does not average them into a new figure. The phase disk is a classroom crescent, not a libration movie.

Sources · public NASA education

Classroom picture of a longer phase cycle. Not an ephemeris, not a phase calendar for observing, not astrology, and not a tide table. Days on the slider are counted from a schematic new Moon. The Sun’s shift is the slider counted with the Earth Fact Sheet’s 365.256-day orbit. “Still to new Moon” at the star stop is 29.53 minus 27.3217, the two Moon Fact Sheet periods, not a new measurement. Earthrise preview: NASA / Bill Anders (public domain).

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