The Moon, Eclipses
& Long-Term Motion

Part A (Worlds & Light)
➤ Week-1: Observing the Sky & The Nature of Light
➤ Topic-2: The Moon, Eclipses & Long-Term Motion

The Moon

Eclipses

The precession

The Moon

Nearest object to Earth and second bright in the sky
We observe two types of change in the Moon's motion in the sky.
- Appearance
- Rise and set times

» ... these changes lead to → Lunar Phases

Distinctive Phases:
- New Moon: not visible (The Moon cannot be distinguished from Sun's light)
- First and Third Quarters: The angle between Sun - Earth - Moon is 90 degrees
- Full Moon: The disk of the Moon is fully illuminated by the Sun.

Lunar Phases. Experiment: Circle around yourself a spherical object while it is lit by an homogeneous light source. Observe how dark regions (not lit) appear, change and disappear.

Sidereal Month: The time required to complete one revolution around Earth with respect to background stars → 27.3 days (360 degree rotation around the Earth).

Synodic Month: The period of completing phase cycle (eg. New Moon to New Moon) → 29.5 days (takes longer than Sidereal Month).

The Moon's phase. We always see (nearly) the same face of the Moon. This is due to the synchronous rotation of the Moon with Earth. Therefore, the Moon's 1 rotation around itself (rotational period) is equal to 1 rotation around Earth (orbital period).

If the Moon orbits Earth every 27.3 days, why do lunar phases repeat every 29.5 days?

Eclipses

Definition of an eclipse: Any time one astronomical object casts a shadow on another.

Due to the geometry of lunar phases one would expect the followings:

A new moon always blocks our view of the Sun.
Earth would always prevent sunlight from reaching a full Moon.
So, why there is not always a solar/lunar eclipse every new/full moon?

» ... Moon's orbit is inclined to the ecliptic plane by ~ 5 degrees.

Eclipse. Casting a shadow on an object.

Why don’t we observe a solar eclipse every New Moon?

Definition of Nodes: The two points in each orbit (Moon's around the Earth and Earth's around the Sun) at which the Moon crosses the ecliptic plane.

The nodes of the Moon's orbit must be nearly aligned with the Sun and Earth.
The phase of the Moon at this alignment must be either new or full.

Predictions: The times when the lines of nodes are directed towards the sun are favorable.

» ... eclipse seasons ~ 18 years, 11 1/5 days → Saros Cycle

Nodes. Eclipse occur only when three objects are aligned at nodes.

Lunar Eclipse. Because of the shadow size Lunar eclipses takes hours.

Solar Eclipses. Since the shadow of the Moon is narrow, its cast on Earth moves fast (Shadow speed: >1700 km/hr ~ 470 m/s) and lasts shorter. Thus, creating three different types of solar eclipses: Total (Moon covers the sun totally), Partial (Moon passes over Sun with an offset), Annual (Moon is not close enough to Earth; main shadow not reaching Earh's surface, creating a ring on the sun).

What geometric alignment must occur for a lunar eclipse?

The precession

We can notice the daily and annual changes.
However a much longer cycle exist: a gradual change in the direction that Earth's axis points in space: precession
Precession can occur with any rotating object.
Each cycle of Earth's precession takes about 26 000 years
In about 13 000 years, the axis will point to the star Vega
Axis tilt remains close to 23.5 degree throughout the cycle.
Why precession:
- It is caused by gravity's effect on a tilted rotating object
- Object should not be a perfect sphere
- Law of conservation of angular momentum
for Earth:
- We observe pulls from the Sun and Moon; they try to reduce the tilt.
- However since Earth continuously rotates around the same axis this tug of war between gravity and rotation precesses the axis.

Precession: One cannot easily feel an annual change in Earth axis. However, it also wobbles on a much longer scale (26 000 years). The region around the celestial pole is given on the right panel. The path of precession of Earth's axis (yellow) is given starting from 1 AD.

If Earth’s axis slowly wobbles (precession), what observable changes would accumulate over thousands of years?

Does precession change Earth’s tilt angle or only its orientation?
Why does that distinction matter for seasons?

Why will Polaris not always be the North Star?

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