Moon Phases and Solar Eclipses

Office Hours Activities and Announcements

Infrared Camera Demonstration: Students experimented with an infrared camera, with one student applying a blowtorch flame to a steel rod. The infrared image showed the tip of the rod as the hottest, with heat diffusing towards the hand holding it.
Reflective Surfaces: Reflections were observed on elevator doors and whiteboards in the classroom ( $121$ ). Initially, reflections on the whiteboard were mistaken for people in an adjacent room ( $131$ Campbell). This highlighted that infrared light passes through gas and dust but not through walls.
Ice Drawings: Students drew shapes (e.g., a heart, 'help') on foreheads and arms with ice, which were visible, as well as on a whiteboard.
Blowtorch on Whiteboard: A blowtorch was applied to a whiteboard, but the heat diffused too quickly for lettering to be clearly visible, and the board was not significantly damaged.
Star Parties: Scheduled for tonight (Monday) and Wednesday, accessible via both front and back doors.
Homework & TAs: Homework $3$ is due on Friday. TA sections are scheduled for Wednesday and Thursday.
First Quiz: The first quiz will be held in discussion sections next week.

Phases of the Moon

Introduction and Common Misconceptions

Familiarity vs. Understanding: While most are familiar with lunar phases, few understand their true causes.
Incorrect Causes: Common belief that phases are caused by Earth's shadow on the Moon (this is only true for lunar eclipses, not phases) or by clouds.
Phases are a Monthly Cycle: The Moon goes through a full cycle of phases approximately every $29.5$ days, which is the origin of the word "month." This period is slightly less than $30$ days, leading to calendar inconsistencies (e.g., $28$ , $30$ , $31$ day months).

Understanding the Causes of Lunar Phases

Vantage Point: The phases are observed from Earth. From a different point in space, the Moon's appearance would differ.
Sun's Parallel Rays: The Sun is extremely distant ( $93$ million miles or $150$ million kilometers), so its light rays arrive at Earth and the Moon essentially in parallel.
Moon's Illumination: The Moon does not produce its own visible light; it reflects sunlight. Therefore, one hemisphere of the Moon is always illuminated by the Sun at any given time.
Observed Phase: The phase we see depends on how much of that sunlit hemisphere is facing Earth.
The Cycle: The Moon orbits Earth approximately once a month, causing the changing views of its illuminated surface:
- New Moon: The Sun-facing hemisphere is entirely away from Earth; the Moon appears dark and is generally not visible.
- Waxing Crescent: A small, growing sliver of the sunlit hemisphere becomes visible after the new moon. "Waxing" means getting bigger.
- First Quarter: Half of the Moon's visible disk is illuminated (the right half as seen from the Northern Hemisphere). This is a quarter of the way through its orbit.
- Waxing Gibbous: More than half, but not all, of the Moon's visible disk is illuminated; it continues to grow.
- Full Moon: The entire sunlit hemisphere faces Earth, appearing as a full disk. Earth usually does not block the sunlight, as the Moon's orbital plane is slightly tilted ( $5^ ext{o}$ ) relative to Earth's orbital plane around the Sun, preventing eclipses most of the time.
- Waning Gibbous: The illuminated portion begins to shrink, but still more than half is visible.
- Third Quarter: Half of the Moon's visible disk is illuminated again (the left half as seen from the Northern Hemisphere).
- Waning Crescent: A small, shrinking sliver of the illuminated Moon is visible before the new moon. "Waning" means getting smaller.
Demonstration: A Styrofoam ball (Moon) and a flashlight (Sun) held by an observer (Earth) can easily demonstrate the phases.
Observer's Rotation (Tricky Point): The apparent 'left' or 'right' illumination of the Moon's visible portion (e.g., first quarter vs. third quarter) as seen from Earth is due to the observer's rotation on Earth and their changing perspective relative to the Moon's orbit.

Visibility of Phases at Different Times of Day

Key Diagram: Understanding the diagram showing the Sun's parallel rays, the Moon orbiting Earth, and Earth rotating on its axis is crucial for predicting Moon visibility.
Example (Eli at Noon): At noon, an observer located centrally on Earth (for simplicity) could potentially see the third quarter moon setting, the waning crescent, the new moon (in the direction of the sun), the waxing crescent, and the first quarter moon rising.
Example (Eli at Sunset): At sunset ( $6$ \,P.M.), placing Eli in the middle of Earth helps in geometric reasoning. Eli would not be able to see the third quarter moon, as it would be below the horizon.
Phase Consistency: The moon's phase does not measurably change over the course of a single day (e.g., $12$ hours) because its movement in orbit is only about $1/30^{ ext{th}}$ of the way around, which is too small to cause a noticeable phase change.

Terminology Inconsistencies

"Quarter Moon" vs. "Half Moon": The term "first quarter" or "third quarter" moon refers to the Moon being a quarter of the way around its orbit. Visually, it appears half illuminated. This is inconsistent with calling the "full moon" a full moon (visually full disk) rather than a "half moon" (halfway around its orbit).

Moon Visible During the Day

Common Misconception: Many believe the Moon is only visible at night.
Reality: The Moon is often visible during the day (about half the time). It's less obvious due to lower contrast against the bright sky compared to its appearance at night.
Example: A waning gibbous moon seen during a morning hike in Joshua Tree.

Why We Always See the Same Face of the Moon

Tidal Locking: This phenomenon, known as synchronous rotation, is due to the gravitational (tidal) interaction between the Earth and the Moon. Early in its history, the Moon's rapid spin caused internal friction (dissipating rotational energy) until its rotation slowed to match its orbital period around Earth. This ensures that the same side of the Moon perpetually faces Earth, as this configuration minimizes energy dissipation from deforming rock. (To be covered in more detail later).

Earthshine

Description: The seemingly "dark" side of the Moon during crescent phases is not entirely dark; it can be faintly lit up by "Earthshine."
Mechanism: When Earth observers see a waxing crescent moon, an astronaut on the Moon would see a mostly illuminated, waxing gibbous Earth. The bright Earth reflects sunlight onto the Moon's "dark" side. Some of this light then reflects off the Moon and travels back to Earth, allowing us to faintly see the unlit portion of the moon.
Visibility: Earthshine is most noticeable during crescent phases because:
- Earth appears nearly full or gibbous from the Moon, reflecting a lot of light.
- The dazzling brightness of the thin crescent makes the fainter Earthshine more noticeable against the dark portion of the Moon.
Appearance: It represents doubly reflected light: Sun $ ightarrow$ Earth $ ightarrow$ Moon $ ightarrow$ Earth.

Total Solar Eclipses

Introduction and Impact

Rarity and Experience: Total solar eclipses are rare and considered a profound, unforgettable experience, distinct from partial eclipses.
Corona: During totality, the Sun's gorgeous, thin gossamer corona (outer atmosphere) becomes visible.

Causes of Total Solar Eclipses

Alignment: A total solar eclipse occurs during a new moon when the Sun, Moon, and Earth are perfectly aligned, with the Moon directly between the Sun and Earth.
Moon's Shadow: The Moon casts a shadow that falls on a small, narrow path on Earth's surface.
Angular Size Coincidence: The staggering coincidence of the Moon and Sun appearing almost exactly the same angular size in the sky ( $0.5^ ext{o}$ ) is crucial.
- The Sun's physical diameter is approximately $390$ times the Moon's physical diameter.
- The Sun is also approximately $390$ times farther away than the Moon.
- When the ratio of physical sizes equals the ratio of distances, objects appear to have the same angular size.
- Analogy: A tennis ball (Sun) and a ping-pong ball (Moon) can be positioned at specific distances to appear the same angular size, with the tennis ball about twice the diameter of the ping-pong ball requiring it to be twice as far away.
Corona Visibility: The Moon perfectly blocks the Sun's bright photosphere, enabling the faint corona to be seen. Normally, sunlight scattered by Earth's atmosphere (atmospheric scattering) makes the corona invisible.

Why Eclipses Aren't Every New Moon

Orbital Plane Tilt: The Moon's orbital plane around Earth is tilted by about $5^ ext{o}$ relative to Earth's orbital plane around the Sun. This means at most new moons, the Moon is slightly above or below the Sun, casting its shadow into space rather than onto Earth.
Alignment Conditions: Eclipses only occur when the Moon is at one of the two nodes (points where its orbit crosses Earth's orbital plane).
Frequency: There are typically a few lunar and solar eclipses per year. The maximum total number of eclipses (all types) in a single year is seven, which is very rare. Most are partial.

The Path of Totality

Narrow Track: As the Moon orbits Earth and Earth rotates, the Moon's shadow traces a very narrow path (the path of totality) across Earth's surface.
Example: The April $8^{ ext{th}}$ , $2024$ , total solar eclipse followed a curved, narrow path (e.g., from Mazatlán, Mexico, across Texas, lasting approximately $4$ minutes and $20$ seconds in some locations).
Rarity for a Given Location: A total solar eclipse occurs at any given location only once every approximately $380$ years on average.

Eclipse Safety and Viewing Methods

Partial Phases Danger: Staring at the partially eclipsed Sun (or an uneclipsed Sun) is dangerous, not because the rays are more harmful, but because people are more inclined to stare at it.
Proper Filters: Special filters are required for viewing the partial phases:
- Shade 14 Welder's Glass: A dark green filter that blocks sufficient light.
- CE Certified Sunglasses: These glasses must cut out all but $1$ part in $100,000$ of visible light, $100^ ext{o}/{ ext{o}}$ of atmospheric UV, and $100^ ext{o}/{ ext{o}}$ of atmospheric IR light. Cheap fakes are dangerous.
Pinhole Camera: A safe and easy way to view partial phases via projection.
- Mechanism: A small hole punctured in an opaque object (e.g., cardboard) allows sunlight to pass through and project an inverted image of the Sun onto a shaded surface (e.g., a bedsheet).
- Optimal Hole Size: Approximately a pencil-width provides a good balance between brightness and focus. Smaller holes give better focus but dimmer images; larger holes give brighter images but less focus.
- Telescope/Binocular Projection: Projecting the Sun's image through a telescope (without looking directly through the eyepiece) or binoculars can create larger, brighter, magnified projected images.
Celestial-themed Candy: Encouraged to get into the spirit of the eclipse (e.g., Eclipse gum, Orbit gum, Milky Way bars).

Stages of Totality

Partial Phases: Last over an hour on either side of totality, requiring filters.
Diamond Ring: A beautiful phenomenon occurring just $1$ or $2$ seconds before and after totality. A tiny bit of the Sun's photosphere is still visible, creating a bright "diamond" on a faint ring of inner corona. It can be viewed briefly (for a couple of seconds) with the unaided eye at this point, but never through a telescope.
Chromosphere and Prominences: The chromosphere (a thin layer of the Sun's atmosphere) and prominences (bright, erupting gas from the Sun's surface) become visible.
Corona: The full, dynamic corona (the Sun's outer atmosphere) is revealed. Its shape varies from eclipse to eclipse.
Environment During Totality: The sky darkens to twilight colors all around a $360^ ext{o}$ horizon, and bright stars and planets can become visible.
Second Diamond Ring: The reverse process occurs as the Sun begins to reappear, marking the end of totality.