Astronomy Lecture Notes — Precession, Eclipses, Moon Phases, and Scientific Notation

Schedule and video assignments

• No in-person class on Friday. There is a video you must watch.
• Video will be posted on Wednesday; please watch before the next Monday class. You can watch it anytime after it’s posted (Thursday, Friday, Saturday, Sunday, or Monday before class).
• In the video, you will take notes and also complete a short Canvas quiz.
• Canvas: discussion post #1 is available in the left menu; the relevant discussion is posted there and is due tonight.
• Friday student hours are canceled; there are two tutoring blocks on Wednesday in Sequoia Hall 238: 10:30–11:20 AM and 11:20 AM–12:10 PM (a total of 50 minutes). Email or message to note the tutoring schedule.
• Plan to meet on Wednesday; no meeting on Friday.
• The instructor will demonstrate items in the planetarium and revisit topics already discussed (preparation for unit material).

Planetarium session: recap and purpose

• The instructor will revisit Sacramento at night; encourage looking up at night and enjoying the full moon this weekend.
• Orientation and landmarks in the sky: rotate to north; the Big Dipper, the two pointer stars pointing to the Little Dipper and Polaris (the North Star).
• Polaris is very close to the North Celestial Pole, which is the axis around which the sky appears to rotate.
• The North Celestial Pole (NCP) is not perfectly at Polaris but is very close today; everything in the sky appears to rotate around the NCP.
• The North Celestial Pole precesses over thousands of years; this is called precession.
• Time scales: the precession cycle is about
  $T_{ ext{precession}} \approx 2.6 \times 10^4 \text{ years}$
• A few thousand years ago, the NCP pointed toward Thuban (in ancient Egypt); the pyramids’ shafts may reflect ancient observations.
• Current and future pole alignments:
  • Today: Polaris near the NCP.
  • In ~5,000 years: near Thuban again.
  • In ~12,000 years: near Vega (in Lyra).
• The concept of precession: the Earth spins like a top, but the axis slowly wobbles over a 26,000-year cycle.
• Visual aids and additional information: a YouTube video is suggested for more intuition; slides are available in Canvas (Week 2, Lecture Notes). The lecturer shows where to find the slides under Week 2 → Lecture Notes; this includes Units 12–15 and a worksheet.

Eclipses: solar and lunar

• Solar eclipses occur when the Moon blocks the Sun from Earth’s view.
• Angular sizes:
  $\theta<em>{\text{Moon}} \approx \theta</em>{\text{Sun}} \approx 0.5^{\circ}$
• Because the Sun and Moon appear the same size from Earth, a total solar eclipse is possible when the Moon exactly covers the Sun.
• Total solar eclipse details:
  • Totality is the moment of perfect alignment; the Sun’s corona is visible.
  • Totality lasts a couple of minutes (roughly 2–5 minutes).
  • Special solar viewing glasses are required while the Sun is only partially eclipsed; during totality glasses can be removed briefly.
  • Upcoming notable eclipses:
  • 2024-04-08: path of totality across parts of the United States (e.g., Texas area).
  • 2026: Northern Spain.
  • 2027: Northern Africa, including Egypt; totality lasting around 6.5 minutes in Luxor, Egypt.
• Lunar eclipses occur when Earth blocks sunlight from reaching the Moon.
• Red color in a total lunar eclipse:
  • Earth’s atmosphere refracts sunlight; reddened light is bent and cast onto the Moon’s surface.
  • The Moon can appear reddish during total lunar eclipses; this is sometimes called a “Blood Moon.”
• Why eclipses don’t happen every month:
  • The Moon’s orbit around Earth is inclined relative to the Moon-Earth-Sun plane (the ecliptic) by about $\Delta i \approx 5^{\circ}$.
  • Because of this tilt, alignment for eclipses only occurs at certain times of the year when the Moon crosses the ecliptic near new or full phase and the shadow falls on land.
• Eclipse geometry:
  • The Moon’s umbra creates a narrow path of totality on Earth (the shadow’s core).
  • The shadow’s penumbra covers a much larger area; partial eclipses occur where observers are within the penumbra but outside the umbra.
• Observational context:
  • NASA and other sources calculate precise shadow paths and land areas for eclipses.
  • Some eclipse opportunities can be observed from the ocean (cruises, ships) to reach the path of totality.

Relative sizes and distances in the solar system

• The Moon is small but much closer to Earth than the Sun; the Sun is enormous but far away.
• The Sun is vastly larger than the Earth and the Moon; distances scale accordingly (1 AU from Earth to the Sun):
  $1\text{ AU} \approx 1.496 \times 10^{11} \text{ m}$
• A quick visual survey of sizes:
  • The Earth and Moon are close to each other; the Sun is far away.
  • Mercury, Venus, Earth, Mars vary in size; Jupiter is very large; Saturn has Titan as a notable moon; Uranus and Neptune are smaller than Jupiter but larger than Earth in some aspects.
  • Pluto and Charon; other Kuiper Belt objects such as Haumea and Makemake appear in diagrams to illustrate scale relationships.
• This section reinforces the idea of size differences among planets, moons, and the Sun, and sets up when we discuss the life cycles of stars and different stellar sizes.

Moon phases and rotation: key concepts

• The Moon orbits Earth roughly every 30 days (the lecturer uses “about thirty days” as the orbital period).
• The Moon also rotates on its axis with a period close to 30 days, resulting in tidal locking: the same hemisphere always faces Earth.
• Implications:
  • We always see the same “face” of the Moon (the near side); there is no permanently dark side, despite popular phrases.
  • The far side receives sunlight at other times during the lunar cycle, just not from Earth.
• Phases explained:
  • The Moon’s phase depends on the relative positions of the Sun, Earth, and Moon.
  • Full Moon occurs when Earth is between the Sun and Moon; the Moon is fully lit from our viewpoint.
  • New Moon occurs when the Moon is between the Sun and Earth; the side facing Earth is dark.
  • First Quarter, Last Quarter: intermediate phases where half of the Moon’s near side is illuminated.
  • From any given vantage, the lit portion changes as the Moon orbits, even though the same face is always presented to Earth.
• Visual aid and a quick note:
  • A common mistake is to call the far side the “dark side.” The near side is the one we see illuminated or darkened over the cycle; both sides receive sunlight at different times.
• The speaker suggests watching a quick explanatory video if this topic is new; a quick video is noted as suitable for beginners.
• Practical observation tip: look at the Moon tonight to see the current phase and figure out where we are in the cycle.

Why the Moon is not always fully dark or fully lit

• The visible portion of the Moon changes because we see different hemispheres of the Moon as it orbits Earth.
• The illuminated portion grows and shrinks according to the Sun-Moon-Earth geometry; the entire Moon is not always illuminated or dark at once.
• The Moon’s phases are a natural consequence of the combination of orbital motion and the Sun’s light.

Solar and lunar eclipses: synthesis and student experiences

• Real-world observations:
  • A total solar eclipse observed in 2017 across parts of the U.S. produced a dramatic darkening and a visible solar corona.
  • Eclipsing events can be partial or total depending on viewer location relative to the path of totality.
  • Observers often wear special protective eyewear when viewing solar eclipses to prevent eye damage; during totality, sunglasses can be removed briefly.
• Lunar eclipses provide a reddish Moon and happen when the Earth’s shadow falls on the Moon during a full Moon.
• People sometimes travel to locations on land or even at sea to maximize the chance of viewing a total eclipse, depending on the predicted path of totality.

Scientific notation and homework tips

• Connecting notation to numbers:
  • Example: the number 1,234,567 can be written in scientific notation as
    $1.234567 \times 10^{6}$ or, approximately, $1.23 \times 10^{6}$ depending on desired precision.
• A practical example used in class:
  • Given a number with trailing zeros, e.g., 3,700,000, you can write it as
    $3.7 \times 10^{6}$
• How to input scientific notation on a calculator:
  • Method 1: enter the mantissa and exponent explicitly, e.g., $3.7 \times 10^{7}$; to compute, press the exponent function (often ^ or a dedicated x^y) and then 7, then equals.
  • Method 2: use the scientific notation shorthand, e.g., enter $3.7\text{e}7$ to represent $3.7 \times 10^{7}$; equals will yield the same value, 37,000,000.
• Practical takeaway: when doing homework, use either method; pick the one your calculator or software supports most comfortably.
• The upcoming homework two will involve these concepts, so review how to convert between standard notation and scientific notation.

Canvas, slides, and coursework logistics (where to find materials and how to submit)

• Slides and lecture notes location in Canvas:
  • Go to the Astro4B course; Week 2 (even though Week 3 may be active) and select Lecture Notes to access slides for Units 12, 13, 14, and 15; there is also a related worksheet.
• Weekly structure:
  • Week-by-week pages contain lecture notes and slides; check the corresponding unit numbers for topics covered.
• Course components mentioned:
  • Video assignments (posted midweek)
  • Short Canvas quizzes embedded in the video modules
  • Discussion posts (Discussion Post #1) in the Canvas Discussion board
  • Office hours and tutoring sessions (Sequoia Hall 238):
  • Wednesday 10:30–11:20 AM
  • Wednesday 11:20 AM–12:10 PM (second block)
• Communications: email or messages should be sent to notify students about changes (e.g., Friday hours cancellation, tutoring schedule adjustments).

Connections to foundational principles and real-world relevance

• Precession connects long-term celestial navigation and historical observations (e.g., Thuban as the pole thousands of years ago).
• Eclipses illustrate alignment geometry, angular sizes, and shadow shapes (umbra vs penumbra), tying into basic geometry and optics.
• Lunar phases illustrate the relative geometry of Sun–Earth–Moon and how illumination changes with position.
• The concept of luminosity and brightness of stars will be addressed in future lectures using size and temperature (and sometimes mass) to compute power output via stellar physics.
• The discussion foreshadows how to compare a star’s power output using the luminosity equation and how mass, temperature, and radius relate to observable brightness.

Key formulas and concepts to remember

• Angular sizes (approximate):
  $\theta<em>{\text{Moon}} \approx \theta</em>{\text{Sun}} \approx 0.5^{\circ}$
• Precession period:
  $T_{ ext{precession}} \approx 2.6 \times 10^{4} \text{ years}$
• Orbital and rotational synchronization of the Moon (approximately 30 days): $P<em>{\text{orbit (Moon around Earth)}} \approx 30 \text{ days}$$P</em>{\text{rotation (Moon on axis)}} \approx 30 \text{ days}$
  • This leads to tidal locking, so we always see the same lunar face.
• Inclination of lunar orbit relative to ecliptic:
  $\Delta i \approx 5^{\circ}$
• Distance indicator: distance Earth–Sun is 1 AU, where
  $1\text{ AU} \approx 1.496 \times 10^{11} \text{ m}$
• Luminosity of a star (based on size and temperature): $L = 4\pi R^{2} \sigma T^{4}$
  • where
    $\sigma \approx 5.670 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4}$
• Observational note: eclipses occur only when the Moon’s orbital plane aligns properly with the ecliptic plane, producing a narrow path of totality (for solar eclipses) and a broader but still limited region for total lunar eclipses.
• Observational practice: protective eyewear is essential for viewing solar eclipses safely outside of totality

Quick study tips

• Review the Moon’s phases by tracing Sun–Moon–Earth geometry and identify current phase from a night sky observation.
• Practice calculating scientific notation inputs on a calculator using both explicit exponent notation and the scientific notation shorthand (e.g., 3.7e7).
• Familiarize yourself with the terms: umbra, penumbra, ecliptic plane, and sidereal vs synodic cycles for Moon orbits.
• Be prepared to relate star luminosity to radius and temperature, and discuss how mass relates to luminosity in special cases.
• Know where to find course materials in Canvas (Lecture Notes under Week/Unit sections) and what each course component (video, quiz, discussion) requires.

Summary of next steps

• Watch the assigned video before the next Monday class; complete the short Canvas quiz embedded in the video module.
• Review Week 2 lecture notes for the final two slides of Unit 6 and the material on precession, eclipses, and lunar phases.
• Prepare questions about precession timelines, eclipse geometry, and the concept of solar and lunar eclipses for discussion during the next session.
• Attend Wednesday tutoring if you need help with the material; note the two time blocks in Sequoia Hall 238.