ASTR 110: 2.1-2.3 notes

  • 2.1 Patterns in the Night Sky

    • The sky looks different from Earth, yet patterns help us understand the cosmos.
    • Naked-eye visibility: on clear, dark nights away from light pollution, more than 2000 stars may be visible.
    • The Milky Way band: a whitish band across the sky.
    • Pattern recognition: people have long observed patterns that repeat over generations; patterns do not change noticeably over thousands of years.
    • Constellations (definition): patterns we recognize are not arbitrary; in astronomy, a constellation is a region of the sky with well-defined borders; the familiar star patterns help locate these border regions.
    • Every point in the sky belongs to some constellation; borders are official.
    • Figure 2.2 shows Orion and neighboring constellations with red borders marking official IAU borders.
    • The 88 official constellations: named and borders chosen by the International Astronomical Union (IAU) in 1928; names are Western-centric because most IAU members at the time were in Europe/US.
    • The Winter Triangle: Sirius, Procyon, Betelgeuse form a prominent asterism spanning several constellations.
    • Practical note: constellations are for locating regions; they are not physical star groups.
    • Example sky patterns: Orion, Canis Major, Canis Minor, Lepus, Monoceros, Rigel, Betelgeuse, Sirius, Procyon; these figures help orient observers.
    • Think about it / common misconceptions:
    • The Sun signs and astrology are based on ancient positions; due to precession, they no longer align with the current constellations (see 2.2 and 2.4).

  • 2.2 The Reason for Seasons

    • Earth’s tilt (axial tilt) causes seasons, not large changes in Earth-Sun distance.
    • Key concept: tilt of Earth's axis keeps pointing toward Polaris, so the orientation relative to the Sun changes over the year.
    • Two hemispheres experience opposite seasons because when one is tilted toward the Sun, the other is tilted away.
    • Step-by-step idea (as in Figure 2.15):
    • Step 1: the axis is tilted relative to the ecliptic; tilt remains pointed roughly toward Polaris throughout the year.
    • Step 2: the tilt angle causes sunlight to strike Earth at different angles over the year.
    • Step 3–4: as Earth orbits, the tilt means one hemisphere receives more direct sunlight for longer periods, creating summer, while the other receives less direct sunlight, creating winter.
    • The effect of axial tilt on seasons is the dominant cause; distance variations between Earth and Sun have only a small effect.
    • Seasonal distance effect: Earth is about 3% farther from the Sun at aphelion (July) than at perihelion (January); the distance difference is too small to drive seasons compared to tilt effects.
    • Common Misconceptions:
    • The Cause of Seasons SOP: variations in Earth-Sun distance do not drive seasons; tilt is responsible.
    • How the tilt explains the seasons (in brief):
    • When the Northern Hemisphere is tilted toward the Sun in June, sunlight is more direct and days are longer, yielding summer.
    • When tilted away in December, sunlight is less direct and days are shorter, yielding winter.
    • March and September equinoxes mark the transition points when both hemispheres receive roughly equal daylight (12 hours) and the Sun rises due east and sets due west.
    • Solstices and equinoxes:
    • June solstice (around June 21): Northern Hemisphere tilt toward Sun; longest/most-direct sunlight; Sun rises farthest north of due east and sets farthest north of due west; longest daylight.
    • December solstice (around December 21): Northern Hemisphere tilt away from Sun; shortest daylight; Sun rises and sets farthest south of due east/west.
    • March equinox (around March 21): start of spring in Northern Hemisphere; Sun rises due east; daylight equals night.
    • September equinox (around September 22): start of fall in Northern Hemisphere; Sun rises due east; daylight equals night.
    • Dates and times vary by up to a couple of days due to the leap-year cycle; leap years are used to keep solstices/equinoxes around the same dates.
    • High Noon concept: Sun is not directly overhead except within the Tropics (between 23.5°S and 23.5°N); at most locations, the Sun is never at zenith.
    • How the Sun’s path changes through the year:
    • The June solstice yields the Sun’s longest/highest path in the Northern Hemisphere.
    • The December solstice yields its shortest/lowest path.
    • First Days of Seasons: historically, the solstices/equinoxes mark the first days of seasons, but the warmest days often occur 1–2 months after the solstice due to time needed to heat the ground/ocean.
    • Seasons Around the World:
    • High latitudes experience more extreme seasons (e.g., Vermont vs. Florida).
    • Arctic Circle: Sun above horizon all day on the June solstice; polar day persists for a period.
    • Antipodal regions (South Pole) have opposite daylight patterns.
    • Equatorial regions experience rainy and dry seasons rather than four distinct seasons; rainfall patterns follow the Sun’s height.
    • Why Southern Hemisphere seasons are milder (on Earth):
    • Most land lies in the Northern Hemisphere, while most ocean lies in the Southern Hemisphere.
    • Oceans heat up/cool down more slowly than land, moderating climate; larger oceans in the Southern Hemisphere reduce seasonal extremes.
    • Why distance from the Sun does not primarily drive seasons: even with orbital distance variation, tilt dominates; on other planets with different orbital shapes, distance can be more influential (e.g., Mars).
    • How the orientation of Earth’s axis changes with time:
    • Precession: a slow wobble that changes axis orientation in space while tilt remains roughly constant (~exttilt≈23.5extoext{tilt} \approx 23.5^ ext{o}).
    • Precession cycle length: about Pextprec≈26,000 yearsP_{ ext{prec}} \approx 26{,}000\text{ years}.
    • Effect: solstices/equinoxes drift to different constellations over millennia; the same solstice/equinox dates occur with different background stars.
    • Tropic of Cancer: due to precession, the Sun’s position at solstices migrates relative to the background constellations; the Tropic of Cancer lies at 23.5exto23.5^ ext{o} north of the equator and marks historical solstice-stellar positions (e.g., the June solstice used to occur in Cancer and now occurs in Gemini).
    • Think about it prompts (study-checks):
    • Was Polaris the North Star in ancient times? Explain. (Answer: No; due to precession, the North Star changes over thousands of years; Polaris is near the current north, but anciently different stars were closest to the pole.)
    • What causes the seasons if not primarily distance to the Sun? (Answer: axial tilt and the changing angle of sunlight with respect to Earth as it orbits the Sun.)
    • What is the relationship between precession and astrology? (Answer: Precession shifts which constellation the Sun is in at a given time of year, so astrological Sun signs no longer align with current constellations.)

  • 2.3 The Moon, Our Constant Companion

    • The Moon is the brightest object after the Sun and travels with the Earth around the Sun.
    • The Moon’s phases result from changing Moon-Earth-Sun geometry as the Moon orbits Earth about every 29½ days, i.e., the synodic month is approximately Textsynodic≈29.53 daysT_{ ext{synodic}} \approx 29.53\text{ days}.
    • The Moon’s orbit appears to move eastward through the zodiac (similar to the Sun’s apparent motion through the year) but on a much shorter timescale: one full lunar orbit per month, i.e., about 360exto360^ ext{o} per month relative to Earth.
    • The term month originates from the Moon's cycle: "moonth".
    • The Sun-Earth-Moon geometry: sunlight comes from the same direction to both Earth and Moon over the course of a month, so the Moon’s phases are a result of the Moon's position relative to the Sun as seen from Earth.
    • Figure 2.21 (1-to-10-billion scale): Sun is about 15 m15\text{ m} away in this scale; the Sun–Moon–Earth geometry means sunlight comes from essentially the same direction along the Moon’s orbit.
    • The Moon’s distance from Earth: about d≈3.56×105 kmd \approx 3.56\times 10^5\text{ km} (356,000 km) on average; this large distance minimizes parallax differences in sunlight direction across the Moon’s orbit.
    • Demonstration for understanding phases (Figure 2.22): a simple outdoor demonstration using a ball and sunlight to visualize how the Moon’s phases arise from the Sun-Earth-Moon geometry.
    • The Moon’s phases cycle includes New Moon, First Quarter, Full Moon, Last Quarter, and intermediate crescents/gibbous phases, corresponding to Moon positions along the Earth-Sun line.
    • Practical note: because the Moon orbits Earth, its rising/setting times shift roughly 50 minutes later each day, causing its phases to appear on different days each month.
    • The Moon’s orbital plane is inclined about 5.1exto5.1^ ext{o} to the ecliptic (Earth’s orbital plane), which explains why eclipses do not occur every month (requires alignment of Sun, Moon, and Earth).
    • Additional context (if included): the Moon’s perigee and apogee vary its apparent size slightly, affecting the apparent brightness and duration of total or near-total solar eclipses.
    • Summary takeaway: the Moon’s phases are driven by relative geometry to the Sun; the cycle’s period is about 29.5 days (synodic), and the Moon’s path across the sky is an eastward drift through the zodiac each month.

  • Connections and broader context

    • Observational astronomy emphasizes a hands-on approach: observing the sky outside, noting star patterns, and connecting to larger cosmological principles.
    • The historical development of astronomical ideas (patterns, seasons, and Moon phases) connects to concepts such as axis tilt, precession, and orbital dynamics.
    • Real-world relevance: understanding seasons informs agriculture, climate, and daily life; Moon phases influence tides and cultural calendars; knowledge of precession connects historical astronomy to modern celestial navigation.

  • Formulas and numerical references (LaTeX)

    • Axial tilt of Earth: ϵ≈23.5∘\epsilon \approx 23.5^\circ
    • Solstices/equinoxes approximate dates:
    • June solstice: around June 21\text{June } 21
    • December solstice: around December 21\text{December } 21
    • March equinox: around March 21\text{March } 21
    • September equinox: around September 22\text{September } 22
    • Orbital cycle lengths:
    • Earth’s precession period: Pprec≈2.6×104 yrP_{\text{prec}} \approx 2.6\times 10^4\ \text{yr}
    • Moon’s synodic month (Earth-Sun-Moon alignment): Tsynodic≈29.53 daysT_{\text{synodic}} \approx 29.53\ \text{days}
    • Moon’s sidereal month (Moon’s orbit relative to the stars): Tsidereal≈27.32 daysT_{\text{sidereal}} \approx 27.32\ \text{days}
    • Distance scales (illustrative): Sun distance on scale ≈ 15 m15\ \text{m}; Moon-Earth distance ≈ 3.56×105 km3.56\times 10^5\ \text{km}
    • Arctic daylight extremes and latitude references: Arctic Circle at ≈66.5∘\approx 66.5^\circ latitude; Tropic of Cancer at ≈23.5∘N\approx 23.5^\circ\text{N}
    • Earth-Sun distance variation: Earth is about ∼3%\sim 3\% farther from the Sun at aphelion than at perihelion; the effect on seasons is minor compared to tilt.

  • Visuals and terminology to remember

    • Milky Way: prominent band of the sky; visible on clear, dark nights away from light pollution.
    • Constellations: defined by official borders; used to locate regions of the sky; 88 official IAU constellations.
    • Analemma: the figure-8 path of the Sun in the sky over a year due to tilt and orbital eccentricity (as seen in Fig. 2.17).
    • Precession: slow wobble of Earth’s axis that changes the background constellations seen at solstices/equinoxes over thousands of years; axis tilt remains roughly constant.

  • Extra notes (context from the transcript)

    • The chapters emphasize an experiential approach: look up, observe, and relate sky patterns to cosmic concepts.
    • Historical and cultural notes include the evolution of asterisms into formal constellations and the IAU’s role in defining official borders.
    • There are additional graphics and figures (e.g., Fig. 2.16, 2.17, 2.18) describing Sun paths, analemma, and the solstices/equinoxes for Northern Hemisphere observers, along with latitude-specific differences.