Park Tutoring, PARC Resources, and Unit 6 & 10 Astronomy Notes

Park Tutoring and PARC Resources

• Park tutoring options on campus include Park after dark (PARC) from 5:00 PM to 7:00 PM, Monday through Thursday.
  • Emily is expected to head the after-hours PARK session.
  • If you are totally busy up to 5:00 PM, you can drop in for after-hours tutoring and possibly get help from Natalie.
  • It is implied that there may be fewer tutors during Park after dark.
• The main message: Park is a free tutoring resource on campus. Contact details and scheduling:
  • Appointments are recommended because they lock in a time and reduce waiting: walk-ins may require waiting or may not be available if tutors are helping other students.
  • The tutor(s) mentioned include Natalie (after-hours), with Sam and Emily as other tutors available for astronomy and class-related help.
• How to access and promote Park:
  • Sam and Emily are students who can help with astronomy, and they also provide support for other questions you might have.
  • The instructor will post information on Canvas and provide a PDF in-class activity, which is also accessible via Canvas.
• Encouragement to use Park for exam prep:
  • If you are planning on studying for Exam One (end of the month), contact Sam or Emily for possible free tutoring.
  • The resource is useful not only for this class but for other classes as well.
• Communication and contact details:
  • csus.edu/park is the Park resource page (includes social media: Instagram and Facebook).
  • The instructor will post the information on Canvas for easy access.
• Acknowledgments:
  • Sam and Emily are former students of the instructor who did well and are enthusiastic about astronomy; they can answer astronomy questions well.

Today’s Class Plan and Context

• The class plan: Begin Unit 6 (The Year) focused on the annual motion of the Earth around the Sun and how that relates to the ecliptic plane and the zodiac.
• The weekly unit order: This week's units are 6, 10, 6, 8, 10, and 11. The plan is to cover 6 first, then 10, then 8, and 11, with a math-focused segment toward the end of class.
• Assessment: A short Canvas quiz will be given in the last 3–5 minutes of class, similar to a quiz from the prior Friday. If devices are unavailable, the instructor will display questions and students can answer on paper.
• Class logistics:
  • Dim the lights for a moment to show a demonstration, then resume with the lecture.
  • Slides and an in-class activity PDF are available on Canvas; the activity will be discussed briefly in class.

Review of Last Class: The Night Sky and the Ecliptic Plane

• Night sky observations in Sacramento include light pollution; porch and street lights should be aimed downward to reduce glare and improve sky visibility.
• The Moon is almost full tonight; the Milky Way is not visible in Sacramento but can be seen in darker, desert locations.
• A rotation to the north helps identify major asterisms and constellations:
  • Asterism: The Big Dipper (part of Ursa Major, the Great Bear). The two pointer stars (in Ursa Major) point toward Polaris.
  • Polaris is near the North Celestial Pole, which is close to the location of Polaris.
  • Ursa Minor (the Little Bear) contains Polaris, though it may be hard to see without clear skies.
• Constellation context: 88 constellations exist; the zodiacal constellations lie on the ecliptic plane, which is the Sun–Earth–planet orbital plane.
• The ecliptic plane concept:
  • The Sun and the planets all orbit roughly in the same plane—the ecliptic.
  • The zodiacal constellations (e.g., Cancer, Gemini, Taurus, Aries, Pisces, Aquarius, etc.) lie along the ecliptic.
• The key takeaway: The plane of the ecliptic defines the path of the Sun across the sky and the apparent positions of the planets and zodiacal constellations.

The Year, the Earth’s Tilt, and Seasonal Motion

• Core idea: The year is driven by Earth’s orbit around the Sun; however, the apparent position of the Sun in the sky changes due to Earth's tilt, not primarily due to distance variation.
• Earth's axial tilt: The rotational axis is inclined by approximately $23.5^ ext{o}$ relative to the perpendicular to the ecliptic plane. This tilt is not unique to Earth; other planets (e.g., Mars) have their own tilt values.
• Seasons are caused by this tilt, not by distance changes alone. The distance from Earth to the Sun changes a little over the year, but the tilt has a much larger impact on insolation and day length.
• Northern Hemisphere perspective: Summers are hot and winters are cold due to tilt and longer daylight in summer, not primarily due to being closer to the Sun.
• A common misconception highlighted: Summers are warmer because the Earth is closer to the Sun is incorrect; the tilt and longer daylight are the main causes.
• Visual demonstration (light-flashlight worksheet): An at-home or in-class experiment with a flashlight and a cardboard to illustrate how tilt concentrates sunlight:
  • Four scenarios A, B, C, D were discussed to show how tilt affects light concentration.
  • Scenario C (most direct illumination) yields the brightest light on the target; Scenario D yields the dimmest light due to the greatest tilt.
  • The analogy explains why tilt affects the intensity of sunlight on the ground.
• Two important seasonal effects from tilt:
  • Summer: In the Northern Hemisphere, the ground receives sunlight more directly and for a longer portion of the day.
  • Winter: The tilt reduces direct sunlight and shortens the daylight period.
• Equinox concept: The year includes two equinoxes near March and September (approximately March 21 and September 22):
  • These are the days when the Sun is directly above the equator, and day length is roughly equal to night length.
• Solstices: The year also includes summer and winter solstices (approximately June 21 and December 21):
  • Solstices mark the longest and shortest days of the year in a given hemisphere.
• Sunrise and sunset directions:
  • The Sun rises in the East and sets roughly in the West, but the exact azimuth changes seasonally.
  • In summer, sunsets are farther north of due West; in winter, sunsets are farther south of due West.
  • By Sept 22 (the autumnal equinox), the Sun sets more directly due West.
• Variation by latitude:
  • At higher latitudes (e.g., North Pole), summers can have continuous daylight (midnight sun) and winters can have continuous darkness.
  • At the equator, day length remains nearly constant year-round.

Linking the Year to Geometry: The Role of the Ecliptic and the Tilt

• The ecliptic is the plane of Earth’s orbit around the Sun; the tilt of Earth’s axis relative to this plane creates seasonal changes in insolation and day length.
• The Sun’s apparent path in the sky changes with the season: high in the sky in summer, low in winter.
• The ecliptic also defines the path of the Sun through the zodiacal constellations; this ties the concept of the year to observable star positions.
• The relationship between the Sun’s apparent position in a given month (e.g., Taurus in June, Cancer around August) illustrates the Sun’s annual motion against the backdrop of the stars; the exact constellations associated with each month shift slowly over centuries due to axial precession and other factors.
• A brief look ahead: Unit 10 will cover geometry of the Earth–Moon–Sun system, and there will be discussion of historical measurements (e.g., Aristarchus, Eratosthenes) and early attempts to determine sizes and distances in the solar system.

Unit 10: Geometry of the Earth–Moon–Sun and Dimensional Measurements

• Historical context: Aristarchus used eclipses to estimate distances and sizes; Aristarchus also attempted to estimate the distance to the Sun and the Sun’s size. Eratosthenes measured the Earth’s diameter using shadows in wells/obelisks in Egypt.

• The key mathematical task introduced: determining an object’s size given distance to the object and the angular size it subtends in the sky.

• The fundamental relationship (small-angle approximation):

  • When an object subtends angle

  
  \alpha
  
  in the sky and the distance to the object is $D$, the linear size $L$ is approximately:

  
  L \approx D \cdot \frac{\alpha}{57.3}
  

  • Here, $\alpha$ must be in degrees, and 57.3 is the approximate conversion factor from degrees to radians (since $1 \text{ rad} = \frac{180}{\pi} \text{ deg} \approx 57.3\text{ deg}$).
  • A more general form relates size to distance and angle in radians: $L \approx D \cdot \alpha\quad(\text{with }\alpha\text{ in radians})$.

• Practical note for students:

  • You will use the equation above in Homework 2 and on the exam; memorize not the derivation but how to apply it.
  • If you prefer, you can derive from the radian definition: angular size in radians ≈ linear size / distance for small angles.

• In-class demonstration and example problem:

  • Example provided: If the distance to a galaxy is $D = 2.200 \times 10^{6} \text{ ly}$ and the angular size is $\alpha = 0.05^{\circ}$, then

  
  L = D \cdot \frac{\alpha}{57.3} = 2.200 \times 10^{6} \cdot \frac{0.05}{57.3} \approx 1.919 \times 10^{3}\text{ ly}
  

  • Therefore, the galaxy’s diameter is about $1.92 \times 10^{3} \text{ ly}$ (approximately 1,919 ly).

• Unit handling and conversions:

  • The distance D can be given in various units (light years, kilometers, AU, etc.). The same formula applies as long as units are consistent.
  • In the example, converting the result to plain light-years yields about 1.9×10^3 ly.

• Calculator advice and exam readiness:

  • Students are advised to bring a scientific calculator to the exam; calculators can be borrowed or used during in-class activities.
  • Online calculators (e.g., Google calculator) can be used to verify computations during class.

• Additional practical note:

  • The instructor shared an anecdote about using this method to estimate the size of a palm tree from a distance, illustrating how size-distance-angle relationships work in everyday contexts.

• Summary of the method: to find a linear size L of an object when you know distance D and angular size α:

  
  L = D \cdot \frac{\alpha}{57.3}
  
  with α in degrees.

Worked Galaxy Example and Unit Clarifications

• Example recap: Given D = 2{,}200{,}000 light years and α = 0.05°, compute L:
  • $L = 2{,}200{,}000 \cdot \frac{0.05}{57.3} \approx 1.919 \times 10^{3} \text{ ly}$ (≈ 1,919 ly).
  • This demonstrates how angular size translates into a physical size via the distance and the small-angle approximation.
• Alternate computation order is acceptable: compute (D × α) ÷ 57.3 or α ÷ 57.3 × D; both yield the same result.
• Final note on units: the result’s units depend on the unit chosen for D. If D is in light years, L will be in light years; if D is in kilometers, L will be in kilometers, etc.

Practical Takeaways for Exam Preparation

• Remember the key relation for angular size: $\boxed{L = D \cdot \frac{\alpha}{57.3}}$
  • α must be in degrees; 57.3 is the degree-to-radian conversion constant (approximately).
• Use this to estimate sizes of astronomical objects when given distance and angular size; practice with different units and conversions.
• Appreciate the conceptual separation between tilt-driven seasons and distance-driven temperature changes: tilt controls insolation concentration and day length, which together create seasonal patterns.
• Be familiar with: the ecliptic plane, zodiacal constellations, major asterisms (Big Dipper in Ursa Major, Little Dipper in Ursa Minor), and Polaris as the North Star near the north celestial pole.
• Know the approximate values for key seasonal markers:
  • Equinoxes: around March 21 and September 22
  • Solstices: around June 21 and December 21
• Understand that the Sun’s apparent path changes with seasons, being higher in the sky and with longer daylight in summer, and lower with shorter daylight in winter.
• Recognize that at the poles, daylight can be continuous in summer and darkness in winter; at the equator, day length remains relatively constant.
• Prepare for Canvas quizzes: two quick questions may be asked; be ready to discuss or write answers based on the lecture.
• Resources:
  • Park (PARC) tutoring resource: csus.edu/park; Instagram; Facebook
  • Canvas postings will include slides and in-class activity PDFs
  • For help with astronomy questions, Sam and Emily are available; they are former students who are enthusiastic about astronomy.

Quick Reference: Key Names and Concepts Mentioned

• Park tutoring and PARC: free tutoring resource on campus; schedule and contact details provided.
• Emily and Sam: tutors; Emily may head Park after dark; Sam also assists with astronomy.
• Natalie: potential tutor during Park after dark sessions.
• Ursa Major: the Great Bear, contains the Big Dipper asterism.
• Big Dipper: the asterism used as a pointer to Polaris (via its two pointer stars).
• Polaris: near the North Celestial Pole; highlighted as a guiding star for north orientation.
• Ursa Minor: the Little Bear (the Little Dipper) surrounding Polaris.
• Taurus, Cancer, Gemini, Taurus, Aries, Pisces, Aquarius: zodiacal constellations lying on the ecliptic plane.
• Aristarchus, Eratosthenes: historical figures referenced for early astronomical measurements (distance and size estimates; Earth’s diameter).
• Aristarchus’ and Eratosthenes’ contributions: foundational historical context for measuring sizes and distances in astronomy.
• L = D × α / 57.3: angular size formula used to compute a linear size from distance and angular size (α in degrees).

Note: If you want this broken into more granular sections or tailored to a specific exam subset (e.g., only Unit 6 and Unit 10 math), tell me which parts to expand or compress for you.