Lecture 3: Seasons and Constellations

Lecture 3: Seasons and Constellations (September 10, 2025)

Astronomy Context

• The constellation Cassiopeia, recognizable by its distinct 'W' or 'M' shape, is observable above the MMT observatory located outside Tucson, AZ. This constellation is circumpolar for many northern latitudes, meaning it never sets below the horizon.

• Star trails, which are arcs formed in long-exposure photographs due to the Earth's rotation, can be seen above SALT (the Southern African Large Telescope), a telescope co-owned by Rutgers, located in South Africa. The SALT is one of the largest optical telescopes in the Southern Hemisphere.

Homework and Quizzes

• Chapter Readings: Read Chapter 4, sections 4.1 to 4.4, focusing on the fundamental concepts of celestial mechanics and Earth's orbital dynamics.

• Homework Assignment: Complete Homework 2, which will cover topics related to Earth's motion and coordinate systems.

• Introduce Yourself Assignment: Due now, this assignment is designed to foster community and active participation.

• Homework Quiz explores Earth's axial alignment during different seasons:

  • A. The axis still points towards Polaris.

  • B. The axis points to the star Vega.

  • C. The axis points towards the Sun.

  • D. The axis points to some other constellation in the zodiac.

  • E. The axis is too cold to point anywhere.

  • Fact: In summer (for the Northern Hemisphere), the Earth’s axis points towards Polaris, the North Star. The direction of the Earth's axis remains nearly constant relative to the stars throughout the year.

• Reading Quiz: Focuses on the timing of the sun being directly overhead in New Jersey.

  • A. Every day around noon.

  • B. Only in the winter.

  • C. Only in the summer.

  • D. Never.

  • E. When forgetting sunscreen.

  • Fact: The correct answer is D. Never. New Jersey is located north of the Tropic of Cancer, so the sun is never directly overhead.

Earth Coordinates Review

• Latitude: Defines a position north or south of the Equator.

  • Measured in degrees from $0^ ext{o}$ (Equator) to $90^ ext{o} ext{N}$ (North Pole) or $90^ ext{o} ext{S}$ (South Pole).

• Longitude: Defines a position east or west of the Prime Meridian, which passes through Greenwich, England (longitude = $0^ ext{o}$).

  • Measured in degrees ranging from $0^ ext{o}$ to $180^ ext{o} ext{E}$ or $180^ ext{o} ext{W}$. The 180° meridian is approximately the International Date Line.

• Example: Miami's coordinates: latitude = $26^ ext{o} ext{N}$, longitude = $80^ ext{o} ext{W}$. These coordinates precisely locate Miami on the Earth's surface.

Earth's Movement in the Solar System

• Contrary to our daily perception, Earth is not stationary in space; it is constantly in motion.

• Rotation: Earth rapidly spins on its axis, completing approximately one full rotation every 24 hours. This rotation causes the cycle of day and night. At the Equator, the Earth's surface rotates at a speed of about $1670 ext{ km/hr}$.

• Orbital Movement: Earth revolves around the Sun once a year, tracing an elliptical path, at an average distance of 1 AU (Astronomical Unit), which is approximately $150 ext{ million km}$. Earth's orbital speed is nearly $107,000 ext{ km/hr}$. The plane of Earth's orbit is known as the ecliptic plane.

  • Earth's rotation axis is tilted by $23.5^ ext{o}$ relative to its orbital plane (the ecliptic) and rotates in the same direction it orbits (counterclockwise when viewed from above the North Pole).

Gravity and Earth's Motion

• Despite Earth's rapid rotation and orbital speed, gravity prevents us from flying off the Earth's surface. The gravitational force is significantly stronger than the outward centrifugal force due to rotation.

  • The calculation of acceleration due to Earth's rotation at the Equator is given by:

    $a = \frac{v^2}{R} = \frac{(1670 \text{ km/hr} \times 1000 \text{ m/km} \times \frac{1 \text{ hr}}{3600 \text{ s}})^2}{6378 \text{ km} \times 1000 \text{ m/km}} \approx 0.0337 \text{ m/s}^2$

• Gravitational acceleration (g): The acceleration due to Earth's gravity is approximately $9.8 \text{ m/s}^2$. This value is vastly greater than the rotational acceleration, which is why we remain firmly on the ground.

Reasons for Seasons

• The primary cause of Earth's seasons is the tilt of Earth’s axis relative to its orbital plane, which affects both the intensity and the directness of sunlight reaching different parts of the planet, as well as the duration of daylight.

• Key Point: The variation in distance from the Sun throughout the year (perihelion, closest approach in early January; aphelion, farthest in early July) is not a significant factor in causing seasons. The difference in distance is only about 3%, which is negligible compared to the effect of the axial tilt. In fact, when the Northern Hemisphere experiences winter, Earth is actually closer to the Sun.

Effects of Earth's Axis Tilt

• The Real Reason for the Seasons: The Earth’s inclination towards the Sun changes the angle at which sunlight strikes specific regions as Earth orbits. This results in varying heating efficiency.

  • During summer in a hemisphere, that hemisphere is tilted towards the Sun, causing sunlight to hit more directly. Direct sunlight is more concentrated, delivering more energy per unit area, and also results in longer daylight hours.

  • During winter, that hemisphere is tilted away from the Sun, causing sunlight to strike at a more oblique angle. Oblique sunlight is spread over a larger area, reducing its intensity, and leads to shorter daylight hours.

• If the axial tilt were to increase to $40^ ext{o}$ (instead of $23.5^ ext{o}$), the seasons would become significantly more intense. Summers would be hotter due to more direct sun and longer days, while winters would be colder due to more oblique sun and shorter days, leading to greater temperature extremes.

Marking Progression of Seasons

• Seasons are astronomically defined by four critical points in Earth's orbit, marked by solstices and equinoxes:

  • Summer Solstice: Occurs around June 20-21. For the Northern Hemisphere, this is when the North Pole is tilted most directly towards the Sun. The Sun reaches its highest path in the sky, resulting in the longest day of the year and direct sunlight striking the Tropic of Cancer (latitude $23.5^ ext{o} ext{N}$).

  • Winter Solstice: Occurs around December 21-22. For the Northern Hemisphere, this is when the North Pole is tilted most directly away from the Sun. The Sun reaches its lowest path, resulting in the shortest day of the year and direct sunlight striking the Tropic of Capricorn (latitude $23.5^ ext{o} ext{S}$).

  • Spring (Vernal) Equinox: Occurs around March 20-21. At this point, the Earth's axis is not tilted toward or away from the Sun, so sunlight is equal in both hemispheres. Day and night are approximately equal in length across the globe, and direct sunlight falls on the Equator.

  • Fall (Autumnal) Equinox: Occurs around September 22-23. Similar to the spring equinox, the Earth's axis is again not tilted toward or away from the Sun. Sunlight is equally distributed, leading to equal day and night lengths, and direct sunlight falls on the Equator.

The Local Sky and Celestial Movements

• An object’s altitude (its angle above the horizon, ranging from $0^ ext{o}$ to $90^ ext{o}$ at the zenith) and direction (its azimuth, measured clockwise from North, $0^ ext{o}$ to $360^ ext{o}$) specify its precise location in the local sky.

• The sun’s path across the sky throughout the year reveals seasonal changes:

  • The Sun rises precisely due east and sets precisely due west only at the spring and fall equinoxes.

  • During the solstices, the Sun rises and sets at its extreme points along the horizon; farthest north of east/west in summer and farthest south of east/west in winter.

• Latitude Impact: Seasonal changes, particularly variations in daylight hours and the Sun's maximum altitude, are much more pronounced at higher latitudes (closer to the poles) and less significant near the Equator.

Summary of Key Learning Points

• Earth rotates once every 24 hours on its axis and revolves around the Sun annually along its orbit.

• The Earth's axis is tilted by $23.5^ ext{o}$ relative to its orbital plane, influencing seasons through varying sunlight intensity and duration of daylight.

• Constellations are observable regions of the sky whose appearance and visibility are determined by the observer's geographic location (latitude) and the time of year.

Constellations & Celestial Sphere

• A constellation strictly refers to one of the 88 official regions of the celestial sphere, while recognizable patterns formed by groups of stars within or across these regions are called asterisms (e.g., the Big Dipper within Ursa Major).

• There are 88 officially recognized constellations, covering the entire celestial sphere.

• Stars reside at widely varying physical distances from Earth but appear to be projected onto an imaginary surface called the celestial sphere, which helps us visualize their positions.

• The North Celestial Pole is the point in the sky directly above the Earth's North Pole, while the South Celestial Pole is directly above the Earth's South Pole.

• The Celestial Equator represents the projection of the Earth's equator into the sky, dividing the celestial sphere into northern and southern hemispheres. The sun's apparent path, called the ecliptic, is tilted by $23.5^ ext{o}$ with respect to the celestial equator.

Angular Measurements

• Angular movements and positions in astronomy are precisely expressed using degrees, arcminutes, and arcseconds:

  • A Full Circle measures $360^ ext{o}$ (degrees).

  • 1 degree ( $1^ ext{o}$ ) is equivalent to $60 \text{ arcminutes}$ ( $60'$ ).

  • 1 arcminute ( $1'$ ) is equivalent to $60 \text{ arcseconds}$ ( $60''$ ).

Precession of the Earth

• Precession: A slow, conical wobble of the Earth’s rotation axis, caused by the gravitational torque exerted by the Sun and Moon on Earth's equatorial bulge.

• Earth completes one full precession cycle, meaning its axis traces a complete cone, approximately every 26,000 years. This phenomenon causes the celestial poles to shift over thousands of years (e.g., Polaris will not always be the North Star) and also results in the slow shift of the equinoxes against the background constellations (precession of the equinoxes).

Practical Application of Astronomical Knowledge

• Nautical Navigation: Sailors historically oriented themselves and determined their latitude using celestial objects.

  • They used Polaris (the North Star) because its angular altitude above the northern horizon is almost exactly equal to the observer's terrestrial latitude in the Northern Hemisphere.

  • Tools used for this purpose include the Marine Sextant, which measures the angle between the horizon and a celestial body, and the Mariner’s Quadrant, an older instrument for similar measurements.

Homework Assignment

• Read: Chapter 2, section 2.1 and Chapter 4, sections 4.5 to 4.7. These readings will delve deeper into orbital mechanics and related astronomical concepts.

• Complete Homework 3 before the next class. This assignment will likely incorporate knowledge from the newly detailed sections.