ASTR 111: Solar System Motion and Foundations of Astronomy

Course Overview and Administrative Guidelines

Astronomy 111 section 001 (CRN 11320), titled "The Solar System," is a comprehensive introductory course scheduled for Spring 2026. Taught by Dr. Peter A. Becker, the course offers an overview of the solar system and the observational and theoretical methods of modern astronomy. Designed specifically for non-science majors seeking a deeper comprehension of the universe, the course assumes a mathematical foundation encompassing high school algebra, geometry, and trigonometry. The curriculum spans five foundational domains: the historical evolution of astronomy from prehistory through contemporary discoveries; the intrinsic properties of solar system planets and mechanisms of solar system evolution; the application of the scientific method and critical thinking; the physical nature of electromagnetic radiation and modern telescope design principles; and the key characteristics of extra-solar planetary systems. While Astronomy 112 (ASTR 112 Astronomy Lab) is strongly recommended as an accompanying laboratory component, it is treated as a separately graded course and is not mandatory for completing Astronomy 111.

Lectures take place live in Engineering Building room 1103 with an optional mask protocol. To accommodate students who are unwell, uncertain of their health status, or preferring remote attendance, each lecture is broadcast synchronously via Zoom. The corresponding Zoom link is published directly on the course Canvas website. Although the course instructor does not record lectures, enrolled students are granted explicit permission to record Zoom sessions for individual study and reference throughout the semester. Student questions during instruction are addressed either directly within the physical classroom or through the Zoom chat feature. All supplemental instructional resources, including PowerPoint lecture slides, syllabus documentation, lecture lists, exam review guides, and general astronomy or science links, are hosted on the Canvas platform. Course lectures follow the textbook Astronomy Today, 9th Edition, Volume 1, authored by Chaisson & McMillan, augmented by audio-video demonstrations, space mission datasets, and observational images from the James Webb Space Telescope, Hubble Space Telescope, Galileo, Pathfinder, Chandra, Kepler, Fermi, and Mars Rovers.

Student performance evaluation is structured around five discrete Exam Units, comprising three scheduled Semester Exams, one comprehensive Final Exam, and a cumulative Quiz average derived from $10$ Canvas-based quizzes. The primary semester grade is calculated by averaging the top $3$ Exam Unit grades out of these $5$ total units. The three mid-semester exams and the optional final exam each represent one Exam Unit, while the average score across all $10$ quizzes represents the fifth Exam Unit. All exams and quizzes are administered digitally via Canvas using the Honorlock proctoring framework, which permits testing either at home or in person at the COS Testing Center located on the Fairfax campus (accessible at www.science.gmu.edu/ttc). Exam dates are fixed: Exam 1 occurs February 19–23, Exam 2 occurs March 19–23, Exam 3 occurs April 16–20, and the optional Final Exam occurs May 11–12. Makeup examinations are strictly restricted to cases supported by a signed medical excuse from a physician or documented family emergencies. Final letter grades are assigned strictly on an exam-only basis without extra credit options, adhering to the following numeric scale: A = $90\text{--}100$, A- = $85\text{--}90$, B+ = $80\text{--}85$, B = $75\text{--}80$, B- = $70\text{--}75$, C+ = $65\text{--}70$, C = $60\text{--}65$, D = $50\text{--}60$, and F = $0\text{--}50$.

Astronomical Revolutions and the Scale of the Cosmos

Contemporary astronomy resides in a revolutionary state comparable to the transformative era of Galileo, driven by rapid advancements in observational technology and foundational theoretical paradigms. The scientific method, which established its roots during the Renaissance, continues to serve as the definitive framework for determining empirical truth about the cosmos. Major cosmological developments reveal that the universe is undergoing continuous expansion, and the rate of this expansion is actively accelerating. This cosmic acceleration is attributed to Dark Energy, a pervasive phenomenon being investigated through ongoing observational programs, including specialized studies conducted by the Hubble Space Telescope.

Understanding the spatial architecture of the cosmos requires spanning vast physical scales across many orders of magnitude. A standard reference point begins at the human scale of $1\,m$, expanding to geological landforms such as mountains and oceans at $1\,km = 0.6\,miles$, continental spans at $5{,}000\,km = 3{,}000\,miles$, and the total diameter of the Earth at $13{,}000\,km = 8{,}000\,miles$. On celestial scales, the Sun exhibits a physical diameter of $1{,}400{,}000\,km = 864{,}000\,miles$, while the mean separation distance between Earth and the Sun defines the Astronomical Unit ($AU$), equivalent to $150{,}000{,}000\,km = 93{,}000{,}000\,miles = 1.5 \times 10^8\,km$. Interstellar distances are measured in light-years, where one light-year represents $9.5 \times 10^{12}\,km = 5.9 \times 10^{12}\,miles$. In mathematical notation, exponential powers of ten simplify these expressions, where $10^3 = 1{,}000$, $10^4 = 10{,}000$, and $1.4 \times 10^4 = 14{,}000$.

Cosmic organization forms a distinct structural hierarchy, stepping outward from local to universal bounds. Earth sits within the Solar System, which resides in a local stellar neighborhood spanning a scale factor $\times 20$ times larger. Expanding by another factor of $\times 250$ reveals the Milky Way Galaxy, a spiral galaxy containing billions of individual stars. Groupings of stars and planetary systems coalesce into galactic environments, which themselves organize into the Local Group of galaxies at a scale factor of $\times 15{,}000$. On the vastest scales, galaxy clusters—which can encompass up to $1{,}000$ individual galaxies—assemble into large-scale cosmic structures, expanding the spatial domain across scale factors from $\times 10{,}000$ to $\times 1{,}000{,}000$ relative to regional galactic bounds.

Solar System Physical Properties and Classification

The Solar System consists of a central star, the Sun, surrounded by eight major planets, multiple dwarf planets, moons, and smaller celestial bodies. The primary planets are categorized into two major groups: inner terrestrial planets (Mercury, Venus, Earth, and Mars) and outer Jovian gas giants (Jupiter, Saturn, Uranus, and Neptune). Beyond or between these principal bodies reside recognized dwarf planets, including Ceres in the asteroid belt, alongside Pluto, Haumea, Makemake, and Eris in the outer reaches of the system. The spatial distribution of planets places Earth within the circumstellar habitable zone, where thermal conditions permit liquid water to persist on a planetary surface.

A comparative analysis of physical and orbital parameters highlights structural differences between solar system bodies. The Sun possesses a radius $109$ times that of Earth, a mass of $332{,}800$ Earth masses, a differential rotation period between $25$ and $36$ Earth days, a mean density of $1.410\,g/cm^3$, and $9$ listed satellite bodies in fundamental comparative datasets. Mercury orbits at $0.39\,AU$ with a radius of $0.38$ Earth radii, a mass of $0.05$ Earth masses, a rotation period of $58.8$ Earth days, no moons, an orbital inclination of $7^\circ$, an eccentricity of $0.2056$, an axial obliquity of $0.1^\circ$, and a density of $5.43\,g/cm^3$. Venus orbits at $0.72\,AU$ with a radius of $0.95$ Earth radii, a mass of $0.89$ Earth masses, a retrograde rotation period of $244$ Earth days, no moons, an orbital inclination of $3.394^\circ$, an eccentricity of $0.0068$, an obliquity of $177.4^\circ$, and a density of $5.25\,g/cm^3$. Earth orbits at $1.0\,AU$ with a radius of $1.00$ Earth radii, a mass of $1.00$ Earth mass, a rotation period of $1.00$ Earth day, $1$ moon, an orbital inclination of $0.000^\circ$, an eccentricity of $0.0167$, an obliquity of $23.45^\circ$, and a density of $5.52\,g/cm^3$. Mars orbits at $1.5\,AU$ with a radius of $0.53$ Earth radii, a mass of $0.11$ Earth masses, a rotation period of $1.029$ Earth days, $2$ moons, an orbital inclination of $1.850^\circ$, an eccentricity of $0.0934$, an obliquity of $25.19^\circ$, and a density of 3.95\,g/cm^3$.\n\nOuter solar system bodies demonstrate marked contrasts in mass, size, and composition. Jupiter orbits at 5.2\,AU$with a radius of$11$Earth radii, a mass of$318$Earth masses, a rapid rotation period of$0.411$Earth days,$16$listed major moons, an orbital inclination of$1.308^\circ$, an eccentricity of$0.0483$, an obliquity of$3.12^\circ$, and a density of$1.33\,g/cm^3$. Saturn orbits at$9.5\,AU$with a radius of$9$Earth radii, a mass of$95$Earth masses, a rotation period of$0.428$Earth days,$18$listed major moons, an orbital inclination of$2.488^\circ$, an eccentricity of$0.0560$, an obliquity of$26.739^\circ$, and a density of$0.69\,g/cm^3$. Uranus orbits at$19.2\,AU$with a radius of$4$Earth radii, a mass of$17$Earth masses, a rotation period of$0.748$Earth days,$15$listed moons, an orbital inclination of$0.774^\circ$, an eccentricity of$0.0461$, an obliquity of$97.86^\circ$, and a density of$1.29\,g/cm^3$. Neptune orbits at$30.1\,AU$with a radius of$4$Earth radii, a mass of$17$Earth masses, a rotation period of$0.802$Earth days,$8$listed moons, an orbital inclination of$1.774^\circ$, an eccentricity of$0.0097$, an obliquity of$29.56^\circ$, and a density of$1.64\,g/cm^3$. The dwarf planet Pluto orbits at$39.5\,AU$with a radius of$0.18$Earth radii, a mass of$0.002$Earth masses, a rotation period of$0.267$Earth days,$1$listed major moon (Charon), an orbital inclination of$17.15^\circ$, an eccentricity of$0.2482$, an obliquity of$119.6^\circ$, and a density of$2.03\,g/cm^3$.

Thermal profiles across the solar system dictate planetary condensation sequences and chemical composition during formation. High formation temperatures near the Sun, reaching up to $2000\,K$, restricted condensed material in the inner solar system to refractory metals, silicates, and rocky compounds. Outside the freezing threshold of water ($273\,K$) and well below the boiling point ($373\,K$), volatile substances condensed into solid ice structures. Inner terrestrial planets are thus composed predominantly of dense rock and metal, whereas outer Jovian planets incorporated vast quantities of water ice and ammonia ice, forming massive icy-gaseous worlds.

Terrestrial Sky Dynamics and Diurnal Motion

Observing the sky from Earth reveals dynamic optical effects generated by planetary rotation and orbital movement. On a clear, dark night, approximately $3{,}000$ stars are visible to the naked eye across the entire celestial sphere, though urban light pollution reduces this visible count to roughly $100$ in locations such as Fairfax. Human civilizations historically grouped these stars into patterns known as constellations. While these groupings represent chance alignments of stars situated at widely varying physical distances, constellations possess rich historical and cultural value and remain functional modern tools for segmenting and referencing specific directions in the night sky.

The primary visual motion observed in the sky is diurnal motion, which is the apparent daily rotation of celestial objects along circular paths. Diurnal motion is caused by Earth's spin on its rotation axis, causing stars, planets, the Sun, and the Moon to rise in the East and set in the West every day. Extending Earth's rotational axis outward into space establishes the North Celestial Pole and South Celestial Pole. In the Northern Hemisphere, the star Polaris sits directly adjacent to the North Celestial Pole, serving as the North Star.

The Celestial Sphere and Coordinate Systems

To map astronomical objects, astronomers project celestial bodies onto an imaginary construct surrounding Earth called the Celestial Sphere. Prominent terrestrial reference points project directly onto this sphere: Earth's equator extends to form the Celestial Equator, while Earth's rotational poles extend to define the North Celestial Pole at $+90^\circ$ and the South Celestial Pole at $-90^\circ$. Major constellations visible across the celestial sphere include Ursa Major (containing the Big Dipper), Cassiopeia, Lyra, Gemini, Virgo, Orion, Sagittarius, Pisces, and the Southern Cross. Local observational geometry defines the Zenith as the point in the sky directly above an observer, the Horizon as the circular boundary where Earth meets the sky, and the Meridian as the great circle passing through the celestial poles and the local zenith.

Positions on the celestial sphere are specified using celestial coordinates analogous to geographic latitude and longitude: Declination ($\text{DEC}$) and Right Ascension ($\text{RA}$). Declination functions as cosmic latitude, measuring angular distance north or south of the Celestial Equator. Declination values range from $-90^\circ$ at the South Celestial Pole to $+90^\circ$ at the North Celestial Pole, with the Celestial Equator set at $0^\circ$. Angular units for declination are expressed in degrees ($^\circ$), arc-minutes ($'$, where $1^\circ = 60'$), and arc-seconds ($''$, where $1' = 60''$), with a complete circular revolution spanning $360^\circ$. For instance, the star Betelgeuse in Orion has a declination recorded as $+7^\circ\,24'$ (or $+17^\circ\,24'$ in catalog indices), while Alnitak in Orion has a declination of $-1^\circ\,56'$.

Right Ascension functions as cosmic longitude, measuring position eastward along the Celestial Equator relative to a prime reference point. Because Earth rotates once every $24$ hours, Right Ascension is measured in time units: hours ($\text{h}$), minutes ($\text{m}$), and seconds ($\text{s}$), spanning a full range from $0\,\text{h}$ to $24\,\text{h}$. Exactly $1\,\text{hour}$ of Right Ascension sweeps through the field of view of a fixed telescope during each sidereal hour. For example, Betelgeuse possesses a Right Ascension of $5\text{h}\,55\text{m}$, whereas Alnitak possesses a Right Ascension of $5\text{h}\,41\text{m}$. The primary reference zero-point for Right Ascension is the Vernal Equinox, where $\text{RA} = 0\,\text{h}$ and \text{DEC} = 0^\circ$.\n\n# Solar Motion, Ecliptic, and Seasonal Cycles\n\nThe apparent annual path of the Sun across the celestial sphere is known as the Ecliptic. Earth's rotational spin axis is tilted by 23.5^\circ$relative to the perpendicular of its orbital plane around the Sun. This$23.5^\circ axial tilt causes the Sun's apparent position to move north and south across the Celestial Equator over the course of a year. The tilt directly generates Earth's seasonal cycles by altering solar zenith angles and modulating the intensity and duration of solar heating received by the Northern and Southern Hemispheres.\n\nAs Earth orbits the Sun, the shifting solar position causes different stellar regions to become visible during nighttime, creating distinct seasonal constellations. Major prominent constellations during seasonal viewing include Orion (featuring the supergiant stars Betelgeuse and Rigel, alongside the belt star Alnitak), Canis Major (containing Sirius, the brightest star in the night sky), Canis Minor (containing Procyon), Gemini (marked by Pollux and Castor), Taurus (featuring Aldebaran and the Pleiades star cluster), Auriga (containing Capella), Monoceros, and Eridanus. Key cardinal points along the ecliptic define seasonal transitions: the Vernal Equinox (\text{RA} = 0\,\text{h}$,$\text{DEC} = 0^\circ$) in spring, the Summer Solstice (where the Sun reaches maximum northern declination at$+23.5^\circ$), the Autumnal Equinox in fall, and the Winter Solstice (where the Sun reaches maximum southern declination at$-23.5^\circ).\n\n# Sidereal versus Solar Timekeeping\n\nAstronomical timekeeping distinguishes between Earth's rotation relative to background stars and its rotation relative to the Sun. A Sidereal Day is defined as the time required for Earth to complete one full 360^\circ$rotation relative to distant fixed stars. One sidereal day equals$23\,\text{hours}, 56\,\text{minutes}$of standard solar time, which corresponds to$24\,\text{sidereal hours}.\n\nA Solar Day (or Synodic Day) is defined as the time interval between consecutive solar noons, when the Sun reaches its highest point on the local meridian. One standard solar day equals exactly 24\,\text{solar hours}$. A solar day is approximately$4\,\text{minutes}$longer than a sidereal day because, while Earth rotates on its axis, it simultaneously progresses along its orbital arc around the Sun. Earth must rotate approximately$1^\circ$beyond a full$360^\circ rotation for the Sun to realign with the local meridian each day.\n\n# Lunar Mechanics, Orbital Locking, and Phase Cycles\n\nThe Moon orbits Earth with a revolution period of approximately one month. Lunar rotational motion is tidally locked to Earth, meaning the Moon's rotation period on its axis precisely matches its orbital period around Earth. Consequently, the Moon constantly presents the same hemispheric face toward Earth. The lunar orbit is non-circular, displaying measurable orbital eccentricity, and is inclined at an angle of 5.2^\circ relative to the plane of the ecliptic.\n\nThe Moon progresses through a recurring sequence of visual phases as its illuminated hemisphere shifts relative to an observer on Earth over a 29.5\text{-day}$synodic cycle. The phase progression begins at New Moon ($0\,\text{days old}$, non-visible), advancing through Waxing Crescent ($4\,\text{days old}$), First Quarter ($7\,\text{days old}$), Waxing Gibbous ($10\,\text{days old}$), Full Moon ($14\,\text{days old}$), Waning Gibbous ($18\,\text{days old}$), Third Quarter ($22\,\text{days old}$), and Waning Crescent ($26\,\text{days old}), before returning to New Moon.\n\nLunar timing incorporates two distinct orbital periods: the Sidereal Month and the Synodic Month. A Sidereal Month represents the time required for the Moon to complete a 360^\circ$orbit around Earth relative to distant background stars, lasting$27.3\,\text{solar days}$. A Synodic Month represents the time required to complete a full phase cycle (from New Moon to New Moon) or align Earth, Moon, and Sun, lasting$29.5\,\text{solar days}. The synodic month is longer due to Earth's simultaneous orbital movement around the Sun.\n\n# Eclipse Dynamics, Geometry, and Shadow Tracking\n\nEclipses occur when the Earth, Moon, and Sun achieve precise linear alignment. Because the Moon's orbital plane is inclined by 5.2^\circ relative to the ecliptic plane, monthly eclipses do not take place. Instead, alignments occur only when the Sun and Earth sit along the Line of Nodes, which is the intersection line between the lunar orbital plane and the ecliptic plane. Eclipse Seasons occur twice per year when the Line of Nodes points directly toward the Sun. Even during an eclipse season, an eclipse will only occur if the Moon is positioned at or near a node during the phase alignment.\n\nSolar Eclipses occur during New Moon when the Moon passes directly between Earth and the Sun, casting a shadow onto Earth's surface. The shadow structure consists of two main regions: the umbra, an inner dark cone where the Sun is completely obscured, spanning a central path approximately 270\,km$wide; and the penumbra, an outer shadow zone where the Sun is partially obscured, spanning approximately$7{,}000\,km$across. Total solar eclipses last up to$7.5\,\text{minutes}$at any given geographic location. Because of Earth's rotational spin and the Moon's orbital motion, the lunar shadow travels across Earth's surface from West to East at speeds of$1{,}700\,km/h, causing solar eclipses to begin at sunrise in western locations. When the Moon is near apogee (farther from Earth in its eccentric orbit), its angular diameter is smaller than the Sun's, resulting in an Annular Eclipse where a thin outer ring of sunlight remains visible.\n\nLunar Eclipses occur during Full Moon when Earth passes directly between the Sun and the Moon, casting Earth's shadow across the lunar disc. A total lunar eclipse can last up to approximately 100\,\text{minutes}$. The apparent angular diameter$\theta$of a celestial body is calculated from its linear radius$R$and distance$D using the proportional geometric relation:\n\theta = \frac{R}{D}\nRearranging this relationship yields the physical radius:\nR = \theta \times D\n\n# Axial Precession and Long-Term Astronomical Shifts\n\nEarth's rotational axis acts like a spinning top, undergoing a slow, conical motion known as precession. Precession is caused by gravitational torque exerted on Earth's equatorial bulge by the Sun and the Moon. A complete precession cycle lasts approximately 26{,}000\,\text{years}.\n\nPrecession continuously shifts the orientation of the rotational axis in space, altering which star serves as the celestial pole star. Polaris is the present North Star. Around 3000\,\text{BC}$, the pole star was Thuban in the constellation Draco. By$\text{AD } 14{,}000$(or$16{,}000\,\text{AD}$), the North Celestial Pole will point toward Vega in the constellation Lyra. Intermediate pole star transitions include Deneb in Cygnus around$8000\,\text{AD}$. Precession alters the Right Ascension and Declination coordinates of all sky objects over time, gradually shifts calendar dates associated with seasonal equinoxes and solstices, and causes the Line of Nodes to rotate, moving eclipse seasons roughly$20\,\text{days} earlier each calendar year.\n\n# Foundations of the Scientific Method and Ancient Measurements\n\nFor most of human existence, Earth was assumed to be the immobile center of the universe. Although modern humans have existed for millions of years, the scientific revolution began only a few thousand years ago, originating within the Natural Philosophy of ancient Greece. Early Greek thinkers emphasized pure thought and ideal geometric principles, disregarding real-world empirical observations as imperfect. This philosophy evolved when Aristotle (384\,\text{BC}\text{--}322\,\text{BC}) introduced systematic empirical principles: Observation, Theory, Prediction, and Testing.\n\nAristotle demonstrated the empirical scientific method through deductions regarding Earth's shape:\n1. Observation: During a lunar eclipse, Earth's shadow projected onto the Moon is always curved.\n2. Theory: Earth must possess a spherical shape.\n3. Prediction: If Earth is spherical, the apparent altitude and positions of bright stars in the sky will vary with the latitude of the observer.\n4. Testing: Subsequent observations taken across different northern and southern latitudes confirmed variable stellar positions, proving Earth's spherical geometry.\n\nEratosthenes (276\,\text{BC}\text{--}194\,\text{BC}$) utilized Aristotle's geometric framework to calculate the physical radius of Earth. On June 22 at solar noon, Eratosthenes noted that the Sun was positioned at the exact zenith in Syene (Aswan), Egypt, casting no vertical shadows. At the same date and time in Alexandria, Egypt—located$5{,}000\,\text{stadia}$directly north of Syene—the Sun measured$7.2^\circ$south of the zenith. Because$7.2^\circ$represents a fraction of a full$360^\circ circle:\n\frac{7.2^\circ}{360^\circ} = \frac{1}{50}\n\nUsing geometric proportions, Eratosthenes set the ratio of the distance between Alexandria and Syene to Earth's total circumference:\n\frac{7.2^\circ}{360^\circ} = \frac{5000\,\text{stadia}}{2 \pi R}\n\nSolving for Earth's circumference yields:\n2 \pi R = 5000\,\text{stadia} \times \left(\frac{360^\circ}{7.2^\circ}\right) = 250{,}000\,\text{stadia}\n\nSolving directly for Earth's radius R gives:\nR = \frac{5000\,\text{stadia}}{2 \pi} \times \left(\frac{360^\circ}{7.2^\circ}\right) = 39{,}789\,\text{stadia}\n\nApplying the conversion factor of 0.16\,km/\text{stadium}:\nR = 39{,}789\,\text{stadia} \times 0.16\,km/\text{stadium} = 6{,}366\,km\n\nThis calculated radius of 6{,}366\,km$aligns closely with modern satellite measurements of Earth's mean radius at$6{,}378\,km$.

Historical Geocentric Models and Planetary Motion

Ancient Greek astronomers retained a geocentric universe model—placing Earth unmoving at the center—due to three primary empirical objections to Earth's motion:

1. Reason #1: Observers on Earth experience no physical sensation of movement.

2. Reason #2: It was believed that if Earth traveled rapidly through space around the Sun, a continuous, powerful wind would sweep across the planet's surface.

3. Reason #3: Observers could detect no visible stellar parallax (the apparent shift in stellar positions caused by viewing from opposite sides of Earth's orbit), because stars are located at distances far too vast to detect parallax without modern telescopic instruments.

While stars, the Sun, and the Moon moved predictably, planetary behavior presented challenges to geocentric models. Planets ("wanderers") generally exhibit prograde motion, moving steadily eastward relative to background stars each sidereal day. However, planets periodically undergo retrograde motion, briefly slowing, stopping, and moving westward relative to background stars.

To explain retrograde motion within a geocentric framework while upholding Aristotle's principle of uniform circular motion, Ptolemy ($150\,\text{AD}$) constructed the Ptolemaic Model. In this model, each planet moves along a small circular path called an epicycle. The center of the epicycle moves along a larger circular path, called a deferent, centered near Earth. As the planet rotates along its epicycle while traveling along the deferent, the combined geometry creates a looping motion that produces apparent retrograde motion as viewed from Earth.