Astronomy: From Geocentric to Newtonian Mechanics – Vocabulary Flashcards

Ancient Astronomy

Ancient civilizations observed the skies.
Many built structures to mark astronomical events.
Example: Summer solstice sunrise at Stonehenge in southern England.

The Weekdays Named After Astronomical Objects

The days of the week are named after seven astronomical objects visible to ancient peoples.
Table of day ↔ object ↔ name forms in various languages:
- Monday — Moon — Dies Lunae — lunes — lundi — lunedi
- Tuesday — Mars — Dies Martis — martes — mardi — martedi
- Wednesday — Mercury — Dies Mercurii — miércoles — mercredi — mercoledì
- Thursday — Jupiter — Dies Jovis — jueves — jeudi — giovedì
- Friday — Venus — Dies Veneris — viernes — vendredi — venerdì
- Saturday — Saturn — Dies Saturni — sábado — samedi — sabato
- Sunday — Sun — Dies Solis — domingo — dimanche — domeni

The Geocentric Universe

Celestial objects observed by ancient astronomers:
- Sun, Moon, Stars, Comets, Five planets: Mercury, Venus, Mars, Jupiter, Saturn

Objects Move in the Sky

General motions:
- Sun, Moon, and stars rise in the east and set in the west.
- Planets move with respect to fixed stars (usually west to east).
- Planets show changes in brightness and speed.
- Planets undergo retrograde motion — they appear to move in a reverse direction (east to west) relative to the stars.

Planets and Retrograde Motion (Visual Concept)

The apparent retrograde motion can be understood via the relative motions of Earth and the other planets against a fixed stellar backdrop.
Diagrams show Mars’ apparent motion against the ecliptic plane, with the Sun-Earth-planet geometry producing retrograde episodes.

Planet Types and Qualifying Locations

PLANET ARE CATEGORIZED BY:
- Type: Inferior or Superior
- Location from Earth: Opposition, Conjunction, Inferior conjunction, Superior conjunction
PLANET TYPES:
- Inferior planets: Mercury, Venus (orbits closer to the Sun than Earth)
- Superior planets: Mars, Jupiter, Saturn (orbits farther from the Sun than Earth)
PLANET LOCATIONS (definitions):
- Opposition: from Earth, look away from the Sun (planet opposite the Sun in the sky)
- Conjunction: from Earth, look toward the Sun (planet near the Sun in the sky)
- Inferior conjunction: inferior planets on our side of the Sun
- Superior conjunction: inferior planets on the far side of the Sun

Early Observations of Planet Movement

Inferior planets never appear far from the Sun in the sky.
Inferior planets are brightest near inferior conjunction.
Superior planets are not tied to the Sun and are brightest at opposition.

Ye Olden Models of the Solar System

Early models placed the Earth at the center (Geocentric).
Ptolemaic geocentric model: Earth-centered solar system with epicycles to reproduce observed planetary motions.
These models required many compensating complications to match observations.

The Heliocentric Model of the Solar System

Nicolaus Copernicus proposed a Sun-centered model.
Key idea: The Sun is at the center; the Moon orbits Earth; planets orbit the Sun.

The Copernican Revolution

Core claims:
- Earth is not the center of everything.
- The center of Earth is the center of the Moon’s orbit.
- All planets revolve around the Sun.
- The stars are very far away.
- The apparent motion of the stars around the Earth is due to the Earth’s rotation.
- The apparent motion of the Sun around the Earth is due to the Earth’s rotation.
- Retrograde motion of planets is explained by Earth’s motion around the Sun.

The Birth of Modern Astronomy

Telescope invented around 1600 (historical note).
Galileo Galilei built his own telescope and used it to collect data in 1609.
Galileo’s observations provided new data in support of Copernicus’ heliocentric model.

Galileo’s Observations

Moon has mountains and valleys (lunar topography).
Sun has sunspots and rotates.
Saturn has rings (visible due to telescope observations).
Jupiter has moons (Galilean moons).
Venus shows phases (observations inconsistent with a strictly geocentric model).

The Phase of Venus

Phases of Venus cannot be explained by the geocentric (Ptolemaic) model.
In a Sun-centered model, Venus exhibits a full sequence of phases (new, crescent, quarter, gibbous, full) as it orbits the Sun.
Visual representations include comparisons between the Sun-centered model and Ptolemy’s model, illustrating why geocentric models fail to explain Venus’ phases.

Kepler’s Laws of Planetary Motion

Tycho Brahe made extensive astronomical observations (star catalog, supernova, comets, lunar orbit).
Johannes Kepler used Tycho’s data to develop three laws of planetary motion.

Kepler’s Laws (Overview)

Law 1 (Ellipse): Planetary orbits are ellipses with the Sun at one focus.
- If the two foci coincide, the ellipse becomes a circle.
- The more distant the two foci are from each other, the more elongated (eccentric) the ellipse.
- Key ellipse-related terminology:
- Focus, major axis, semimajor axis, eccentricity e
Law 2 (Equal Areas): An imaginary line joining the Sun and a planet sweeps out equal areas in equal times.
- Planets move fastest when nearest the Sun (near perihelion).
Law 3 (Harmonic Law): The square of the orbital period is proportional to the cube of the semimajor axis:
- P^2 = a^3 where P is the orbital period and a is the semimajor axis.
- In practice, inner planets have shorter periods and move faster; outer planets have longer periods and move slower.

Properties of Planetary Orbits (Ellipse Details)

Eccentricity e measures how round an ellipse is (0 = circle, 0 < e < 1 = ellipse).
Perihelion distance: r_ ext{peri} = a(1 - e)
Aphelion distance: r_ ext{apo} = a(1 + e)
Major axis length, semimajor axis a, and radius at perihelion/aphelion relate to orbital geometry.

Kepler’s Laws in Action

The imaginary Sun–planet line sweeps out equal areas in equal times (Law 2).
Speed variation: planets move faster near the Sun (perihelion) and slower farther away (aphelion).
Law 3 connects orbital size to orbital period: P^2 = a^3 (in appropriate units).

The Dimensions of the Solar System

Astronomical Unit (AU): mean distance between Earth and the Sun.
1 AU is a convenient scale for planetary distances.
History of distance measurements:
- First measured during transits of Mercury and Venus using triangulation.
- Distances can also be measured with radar-ranging to planets (reflected radar signals).

Newton’s Laws and Gravitation

Newton’s laws describe how objects interact:
- 1st Law (inertia): An object at rest stays at rest, and an object in motion stays in straight-line motion unless acted on by an external force.
- 2nd Law (F = ma): Acceleration is proportional to applied force and inversely proportional to mass.
- 3rd Law (action-reaction): Every action has an equal and opposite reaction.
Gravity as a universal force:
- On Earth’s surface, gravity is approximately constant, directed toward the Earth's center (g ≈ 9.8 m/s^2).
- For two masses, gravitational force follows the inverse-square law:
- F = rac{G \, m1 \, m2}{r^2}
- The gravitational constant is G = 6.67 imes 10^{-11} \, \mathrm{N\,m^2/kg^2}.
How gravity can be reduced:
- Reduce one or both masses, or increase the distance between them: F ext{ scales as } 1/r^2.

Newtonian Mechanics and Planetary Orbits

Kepler’s laws emerge as a consequence of Newton’s laws.
Kepler’s first law is refined: the orbit of a planet around the Sun is an ellipse with the center of mass of the planet–Sun system at one focus.
The same reasoning explains why Pluto is not classified as a planet: the center of mass of the Pluto–Charon system lies outside Pluto.
For the Earth–Moon system, the center of mass lies inside the Earth (Earth is much more massive).

Mass of the Sun from Orbital Dynamics

The gravitational force governing planetary orbits allows calculation of the Sun’s mass if you know the orbit.
General relation (derived from dynamics of a central gravitational field):
M_ ext{sun} = rac{4\pi^2 \, a^3}{G \, P^2}
Using Earth's orbit data yields M_ ext{sun} \approx 2.0 \times 10^{30} \, \text{kg}.

Escape Speed

Escape speed is the minimum speed needed to escape a planet’s gravitational field.
If speed is lower, the body either falls back or remains bound in orbit.
Escape velocity formula:
v_ ext{esc} = \sqrt{\frac{2 \, G \, M}{r}}

Galilean Milestones and Features

Galileo’s role in modern astronomy:
- Built a telescope (and improved observations) around the early 1600s, with key observations around 1609 onward.
- Observations provided strong support for the Copernican model.
Name-that-feature slides (interactive practice) illustrate recognition of solar-system objects (Sun, planets, Moon, Earth) and features of their orbits.

Phases of Venus and Evidence for Heliocentrism

Illustration of Venus phases demonstrates a Sun-centered arrangement:
- In a geocentric model (Ptolemy), Venus would not show a full phase progression.
- In a heliocentric model, Venus’ phases (new, crescent, quarter, gibbous, full) appear as Venus orbits the Sun from inside Earth's orbit.
- The comparison highlights why the geocentric model cannot explain Venus’ phases.

Kepler’s Laws in Context

Kepler’s laws provided a quantitative description of planetary motion that matched observational data and laid groundwork for Newtonian mechanics.

Quick Review: Key Formulas and Concepts

Elliptical orbits with Sun at a focus:
- Perihelion distance: r_ ext{peri} = a(1 - e)
- Aphelion distance: r_ ext{apo} = a(1 + e)
Kepler’s Third Law (in appropriate units): P^2 = a^3
Law of equal areas (Kepler’s Second Law): imaginary Sun–planet line sweeps out equal areas in equal times.
Newton’s Law of Gravitation: F = \frac{G \, m1 \, m2}{r^2} with G = 6.67 \times 10^{-11} \ \mathrm{N\,m^2/kg^2}.
Mass of the Sun from planetary motion:
- M_ ext{sun} = \frac{4\pi^2 \, a^3}{G \, P^2} \approx 2.0 \times 10^{30} \ \text{kg}.
Escape speed: v_ ext{esc} = \sqrt{\frac{2 \, G \, M}{r}}.
1 AU is the mean Earth–Sun distance and serves as the unit distance for planetary orbits.

Connections to Foundational Principles and Real-World Relevance

The Copernican Revolution reoriented science toward a Sun-centered framework, influencing astronomy, physics, and the scientific method.
Newtonian mechanics unified celestial and terrestrial motion under universal laws, enabling quantitative predictions of planetary positions, satellite orbits, and spacecraft trajectories.
Modern astronomy relies on the interplay between observational astronomy (Galileo’s telescopic data) and theoretical frameworks (Kepler’s laws, Newtonian gravity).

Ethical, Philosophical, and Practical Implications

Demonstrated that common-sense assumptions about cosmovision could be revised in light of data (scientific humility).
Showed that simpler, more elegant theories (heliocentrism) can supersede complicated but accurate-but-clunky models (epicycles in geocentrism).
Highlighted the importance of experimental validation (telescopic observations) in establishing scientific truths.

Quick Quiz Reference (from transcript)

Copernicus’s great contribution: best answer is to create a detailed model of our solar system with the Sun rather than Earth at the center.
Galileo’s not observed by Galileo: Stellar parallax.
Coming up: Topic Discussion due; respond to prompts and peers.

Additional Notes (From the Transcript Structure)

The Contents include: Ancient Astronomy, Geocentric vs. Heliocentric models, Laws of Planetary Motion, Dimensions of the Solar System, Newton’s Laws, Newtonian Mechanics, and weighing the Sun.
The material integrates historical development with fundamental physics equations and observational milestones to illustrate how modern astronomy emerged.