Astro unit 2

Ancient Babylonian, Assyrian, and Egyptian Astronomers: Beginning approximately 3000 years ago.
- Developed the 365-day calendar year.
Ancient Egyptians:
- Observed the rising time of Sirius, which corresponded with the flooding of the Nile River, influencing their agricultural practices.
Ancient Chinese:
- Created a working calendar and meticulously recorded astronomical phenomena such as comets, bright meteors, and dark spots on the Sun.
- Notably recorded guest stars—stars that would suddenly brighten and become temporarily visible to the naked eye, which are still studied for understanding stellar explosions.
Mayan Culture:
- Located in Mexico and Central America, developed a highly sophisticated calendar based on the planet Venus, made astronomical observations from dedicated sites over 1,000 years ago.
Polynesian Navigators:
- Navigated over hundreds of kilometers of ocean using stars, a skill crucial for colonizing distant islands.
British Structures:
- Utilized stones to track the motions of the Sun and Moon.

Note that Astrology will not be covered in detail, though understanding it can help clarify the origins of horoscopes.

Early Greek Concepts of Cosmology:
- Cosmology: Study of the basic structure and origin of the universe, with Greek roots.
- Ancient cosmologies blended observations of the heavens with philosophical and religious beliefs.
- By at least 2000 years before Columbus, educated individuals in the eastern Mediterranean recognized that Earth was round:
- Pythagoras (c. 570-495 BCE) suggested Earth must be a sphere.
- Aristotle (384–322 BCE) provided compelling arguments to support this idea, noting:
  - The phases of the Moon.
  - The round shadow on the Moon during lunar eclipses.

The Greeks viewed the circle as the perfect form, believing the heavens were perfect and made of perfect spheres.
- Atlas holding up the Celestial Heavens: Represented their belief in a structured universe.
Geocentric Model:
- Earth is at the center of the universe.
- Heavens consist of perfect objects moving in perfect circles.
Planetary Motion:
- Geocentric models included features like epicycles to explain retrograde motion of planets.

Aristarchus of Samos (c. 310-230 BCE):
- Advocated for a heliocentric model (Sun-centered), which was not widely accepted at the time.
Understanding Parallax:
- Greeks recognized the lack of stellar parallax as an argument against Earth's motion, presuming it was either stationary or that stars were exceedingly distant.
Eratosthenes (c. 200 BCE):
- Developed a geometric method to measure the size of Earth using observations of the Sun's position.

Ptolemy (A.D. 100–170):
- Formulated the Ptolemaic model, a highly complex geocentric model that remained in use for approximately 1,500 years.
- His work, translated into Arabic as Almagest (meaning "The Greatest Compilation"), included:
- The need for many epicycles to accurately track retrograde motion.
- Each planet orbiting in a smaller circle (epicycle) around Earth, rotating about a larger circle (deferent).
Retrograde Motion:
- Defined as the apparent temporary westward motion of a planet when Earth swings between it and the Sun.

The Sun, Moon, and stars exhibit straightforward movements consistent with an Earth-centered view, but planetary movements are more complex:
- Planets move relative to fixed stars.
- They experience changes in brightness and speed, complicating their description in geocentric terms.

Tycho Brahe (1546–1601):
- Collected precise naked-eye measurements of planetary positions, essential for resolving the heliocentric vs. geocentric debate.
- Although a proponent of Earth-centered theory, he recognized that planets revolve around the Sun.
- Developed larger and more accurate observational instruments.
Johannes Kepler (1571–1630):
- Initially sought to fit planetary orbits to circular forms based on Brahe’s observations but ultimately discovered elliptical pathways.
- His realization stemmed from addressing an 8-arcminute discrepancy from circular models.

First Law: Planetary orbits are ellipses, with the Sun at one focus.
Second Law: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
- This implies planets move faster when closer to the Sun.
- Areas formed by distances vary at different points in orbit, maintaining equivalency in area over time.
Third Law: Relates planet's orbital period to its distance from the Sun.
- Expressed as: $T^2 ext{ is proportional to } a^3$
- Where $T$ is the orbital period and $a$ is the semi-major axis of its orbit.

Newton’s First Law (Law of Inertia):
- An object at rest remains at rest, and an object in motion will maintain its velocity unless acted upon by an external force.
Newton’s Second Law:
- Defines how force affects motion: $a = \frac{F}{m}$ (acceleration of an object is proportional to the force applied and inversely proportional to its mass).
Newton’s Third Law (Action-Reaction):
- For every action, there is an equal and opposite reaction; forces between two bodies are equal in magnitude and opposite in direction.
Gravitational Attraction:
- Every mass exerts gravitational attraction, described mathematically as:
- $F = G \frac{m<em>1 m</em>2}{r^2}$
- Where $F$ is the gravitational force, $G$ is the gravitational constant, $m<em>1$ and $m</em>2$ are the masses involved, and $r$ is the distance between their centers.
Orbital Dynamics:
- As per Newton’s laws, the orbit of a planet around the Sun is an ellipse, with the center of mass of the planet-sun system at one focus of the ellipse.

Initial models of the solar system were geocentric; however, they struggled to account for retrograde motion.
The heliocentric model effectively explained retrograde motion.
Observations made by Galileo further supported the heliocentric theory by showcasing imperfections in celestial bodies, thus challenging the view of perfect heavens.
Kepler formulated three empirical laws of planetary motion, later explained through Newtonian mechanics which also described the gravitational relationship between masses.