2-6 astronomy

Scientific Hypothesis

A collection of ideas that explain observations and generate testable predictions.

Scientific Model

A mathematical or logical framework describing reality based on hypotheses that have survived experimental testing.

Scientific Theory

A series of thoroughly tested hypotheses forming a self-consistent and accurate description of nature capable of verified predictions.

Scientific Law

Proven theories that have stood the test of time and possess broad applicability.

Eratosthenes (~200 BC)

Calculated Earth's circumference to be $\sim 250{,}000\text{ stadia}$ ($\sim 42{,}000\,\text{km}$) by measuring the $7^\circ$ difference ($\frac{1}{50}$th of a circle) in Sun angles between Alexandria and Syene.

Aristarchus of Samos (~280 BC)

Proposed geometric methods to estimate Sun and Moon distances and used lunar eclipse shadow duration to calculate relative sizes.

Relative Sizes of Celestial Bodies

The Sun is $\sim 100\text{ times}$ larger than Earth ($109\times$), Earth is $\sim 4\text{ times}$ larger than the Moon (Moon radius $\sim 1{,}737\,\text{km}$ vs. Earth $\sim 6{,}371\,\text{km}$), and the Sun is $\sim 400\text{ times}$ larger than the Moon.

Astronomical Unit (AU)

The average distance between Earth and the Sun, equal to approximately $1.5 \times 10^8\,\text{km}$.

Light-Year (ly)

The distance light travels in one year, equal to $9.46 \times 10^{12}\,\text{km}$.

Parsec (pc)

The distance at which $1\,\text{AU}$ subtends an angle of $1\text{ arcsecond}$; equal to $3.26\text{ light-years}$ or $3.09 \times 10^{13}\,\text{km}$.

Speed of Light (c) Travel Times

Light travels at $\sim 3 \times 10^5\,\text{km/s}$; it takes $0.14\text{ seconds}$ to circle Earth, $1.3\text{ seconds}$ to reach the Moon, $8\text{ minutes}$ to reach the Sun, and $4\text{ years}$ to reach the nearest star.

Naked-Eye Star Visibility

Under dark and clear conditions, the human eye can see $\sim 6{,}000$ total stars ($\sim 3{,}000$ visible at any single moment).

Constellation

One of 88 official sky regions grouping star patterns across the sky.

Angular Subdivisions

Angles are measured in degrees ($^\circ$), arcminutes ($'$) where $1^\circ = 60'$, and arcseconds ($''$) where $1' = 60''$. An outstretched hand covers $\sim 10^\circ$, while the Full Moon and Sun subtend $\sim 0.5^\circ$.

Diurnal Motion

The daily apparent East-to-West movement of celestial objects caused by Earth rotating on its axis.

Foucault's Pendulum

The physical experiment that provides direct proof of Earth's axial rotation.

Yearly Motion and Seasonal Constellations

The shift in visible constellations throughout the year caused by Earth orbiting the Sun; Orion and Perseus dominate winter, while Sagittarius and Cygnus dominate summer.

Celestial Sphere

An imaginary concentric sphere surrounding Earth containing all astronomical objects. Key reference points include Zenith, Horizon, Celestial Equator, and Celestial Poles.

Precession

The slow wobble of Earth's rotational axis over time, shifting the celestial pole positions.

Declination (Dec) and Right Ascension (RA)

Declination measures angular distance north ($+$) or south ($-$) from the celestial equator in degrees; Right Ascension measures angular distance eastward along the celestial equator from the vernal equinox in hours, minutes, and seconds.

Sidereal Day vs. Solar Day

A sidereal day is one $360^\circ$ rotation relative to stars; a solar day is noon-to-noon. Solar days are longer because Earth advances $\sim 0.986^\circ\text{/day}$ in orbit, requiring a $\sim 360.986^\circ$ rotation.

Ecliptic Plane

The plane of Earth's orbit around the Sun, appearing as the Sun's annual path across the celestial sphere.

Cause of Seasons

Earth's $23.5^\circ$ axial tilt (not changing distance from the Sun), which concentrates sunlight in summer and spreads it out in winter.

Solstices vs. Equinoxes

Equinoxes occur where the ecliptic intersects the celestial equator (March and September); Solstices occur at the Sun's farthest northern (summer) and southern (winter) points.

Synchronous Rotation

The Moon rotates on its axis at the exact same rate it orbits Earth, causing only one face to be seen from Earth.

Sidereal Month vs. Synodic Month

A sidereal month is one full $360^\circ$ orbit ($\sim 27.3\text{ days}$); a synodic month is one full phase cycle (e.g., New Moon to New Moon, $\sim 29.5\text{ days}$).

Line of Nodes

The line where the Moon's $5^\circ$ inclined orbital plane intersects the ecliptic plane, necessary for eclipses to occur.

Red Appearance during Lunar Eclipse

Caused by Earth's atmosphere scattering blue light while refracting red sunlight into Earth's umbral shadow.

Occam's Razor

The principle that among competing hypotheses explaining observation, the one requiring the fewest new assumptions should be favored.

Direct vs. Retrograde Motion

Direct motion is normal eastward planetary movement against stars; Retrograde motion is temporary apparent westward movement.

Ptolemaic System (~140 AD)

A geocentric model explaining retrograde motion using small circular epicycles moving along larger Earth-centered deferents.

Copernican Model (~1500)

A heliocentric model explaining retrograde motion as an optical effect caused by Earth passing slower outer planets.

Inferior vs. Superior Planets

Inferior planets (Mercury, Venus) orbit inside Earth's orbit and stay near the Sun; Superior planets orbit outside Earth's orbit.

Kepler's First Law

Planetary orbits are ellipses with the Sun located at one focus. Shape is determined by eccentricity ($e = \frac{c}{a}$).

Kepler's Second Law

A line connecting the Sun and a planet sweeps out equal areas in equal intervals of time. Planets travel fastest at perihelion and slowest at aphelion.

Kepler's Third Law

The square of a planet's orbital period is proportional to the cube of its semi-major axis ($P^2 = a^3$).

Galileo's Telescopic Proof

Observed Venus exhibiting full phase cycles (gibbous and full phases), which is impossible under the geocentric Ptolemaic model.

Newton's Law of Universal Gravitation

Mathematical gravitational force equation $F = G \frac{m_1 m_2}{r^2}$. Explains Kepler's 2nd law via varying gravitational acceleration with distance.

Light Spectrum Experiment

Newton showed white sunlight is a mixture of all rainbow colors by breaking it apart with a prism and isolating colors with a second prism.

Wave-Particle Duality and Photons

Light behaves both as electromagnetic waves ($c = \lambda \nu$) and discrete energy particles called photons ($E = h \nu$).

Electromagnetic Spectrum Order

Ordered from longest wavelength/lowest energy to shortest wavelength/highest energy: Radio, Microwaves, Infrared, Visible ($400\,\text{nm}$ to $700\,\text{nm}$), Ultraviolet, X-rays, Gamma rays.