Astronomy

Astronomy

The scientific study of celestial objects (stars, planets, and other objects in the universe).

Science process

Observe a problem, form a hypothesis, make predictions, test, and revise if results disagree.

Hypothesis

A structured, testable idea that explains a phenomenon and makes predictions.

Theory

A set of well-tested hypotheses that fit together and successfully predict observations.

Accuracy

Closeness to the true value.

Precision

How tightly repeated measurements cluster.

Scientific notation

mantissa × 10^exponent.

Order of magnitude

The power-of-ten scale factor (10^n) in scientific notation.

Solar mass (M☉)

1.939 × 10^30 kg.

Earth mass (M⊕)

5.972 × 10^24 kg.

Astronomical unit (AU)

Earth-Sun distance = 1.495 × 10^11 m.

Angular size

How large something appears on the sky.

Moon angular diameter

About 0.5° or 30 arcminutes (30′).

Angular separation

The angle between two objects on the sky.

Constellations

Official sky regions; modern astronomy uses 88 covering the whole sky.

Asterism

A recognizable star pattern within constellations (example: Big Dipper).

Horizon

Boundary between ground and sky.

Zenith

Point directly overhead.

Nadir

Point directly down.

Meridian

Arc from north to south through the zenith.

Altitude (Alt)

Angle above the horizon.

Azimuth (Az)

Angle along the horizon measured from north.

Alt-Az limitation

Altitude and azimuth depend on location and time due to Earth's rotation.

Celestial sphere

Model of the sky as a giant sphere around Earth for mapping positions.

Celestial poles

Directions of Earth's rotation axis projected onto the sky.

Declination (Dec)

Sky "latitude," ranges +90° to −90°, celestial equator is 0°.

Right ascension (RA)

Sky "longitude," measured in hours from 0h to 24h.

Ecliptic

The Sun's apparent path over the year.

Latitude

0° at Earth's equator to ±90° at poles.

Longitude

0° at Greenwich to 180° east or west.

Navigation rule

Altitude of the celestial pole above the horizon ≈ your latitude.

Evidence Earth is round (Aristotle)

NCP altitude changes with travel; Earth's lunar-eclipse shadow is round.

Eratosthenes' method

Used differences in Sun angle between two locations to estimate Earth's circumference.

Earth circumference (modern)

About 40,008 km.

Prograde motion

The usual direction of motion on the sky.

Retrograde motion

Apparent backward motion due to perspective.

Classical "wandering stars"

Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn.

Ptolemaic model (geocentric)

Earth-centered; used deferents and epicycles to reproduce retrograde motion.

Epicycle

A circular motion component used to match observed planetary paths in geocentric/early heliocentric models.

Aristarchus model

Early heliocentric idea; predicted stellar parallax.

Geo-heliocentric model

Planets orbit Sun, but Sun orbits Earth (hybrid).

Copernican model

Heliocentric but kept circular orbits, so still used epicycles.

Stellar parallax

Apparent shift of nearby stars relative to distant background due to changing viewpoint.

First successful parallax measurement

Friedrich Bessel (1838), 61 Cygni.

Kepler's 1st law

Planets orbit in ellipses with the Sun at one focus.

Kepler's 2nd law

Equal areas in equal times; planets move faster when closer to the Sun.

Kepler's 3rd law

P^2 ∝ a^3; in solar system units P^2 = a^3 (P in years, a in AU).

Semi-major axis (a)

The "size" of an orbit.

Eccentricity (e)

The "shape" of an orbit; 0 < e < 1 for ellipses.

Pericenter

Closest point in an orbit.

Apocenter

Farthest point in an orbit.

Newton's 1st law (inertia)

Object keeps constant velocity unless acted on by a force.

Newton's 2nd law

F = m a.

Newton's 3rd law

Action-reaction pairs; forces come in equal and opposite pairs.

Linear momentum

p = m v.

Inertia

Resistance to changes in motion.

Angular momentum

Depends on mass, distance from axis, and speed; conserved in many systems.

Universal gravitation

F = G (m1 m2) / r^2.

Mass

Amount of matter; related to inertia.

Weight

Gravitational force on mass: F_g = m g.

g (Earth)

≈ 9.8 m/s^2.

g (Moon)

≈ 1.6 m/s^2.

Weightlessness in orbit

Astronauts are in continuous free fall.

Barycenter

Common center of mass that two bodies orbit.

Pluto-Charon example

Their barycenter is outside Pluto (from notes context).

Halley's Comet eccentricity

Approximately e ≈ 0.97 (highly eccentric).

Neptune discovery

Deviations in Uranus's orbit led to prediction; Neptune observed near predicted location (1846).

Seasons cause

Earth's axial tilt (obliquity), not mainly distance from the Sun.

Vernal equinox

About March 21.

Summer solstice

About June 21.

Autumnal equinox

About September 21.

Winter solstice

About December 21.

Earth's orbit and seasons

Earth is closest in January and farthest in July; effect is small compared to tilt.

Precession

Earth's axis traces a circle over ~26,000 years; pole star changes.

Solar day

24 hours; Sun returns to same position.

Sidereal day

23h 56m; stars return to same position.

Length of year

About 365.2422 days (not an integer).

Synodic month (phase cycle)

≈ 29.53 days.

Moon illumination

Half the Moon is always illuminated; phases depend on geometry.

Moon sidereal orbital period

27.32 days.

Tidal locking

Moon rotates once per orbit, so we mostly see the same face.

Solar eclipse

Moon between Sun and Earth (new Moon).

Lunar eclipse

Earth between Sun and Moon (full Moon).

Tides cause

Mostly Moon's gravity; Sun contributes smaller effect.

Spring tides

Alignment of Sun and Moon gives bigger tidal range.

Neap tides

Misalignment gives smaller tidal range.

Tidal dissipation effect

Transfers angular momentum; Moon moves outward ~38 mm/year.

Light travel time from Sun to Earth

A little over 8 minutes.

Light-year distance

1 ly ≈ 9.46 × 10^15 m.

Rømer's evidence for finite light speed

Used timing of Jupiter's moon to show delays.

Electromagnetic (EM) waves

Predicted by Maxwell's equations; transverse; travel at speed c.

Wavelength (λ)

Distance between wave peaks.

Frequency (f or ν)

Cycles per second (Hz).

Wave relation

c = λ f.

Atmosphere and EM spectrum

Gamma/X-ray/UV mostly blocked; visible mostly observable; many IR absorbed; many radio observable.

Kirchhoff's law (as in notes)

In thermal equilibrium, emissivity = absorptivity (at a given wavelength).

Blackbody

Ideal perfect absorber/emitter.

Wien's displacement law

λ_max = (2.9 × 10^-3) / T.

Stefan-Boltzmann law (flux)

F = σ T^4.

Luminosity (from notes)

L = 4πR^2 σ T^4.