Astronomy + Cosmology Exam 1

Planet

A moderately large object that orbits a star; it shines by reflected light and can be rocky, icy, or gaseous in composition

Star

A large, glowing ball of gas that generates heat and light through nuclear fusion in its core

Nebula

An interstellar cloud of gas and or dust

Galaxy

A great island of stars in space, all held together by gravity and orbiting a common center

Universe

The sum total of all matter and energy; everything within between all galaxies

How was most of the material that makes up earth including life on earth formed?

Inside stars that died before Earth formed

Light-year

The distance light travels in 1 year (9.46 × 10¹² km)

Hierarchical scale (smallest to largest)

Earth—> solar system—> Milky Way galaxy—> local group (galaxy cluster)—> local supercluster

Origin of matter

hydrogen and helium came from the Big Bang; all heavier elements were forged inside stars and recycled into new star systems

How old is the universe?

It is 14 billion light years in radius—> universe=14 billion years old

Light speed

Moon= 1 second light travel time, sun= 8 min light travel time

Cosmic calendar

Compresses the 14-billion year history of the universe into 1 year. Human civilization is a few seconds old, human lifetime= fraction of a second

Arc minutes vs. arc seconds

1 degree= 60 arc minutes/ 1 arc minutes= 60 arc seconds

Latitude

Position north/south of the equator

Longitude

East/west of the prime meridian

Altitude

Angular distance above the horizon (0 degree on horizon to 90 degrees at zenith/straight overhead)

North celestial pole

Point directly above Earth’s North Pole

Ecliptic

The sun’s apparent yearly path across the celestial sphere

What causes the seasons?

Earth’s 23.5 axial tilt, pointing to Polaris all year. It is not distance from the sun, tilt changes the directness of sunlight and the sun’s altitude throughout the year

Higher sun altitude

More direct light, concentrated heating—> summer

Lower sun altitude

Less direct light, spread-out heating—> winter

Summer solstice (June)

Highest path; sun rises/sets at extreme North of East/West, more direct light in Norther Hemisphere

Winter solstice (December)

Lowest path; Sun rises/sets at extreme South of East/West, least direct light in Norther Hemisphere

Equinoxes

Spring/March +Fall/September, sun rises precisely East and sets West; equal sunlight in both hemispheres

The moon

Half of the moon is always lit by the sun. As it orbits Earth, we see changing proportions of the illuminated side

Celestial equator

A projection of Earth’s equator onto the sky

Waxing

Visible afternoon/evening; gets fuller and rises later each day

Waning

Visible late night/morning; gets less full and sets later each day

Which way does the sun appear to move?

Eastward along the ecliptic, as Earth orbits the sun

New moon

Near sun in sky (up during day)

Full moon

Opposite sun in sky (up all night)

Synchronous rotation

We only see one side of the moon because it rotates once per orbit

Lunar eclipse

Earth passes between sun and moon (Earth’s shadow on moon); occurs only at full moon (penumbral, partial, total)

Solar eclipse

Moon passes between sun and earth (moon’s shadow on Earth); occurs only at New moon (partial, total, annular)

Why aren’t there eclipses every month?

Moon’s orbit is tilted 5 degrees to the ecliptic plane, so eclipses occur only during 2 annual eclipse seasons

Apparent retrograde motion

Over weeks, planets appear to slow, stop, move backward relative to background stars, then resume forward motion

Geocentric (Ptolemy)

Earth at center. Used complex epicycles to explain retrograde motion while keeping “perfect circular motion”

Heliocentric (Copernicus)

Sun at center. Retrograde motion is naturally explained when Earth laps outer planets. His explanation is simpler for retrograde motion of the planets than the geocentric model

Stellar paralax objection

Ancient Greeks rejected the heliocentric model because they couldn’t detect stellar parallax; stars are so far away that parallax angle is too small for the naked eye to detect.

Brahe

Compiled the most precise naked-eye planetary movements in history

Kepler

Used Tycho’s data to discover planetary orbits are ellipses, resolving discrepancies

Galileo

Provided decisive telescope evidence for Copernican model

1. Moon craters and sunspots (heavens are not “perfect”

2. 4 moons orbiting Jupiter (proving not everything orbits Earth)

3. Phases of Venus (proved Venus orbits the Sun, not the Earth)

Keplers Laws

1. Planetary orbits are ellipses with the sun at one focus

2. Equal areas swept in equal times (planets move faster near sun/perihelion, slower farther away/aphelion)

3. p²=a³ —> p=period in years; a=average distance in AU

Netwon’s law of motion

1. Constant velocity (speed+direction) unless acted upon by a net force

2. F=ma or a=F/m

3. For every force there is always an equal and opposite reaction

Newton’s law of gravitation

Every mass attracts every other mass: F_g=G m₁m₂/d^2.

Force is directly proportional to masses and inversely proportional to square of distance (d²)

G= gravitational constant (6.67 × 10^-11)

Newton’s version of Kepler’s 3rd law

Extends Kepler’s 3rd law to any orbiting system + allows astronomers to calculate the masses of stars and galaxies

p²=a³/m₁m₂ (p in years, a in AU, M in solar masses)

Light properties

Light exhibits both wave-like and particle-like properties. Particles of light are photons. Photons have a wavelength and a frequency

E=h x f

Shorter wavelength=_______=_______

Higher frequency=Higher photon energy

wavelength

The distance between 2 peaks

wave speed= wavelength x frequency

frequency

the number of times per second that a wave vibrates up and down

wavelength x frequency= c (speed of light 3.08 × 10⁸)

Electromagnetic spectrum

The entire range of wavelengths of light

Gamma ray—X-ray—Ultraviolet—Visibile—Infrared—Microwave—Radio

Continous (thermal) spectrum

The spectrum shows a smooth continuous rainbow of light without interruptions

The typical wavelength of an emitted photon gets shorter for hotter objects

Emission line spectrum

Thin/low density hot gas glows only at specific wavelengths (bright lines) based on chemical composition

Absorption line spectrum

It is absorbing light at certain wavelengths, corresponding to the various atomic elements in the star.

Chemical fingerprints

Each type of atom has a unique special fingerprint

Blueshift

Source moving toward observer —> shorter wavelengths

Redshift

Source moving away from observer —> longer wavelengths

Doppler shift

Light always moves at the speed of light

E=mc²

Mass of 1 helium nucleus is slightly lighter than 4 nuclei; missing mass is converted into energy

Thermostat mechanism

Temperature drops—fusion drops—core contracts and heats back up.

Temp rises—fusion rises—core expands and cools back down

Structure of the sun (inside—out)

Core (fusion center)'

Radiation Zone (Energy leaks out as randomly bouncing photons)

Convection Zone (Energy transported upward by rising hot plasma cells)

Photosphere (visible surface)

Chromosphere (Middle solar atmosphere)

Corona (outermost solar atmosphere)

Solar wind (flow of charged particles streaming into space)

Fission vs fusion

Fission: Big nucleus splits into smaller pieces

Fusion: Nuclei stick together to make a bigger one

Luminosity

Total energy radiated per second (watts).

Powered by nuclear fusion of hydrogen into helium. To measure it we need apparent brightness and distance

Inverse square law: the amount of luminosity passing through each sphere is the same

The sun has the highest ____ of all the stars we can see

apparent brightness: amount of starlight reaching Earth

How do we measure stellar masses?

Using binary stars and Newton’s version of Kepler’s 3rd law

Spectral Types (hottest to coolest)

O—B—A—F—G—K—M

H-R Diagram

Plots luminosity (y-axis) vs. surface temperature (x-axis) increasing to the left

High mass stars

blue, hot, extremely luminous, short-lived (10 million years), large radius

Low mass stars

Red, cool, faint luminosity, long-lived (100 billion years), small radius

Giants/supergiants

Upper right corner of H-R diagram

Stars with lower temperature and higher luminosity have larger radii

White dwarfs

Lower left corner of H-R diagram

Stars with a higher temperature and lower luminosity=smaller radii

Main sequence turnoff point

Point on H-R diagram where stars are leaving the main sequence; cluster age equals the lifespan of stars at the turnoff point

Main sequence stars are fusing hydrogen into helium in their cores

Where do stars form?

In cold dense molecular clouds when gravity overcomes thermal pressure

Lower mass limit

(<0.08m) Core never gets hot enough for fusion:stabilized by electrons degeneracy pressure as a brown dwarf

Upper mass limit

(100-200 m) Radiation pressure blows away accumulating mass

When can gravity create stars?

If it can overcome the force of thermal pressure in a cloud

Thermal pressure

High temps. Cause particles to move around creating an outward pressure that counteracts gravity

Thermal vs degeneracy pressure

Thermal: depends on heat content, main form of pressure in most stars

Degeneracy: Particles can’t be in same state in same place, doesn’t depend on heat content

Brown dwarfs

Starlike objects not massive enough to start fusion

From protostars to main sequence

Contraction must continue until the core becomes hot enough for nuclear fusion of H into HE. Contraction stops when:

1. Gravitational contraction and thermal pressure from the fusion are in balance

2. The energy released by core fusion balances energy radiated from the surface

Open clusters vs Globular stars

Open: Loosely packed and contains a few thousands of stars

Globular: Densely packed and contain hundreds of thousands of stars

Low mass stellar evolution

1. Main sequence: H fuses to He in core

2. Red Giant phase: H fuses into He in shell around the core

3. Helium core fusion: helium fuses into carbon while H fuses to He in shell

4. Double shell burning: hydrogen and helium fuse in surrounding shells around inert carbon core

5. Planetary Nebula + White dwarf: Outer layers are blown off into space as a planetary nebula, leaving the white dwarf behind

High mass stellar evolution

Similar to the stages of low stellar evolution

Hydrogen core fusion (MS)

Hydrogen shell burning (supergiants)

Helium core fusion

How do high mass stars end their lives?

Iron is a dead end for fusion because nuclear fusions involving iron don’t release energy. Iron builds up in the core and no longer resists gravity— causing the core to collapse, creating a supernova explosion

Chandrasekhar limit

Maximum mass of a white dwarf is 1.4 M. Nothing can move faster than light, the electrons move nearly at the speed of light at 1.4

White dwarf supernova

White dwarf accretes material from a companion star, causing its mass to reach Chandrasekhar limit—leading to an explosion destroying the white dwarf

Massive star supernovae

Inert iron core of a massive star collapses into a neutron star or black hole, causing explosion that blows apart the rest of the star

Neutron stars

The ball of neutrons left behind by a massive-star supernova

Degeneracy pressure of neutrons supports stars against gravity

Pulsar

A neutron star that beams radiation along a magnetic axis not aligned with the rotation axis

Black holes

An object whose gravity is so powerful that not even light can escape it

Spacetime is no curved here, nothing can escape it

Accretion disk

Friction between orbiting rings of matter in the disk transfers angular momentum outward + causes the disk to heat up and glow

Nova

When fusion begins suddenly and explosively

Event horizon

Boundary where escape velocity=light speed, no info or light escapes. Time passes more slowly here

Singularity

Beyond neutron star limit— no force can resist the crush of gravity, gravity crushes all the matter into a single point

Motion is not ___

Absolute, we must measure speed of one object relative to another

Spacetime

4 dimensional combo of space and time—forming the fabric of the universe, can be curved—affected trajectory of objects.

Gravity arises from curvature of spacetime