Chapter 0 Charting the Heavens. Stars that appear close in the sky may not actually be close in...

Chapter 0Charting the Heavens

Stars that appear close in the sky may not actually be close in space.

0.1 The “Obvious” View

The celestial sphere:

• Stars seem to be on the inner surface of a sphere surrounding the Earth.

• They aren’t, but we can use two-dimensional spherical coordinates (similar to latitude and longitude) to locate sky objects.

0.1 The “Obvious” View

• Declination: Degrees north or south of celestial equator• Right ascension: Measured in hours, minutes, and seconds eastward from position of the Sun at vernal equinox

0.1 The “Obvious” View

• Daily cycle, noon to noon, is diurnal motion – solar day.

• Stars aren’t in quite the same place 24 hours later, though, due to Earth’s rotation around the Sun; when they are in the same place again, one sidereal day has passed.

0.2 Earth’s Orbital Motion

The 12 constellations the Sun moves through during the year are called the zodiac; path is ecliptic.

0.2 Earth’s Orbital Motion

• Ecliptic is plane of Earth’s path around the Sun; at 23.5° to celestial equator.

• Northernmost point (above celestial equator) is summer solstice; southernmost is winter solstice; points where path crosses celestial equator are vernal and autumnal equinoxes.

• Combination of day length and sunlight angle gives seasons.

• Time from one vernal equinox to next is tropical year.

0.2 Earth’s Orbital Motion

Precession: Rotation of Earth’s axis itself; makes one complete circle in about 26,000 years

0.2 Earth’s Orbital Motion

Time for Earth to orbit once around the Sun, relative to fixed stars, is sidereal year.

Tropical year follows seasons; sidereal year follows constellations – in 13,000 years July and August will still be summer, but Orion will be a summer constellation.

0.2 Earth’s Orbital Motion

The Moon takes about 29.5 days to go through whole cycle of phases – synodic month.

Phases are due to different amounts of sunlit portion being visible from Earth.

Time to make full 360° around Earth, sidereal month, is about 2 days shorter than synodic month.

0.3 The Motion of the Moon

Lunar eclipse: • Earth is between the Moon and Sun • Partial when only part of the Moon is in shadow• Total when all is in shadow

0.3 The Motion of the Moon

Solar eclipse: the Moon is between Earth and Sun

0.3 The Motion of the Moon

0.3 The Motion of the Moon

Solar eclipse is partial when only part of the Sun is blocked, total when all is blocked, and annular when the Moon is too far from Earth for total.

Eclipses don’t occur every month because Earth’s and the Moon’s orbits are not in the same plane.

0.3 The Motion of the Moon

Triangulation: Measure baseline and angles, and you can calculate distance.

0.4 The Measurement of Distance

Parallax: Similar to triangulation, but looking at apparent motion of object against distant background from two vantage points

0.4 The Measurement of Distance

Scientific theories:

• Must be testable

• Must be continually tested

• Should be simple

• Should be elegant

Scientific theories can be proven wrong, but they can never be proven right with 100% certainty.

0.5 Science and the Scientific Method

• Observation leads to theory explaining it.

• Theory leads to predictions consistent with previous observations.

• Predictions of new phenomena are observed. If the observations agree with the prediction, more predictions can be made. If not, a new theory can be made.

0.5 Science and the Scientific Method

• Astronomy: Study of the universe

• Stars can be imagined to be on inside of celestial sphere; useful for describing location.

• Plane of Earth’s orbit around Sun is ecliptic; at 23.5° to celestial equator.

• Angle of Earth’s axis causes seasons.

• Moon shines by reflected light, has phases.

• Solar day ≠ sidereal day, due to Earth’s rotation around Sun.

Summary of Chapter 0

• Synodic month ≠ sidereal month, also due to Earth’s rotation around Sun

• Tropical year ≠ sidereal year, due to precession of Earth’s axis

• Distances can be measured through triangulation and parallax.

• Eclipses of Sun and Moon occur due to alignment; only occur occasionally as orbits are not in same plane.

• Scientific method: Observation, theory, prediction, observation …

Summary of Chapter 0, cont.

Electromagnetic Radiation

(How we get information about the cosmos)

Examples of electromagnetic radiation?

LightInfraredUltravioletMicrowavesAM radioFM radioTV signalsCell phone signalsX-rays

The Motions of the Planets

The Birth of Modern Astronomy

The Laws of Planetary Motion

Newton’s Laws

Summary of Chapter 1

Units of Chapter 1

The Sun, Moon, and stars all have simple movements in the sky, consistent with an Earth-centered system.

Planets:• Move with respect to fixed stars• Change in brightness• Change speed• Have retrograde motion• Are difficult to describe in earth-centered system

1.1 The Motions of the Planets

1.1 The Motions of the Planets

A basic geocentric model, showing an epicycle (used to explain planetary motions)

1.1 The Motions of the Planets

Lots of epicycles were needed to accurately track planetary motions, especially retrograde motions. This is Ptolemy's model.

1.1 The Motions of the Planets

A heliocentric (Sun-centered) model of the solar system easily describes the observed motions of the planets, without excess complication.

1.2 The Birth of Modern Astronomy

Observations of Galileo:

• The Moon has mountains, valleys, and craters.

• The Sun has imperfections, and it rotates.

• Jupiter has moons.

• Venus has phases.

All these were in contradiction to the general belief that the heavens were constant and immutable.

1.2 The Birth of Modern Astronomy

The phases of Venus are impossible to explain in the Earth-centered model of the solar system.

1. Planetary orbits are ellipses, Sun at one focus.

Kepler’s laws:

1.3 The Laws of Planetary Motion

2. Imaginary line connecting Sun and planet sweeps out equal areas in equal times.

Kepler’s laws:

1.3 The Laws of Planetary Motion

3. Square of period of planet’s orbital motion is proportional to cube of semimajor axis.

Kepler’s laws:

1.3 The Laws of Planetary Motion

1.3 The Laws of Planetary Motion

The Dimensions of the solar system

• The distance from Earth to the Sun is called an astronomical unit. Its actual length may be measured by bouncing a radar signal off Venus and measuring the transit time.

Gravity

On Earth’s surface, the acceleration due to gravity is approximately constant, and directed toward the center of Earth.

1.4 Newton’s Laws

Gravity

For two massive objects, the gravitational force is proportional to the product of their masses divided by the square of the distance between them.

1.4 Newton’s Laws

Gravity

The gravitational pull of the Sun keeps the planets moving in their orbits.

1.4 Newton’s Laws

1.4 Newton’s Laws

Massive objects actually orbit around their common center of mass; if one object is much more massivethan the other, the center of mass is not far from the center of the more massive object. For objects more equal in mass, the center of mass is between the two.

Kepler’s laws are a consequence of Newton’s laws.

1.4 Newton’s Laws

• First models of solar system were geocentric, but couldn't easily explain retrograde motion.

• Heliocentric model does.

• Galileo's observations supported heliocentric model.

• Kepler found three empirical laws of planetary motion from observations.

Summary of Chapter 1

• Laws of Newtonian mechanics explained Kepler’s observations.

• Gravitational force between two masses is proportional to the product of the masses, divided by the square of the distance between them.

Summary of Chapter 1, cont.

Units of Chapter 2

Information from the Skies

Waves in What?

The Electromagnetic Spectrum

Thermal Radiation

Spectroscopy

The Formation of Spectral Lines

The Doppler Effect

Summary of Chapter 2

2.1 Information from the Skies

Electromagnetic radiation: Transmission of energy through space without physical connection through varying electric and magnetic fields

Example: Light

2.1 Information from the Skies

Example: Water wave

Water just moves up and down.

Wave travels and can transmit energy.

2.2 Waves in What?

Diffraction: The bending of a wave around an obstacle

Interference: The sum of two waves; may be larger or smaller than the original waves

2.2 Waves in What?

Water waves, sound waves, and so on, travel in a medium (water, air, …).

Electromagnetic waves need no medium.

Created by accelerating charged particles

Radiation travels as waves.Waves carry information and energy.

Properties of a wave

wavelength ()

crest

amplitude (A)

velocity (v)trough

is a distance, so its units are m, cm, or mm, etc.

Period (T): time between crest (or trough) passages

Frequency (): rate of passage of crests (or troughs),

Also, v =

h1T

(units: Hertz or cycles/sec)

Radiation travels as Electromagnetic waves.

That is, waves of electric and magnetic fields traveling together.

Examples of objects with magnetic fields:

a magnetthe EarthClusters of galaxies

Examples of objects with electric fields:

Protons (+)Electrons (-) } "charged" particles that

make up atoms.

Power lines, electric motors, …

Scottish physicist James Clerk Maxwell showed in 1865 that waves of electric and magnetic fields travel together => traveling “electromagnetic” waves.

Applies to all waves – not just radiation. The frequency or wavelength of a wave depends on the relative motion of the source and the observer.

The Doppler Effect

The Doppler Effect

Applies to all kinds of waves, not just radiation.

at restvelocity v1

velocity v1 velocity v3

fewer wavecrests per second => lower frequency!

velocity v1

velocity v2

you encounter more wavecrests per second => higher frequency!

1. Refraction

Waves bend when they pass through material of different densities.

swimming pool

air

water

prism

airairglass

Things that waves do

2. Diffraction

Waves bend when they go through a narrow gap or around a corner.

c =

1 nm = 10 -9 m , 1 Angstrom = 10 -10 m

The Electromagnetic Spectrum

The "Inverse-Square" Law Applies to Radiation

apparent brightness α 1D2

α means “is proportional to”. D is the distance between source and observer.

Each square gets 1/9 of the light

Each square gets 1/4 of the light

cold dust average star (Sun)

frequency increases, wavelength decreases

Approximate black-body spectra of stars of different temperature

very hot stars“cool" stars

infrared visible UV

infrared visible UVB

righ

tnes

s

Laws Associated with the Black-body Spectrum

Stefan's Law:

Energy radiated per cm2 of area on surface every second α T 4

(T = temperature at surface)

Wien's Law:

λmax energy

α 1T

(wavelength at which most energy is radiated is longer for cooler objects)

1 cm2

The total energy radiated from entire surface every second is called theluminosity. Thus

Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2)

For a sphere, area of surface is 4πR2, where R is the radius.

So Luminosity α R2 x T4

Types of Spectra and Kirchhoff's (1859) Laws

1. "Continuous" spectrum - radiation over a broad range of wavelengths (light: bright at every color). Produced by a hot opaque solid, liquid, or dense gas.

2. "Emission line" spectrum - bright at specific wavelengths only. Produced by a transparent hot gas.

3. Continuous spectrum with "absorption lines": bright over a broad range of wavelengths with a few dark lines. Produced by a transparent cool gas absorbing light from a continuous spectrum source.

When an atom absorbs a photon, it moves to a higher energy state briefly

When it jumps back to lower energy state, it emits a photon - in a random direction

So why do stars have absorption line spectra?

..

. ..

..

..

.

.

Simple case: let’s say these atoms can only absorb green photons. Get dark absorption line at green part of spectrum.

hot (millions of K), dense interiorhas blackbody spectrum,gas fully ionized

“atmosphere” (thousandsof K) has atoms and ionswith bound electrons

Stellar Spectra

Spectra of stars differ mainly due to atmospheric temperature (composition differences also important).

“hot” star

“cool” star

Why emission lines?

.

..

...

hot cloud of gas

- Collisions excite atoms: an electron moves to a higher energy level

- Then electron drops back to lower level

- Photons at specific frequencies emitted.

2.7 The Doppler Effect

If one is moving toward a source of radiation, the wavelengths seem shorter; if moving away, they seem longer.

Relationship between frequency and speed:

2.7 The Doppler Effect

The Doppler effect shifts an object’s entire spectrum either toward the red or toward the blue.

Summary of Chapter 2

• Wave: period, wavelength, amplitude

• Electromagnetic waves created by accelerating charges

• Visible spectrum is different wavelengths of light.

• Entire electromagnetic spectrum:

• includes radio waves, infrared, visible light, ultraviolet, X-rays, gamma rays

• can tell the temperature of an object by measuring its blackbody radiation

Summary of Chapter 2, cont.

• Spectroscope splits light beam into component frequencies.

• Continuous spectrum is emitted by solid, liquid, and dense gas.

• Hot gas has characteristic emission spectrum.

• Continuous spectrum incident on cool, thin gas gives characteristic absorption spectrum.

Summary of Chapter 2, cont.

• Spectra can be explained using atomic models, with electrons occupying specific orbitals.

• Emission and absorption lines result from transitions between orbitals.

• Doppler effect can change perceived frequency of radiation.

• Doppler effect depends on relative speed of source and observer.