Transcript Review Powerpoint - Physics and Astronomy

Chapter 0
Charting the Heavens
0.1 The “Obvious” View
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
0.2 Earth’s Orbital Motion
• 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.
0.3 The Motion of the Moon
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
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.
0.3 The Motion of the Moon
Eclipses don’t occur every month because
Earth’s and the Moon’s orbits are not in the
same plane.
0.4 The Measurement of Distance
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
0.5 Science and the Scientific Method
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.
Summary of Chapter 0
• 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, cont.
• 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 …
Electromagnetic Radiation
(How we get information about the cosmos)
Examples of electromagnetic radiation?
Light
Infrared
Ultraviolet
Microwaves
AM radio
FM radio
TV signals
Cell phone signals
X-rays
Units of Chapter 1
The Motions of the Planets
The Birth of Modern Astronomy
The Laws of Planetary Motion
Newton’s Laws
Summary of Chapter 1
1.1 The Motions of the Planets
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
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.
1.3 The Laws of Planetary Motion
Kepler’s laws:
1. Planetary orbits are ellipses, Sun at one focus.
1.3 The Laws of Planetary Motion
Kepler’s laws:
2. Imaginary line connecting Sun and planet
sweeps out equal areas in equal times.
1.3 The Laws of Planetary Motion
Kepler’s laws:
3. Square of period of planet’s orbital motion
is proportional to cube of semimajor axis.
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.
1.4 Newton’s Laws
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
Massive objects actually orbit around their
common center of mass; if one object is
much more massive
than 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.
1.4 Newton’s Laws
Kepler’s laws are a
consequence of
Newton’s laws.
Summary of Chapter 1
• 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, cont.
• 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.
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 (l)
crest
amplitude (A)
trough
velocity (v)
l is a distance, so its units are m, cm, or mm, etc.
Also, v = l n
Period (T): time between crest (or trough) passages
Frequency (n): rate of passage of crests (or troughs), n =
(units: Hertz or cycles/sec)
1
T
 = hn
Radiation travels as Electromagnetic waves.
That is, waves of electric and magnetic fields traveling together.
Examples of objects with magnetic fields:
a magnet
the Earth
Clusters of galaxies
Examples of objects with electric fields:
Power lines, electric motors, …
Protons (+)
"charged" particles that
make up atoms.
Electrons (-)
}
Scottish physicist James Clerk Maxwell showed in 1865
that waves of electric and magnetic fields travel together =>
traveling “electromagnetic” waves.
The Doppler Effect
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
Applies to all kinds of waves, not just radiation.
at rest
velocity v1
velocity v2
velocity v1
velocity v1
velocity v3
you encounter
more wavecrests
per second =>
higher frequency!
fewer wavecrests
per second =>
lower frequency!
Things that waves do
1. Refraction
Waves bend when they pass through material of different densities.
air
water
swimming pool
prism
air
glass
air
2. Diffraction
Waves bend when they go through a narrow gap or around a corner.
The Electromagnetic Spectrum
1 nm = 10 -9 m , 1 Angstrom = 10 -10 m
c= ln
The "Inverse-Square" Law Applies to Radiation
Each square gets 1/4
of the light
Each square gets 1/9
of the light
apparent brightness α
1
D2
α means “is proportional to”. D is the distance
between source and observer.
Approximate black-body spectra of stars of different temperature
average star (Sun)
Brightness
cold dust
infrared visible UV
“cool" stars
very hot stars
infrared visible UV
frequency increases,
wavelength decreases
Laws Associated with the Black-body Spectrum
Wien's Law:
λmax energy α
1
T
(wavelength at which most energy is radiated is longer for cooler objects)
Stefan's Law:
Energy radiated per cm2 of area on surface every second α T 4
(T = temperature at surface)
1 cm2
The total energy radiated from entire surface every second is called the
luminosity. 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.
.
.
.
..
.
. . . .
.
“atmosphere” (thousands
of K) has atoms and ions
with bound electrons
hot (millions of K), dense interior
has blackbody spectrum,
gas fully ionized
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.