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ASTRO 101
Principles of Astronomy
Instructor: Jerome A. Orosz
(rhymes with
“boris”)
Contact:
• Telephone: 594-7118
• E-mail: [email protected]
• WWW:
http://mintaka.sdsu.edu/faculty/orosz/web/
• Office: Physics 241, hours T TH 3:30-5:00
Homework
• Homework due February 19: Question 4 from
Chapter 3 (What are the three main functions
of a telescope?)
• Write down the answer on a sheet of paper and
hand it in before the end of class on February
19.
Coming Up
• Tuesday, February 19: wrap-up, review
• Thursday, February 21: Exam #1
Coming Up:
• The 4 forces of Nature
• Energy and the conservation of energy
• The nature of light
– Waves and bundles of energy
– Different types of light
• Telescopes and detectors
• Spectra
– Emission spectra
– Absorption spectra
The spectrum
• Definition and types:
– Continuous
– Discrete
• The spectrum and its uses:
– Temperature
– Chemical composition
– Velocity
The spectrum
• A graph of the intensity
of light vs. the color (e.g.
the wavelength,
frequency, or energy) is
called a spectrum.
• A spectrum is probably
the single most useful
diagnostic tool available
in Astronomy.
The spectrum
• A spectrum can tell us about the temperature and
composition of an astronomical object.
• There are two types of spectra of concern here:
 Continuous spectra (the intensity varies smoothly
from one wavelength to the next).
 Line spectra (there are discrete jumps in the intensity
from one wavelength to the next).
The spectrum
• Continuous spectrum.
• Discrete or line spectra.
Images from Nick Strobel (http://www.astronomynotes.com)
Thermal Spectra
• The most common type of continuous spectrum
is a thermal spectrum.
• Any dense body will emit a thermal spectrum of
radiation when its temperature is above “absolute
zero”:
– The “color” depends only the temperature;
– The total intensity depends on the temperature and
the size of the body.
• This type of radiation is often called “black
body” radiation.
Thermal Spectra
• The most common type of continuous spectrum
is a thermal spectrum.
Black body radiation
• Sample spectra from black
bodies of different
temperatures. Note that the
area under the curves is
largest for the hottest
temperature.
• There is always a welldefined peak, which crudely
defines the “color”. The
peak is at bluer wavelengths
for hotter temperatures.
Important points
• The luminosity (energy loss per unit time)
of a black body is proportional the surface
area times the temperature to the 4th power:
• Hotter objects have higher intensities (for a
given area), and larger objects have higher
intensities.
Important points
• The peak of the spectrum is inversely
proportional to the temperature (hotter
objects are bluer):
• Hotter objects are bluer than cooler objects.
How light interacts with matter
and
the line spectrum.
What Things Are Made Of
• Atoms are the basic
blocks of matter.
• The number of protons
determines the element.
For example hydrogen
has 1 proton, helium has
2 protons, uranium has
92 protons, etc.
• In most cases, the
number of electrons
equals the number of
protons.
How Light Interacts with Matter.
• Atoms are the basic
blocks of matter.
• In the 1850s, it was
discovered that an
element, when burned,
gave off a unique
emission line spectrum.
How Light Interacts with Matter.
• An electron will interact with a photon.
• An electron that absorbs a photon will gain
energy.
• An electron that loses energy must emit a
photon.
• The total energy (electron plus photon) remains
constant during this process.
How Light Interacts with Matter.
• Electrons bound to
atoms have discrete
energies (i.e. not all
energies are allowed).
• Thus, only photons of
certain energy can
interact with the
electrons in a given
atom.
How Light Interacts with Matter.
• Electrons bound to
atoms have discrete
energies (i.e. not all
energies are allowed).
• Thus, only photons of
certain energy can
interact with the
Image from Nick Strobel (http://www.astronomynotes.com)
electrons in a given
atom.
How Light Interacts with Matter.
• Electrons bound to
atoms have discrete
energies (i.e. not all
energies are allowed).
• Each element has its
own unique pattern of
energies.
How Light Interacts with Matter.
• Electrons bound to
atoms have discrete
energies (i.e. not all
energies are allowed).
• Each element has its
own unique pattern of
energies, hence its
own distinct line
spectrum.
Image from Nick Strobel (http://www.astronomynotes.com)
How Light Interacts with Matter.
• An electron in free space can have any energy.
– It can absorb a photon of any energy
– It can lose any amount of energy (E) by emitting a photon
with energy equal to E
• An electron in an atom can only have very specific
values of its energy E1, E2, E3, … EN)
– The electron can absorb a photon with an energy equal to (E1E2), (E1-E3), (E2-E3), … and jump to a higher level
– The electron can lose an amount of energy equal to a change
between levels (E1-E2), (E1-E3), (E2-E3), … and move down to
a lower level
How Light Interacts with Matter.
• An electron in an atom can only have very specific values
of its energy E1, E2, E3, … EN)
– The electron can absorb a photon with an energy equal to (E1-E2),
(E1-E3), (E2-E3), … and jump to a higher level
– The electron can lose an amount of energy equal to a change
between levels (E1-E2), (E1-E3), (E2-E3), … and move down to a
lower level
• Since each element has its own unique sequence of energy
levels (E1, E2, E3, … EN), the differences between the
levels are also unique, giving rise to a unique line spectrum
Emission spectra
and
absorption spectra.
Emission and Absorption
• If you view a hot gas against a dark background,
you see emission lines (wavelengths at which
there is an abrupt spike in the brightness).
Emission and Absorption
• If you view a continuous spectrum through cool
gas, you see absorption lines (wavelengths where
there is little light).
Emission and Absorption
Image from Nick Strobel (http://www.astronomynotes.com)
The spectrum
• View a hot, dense
source, get a continuous
spectrum.
• View that hot source
through cool gas, get an
absorption spectrum.
• View that gas against a
dark background, get
emission spectrum.
Tying things together:
• The spectrum of a star is approximately a
black body spectrum.
 Hotter stars are bluer, cooler stars are redder.
 For a given temperature, larger stars give off
more energy than smaller stars.
• In the constellation of
Orion, the reddish star
Betelgeuse is a relatively
cool star. The blue star
Rigel is relatively hot.
Tying things together:
• The spectrum of a star is approximately a
black body spectrum.
 Hotter stars are bluer, cooler stars are redder.
 For a given temperature, larger stars give off
more energy than smaller stars.
 However, a closer look reveals details in the
spectra…
The Line Spectrum
• Upon closer
examination, the
spectra of real
stars show fine
detail.
• Dark regions
where there is
relatively little
light are called
lines.
The Line Spectrum
• Today, we rarely
photograph spectra, but
rather plot the intensity vs
the wavelength.
• The “lines” where there is
relatively little light show
up as dips in the curves.
The Line Spectrum
• Today, we rarely
photograph spectra, but
rather plot the intensity vs
the wavelength.
• The “lines” where there is
relatively little light show
up as dips in the curves.
• These dips tell us about
what elements are present
in the star!
Atomic Fingerprints
• Hydrogen has a
specific line spectrum.
• Each atom has its own
specific line spectrum.
Atomic Fingerprints
• These stars have
absorption lines with
the wavelengths
corresponding to
hydrogen!
Atomic Fingerprints
• The Sun (and other stars) have absorption lines
with the wavelengths corresponding to iron.
Atomic Fingerprints.
• One can also look at the
spectra of other objects
besides stars, for example
clouds of hot gas.
• This cloud of gas looks
red since its spectrum is a
line spectrum from
hydrogen gas.
The Doppler Shift: Measuring
Motion
• If a source of waves is
not moving, then the
waves are equally
spaced in all
directions.
The Doppler Shift: Measuring
Motion
• If a source of waves is
moving, then the
spacing of the wave
crests depends on the
direction relative to
the direction of
motion.
The Doppler Shift: Measuring
Motion
• Think of sound waves from a fast-moving car, train,
plane, etc.
 The sound has a higher pitch (higher frequency) when the
car approaches.
 The pitch is lower (lower frequency) as the car passes and
moves further away.
The Doppler Shift: Measuring
Motion
• If a source of light is
moving away, the
wavelengths are
increased, or
“redshifted”.
The Doppler Shift: Measuring
Motion
• If a source of light is
moving closer, the
wavelengths are
shortened, or
“blueshifted”.
The Doppler Shift: Measuring
Motion
• The size of the
wavelength shift
depends on the relative
velocity of the source
and the observer.
The Doppler Shift: Measuring
Motion
• The size of the wavelength
shift depends on the relative
velocity of the source and the
observer.
• The motion of a star towards
you or away from you can be
measured with the Doppler
shift.
Using a Spectrum, we can…
• Measure a star’s temperature by measuring
the overall shape of the spectrum
(essentially its color).
• Measure what chemical elements are in a
star’s atmosphere by measuring the lines.
• Measure the relative velocity of a star by
measuring the Doppler shifts of the lines.
Review
• Thursday: Exam #1: Chapters 1-3
• Bring the Scantron No. F-288-PAR-L
Breakdown
• There will be three types of questions:
– multiple choice questions (2 pts each)
– long answer (5 pts each)
– “fill in the blank” (1 pt each)
Highlights
• Astronomy without a telescope
– Celestial sphere
– Stellar coordinates
– Stellar brightnesses
• The clockwork of the Universe
– The day/night cycle
– The reason for the seasons
– The phases of the moon
Highlights
• A brief history of Astronomy
– The geocentric model: Aristotle, Ptolomy
– The heliocentric model: Copernicus, Galileo, Kepler
• Isaac Newton
– Gravitation
– Physical model
Highlights
• Energy
– Definition
– Forms of energy
– Conservation of energy
– Light as a form of energy
• Light
– Light as particles
– Light as a wave
– The electromagnetic spectrum
• Emission lines and absorption lines
• The uses of a spectrum
Highlights
• Observational astronomy: collecting and detecting
photons.
– Telescopes
• Refracting (ones with lenses)
• Reflecting (ones with mirrors)
– Detectors
Good Review Questions, Chapter 1
7. What is the celestial sphere, and why is this ancient
concept still useful today?
8. What is the celestial equator, and how is it related to
Earth’s equator? How are the north and south celestial
poles related to Earth’s axis of rotation?
11. Why does the tilt of Earth’s axis relative to its orbit
cause the seasons as Earth revolves around the Sun?...
15. Why is it warmer in the summer than in winter?
16. Why does the Moon exhibit phases?
23. At which phase(s) of the Moon does a solar eclipse
occur? A lunar eclipse?
Good Review Questions, Chapter 2
6. How did Copernicus explain the retrograde motions of
the planets?
10. What are Kepler’s three laws? Why are they
important?
11. In what ways did the astronomical observations of
Galileo support a heliocentric cosmology?
12. How did Newton’s approach to understanding planetary
motion differ from that of his predecessors?
15. Why does an astronaut have to exert a force on a
weightless object to move it?
Good Review Questions, Chapter 3
4. What are the three major functions of a telescope?
12. Why must astronomers use satellites and Earth-orbiting
observatories to study the heavens at X-ray
wavelengths?
13. What is a blackbody? What does it mean to say that a
star appears almost like a black body? …
15. What is Wien’s Law? How could you use it to
determine the temperature of a star’s surface?
16. What is the Stefan-Boltzmann law? How do
Astronomers us it?
Good Review Questions, Chapter 3
18. What is an element? List the names of five different
elements…
20. Explain how the spectrum of hydrogen is related to the
structure of the hydrogen atom.
Good Review Questions, Chapter 1
7. What is the celestial sphere, and why is this ancient
concept still useful today?
8. What is the celestial equator, and how is it related to
Earth’s equator? How are the north and south celestial
poles related to Earth’s axis of rotation?
11. Why does the tilt of Earth’s axis relative to its orbit
cause the seasons as Earth revolves around the Sun?...
15. Why is it warmer in the summer than in winter?
16. Why does the Moon exhibit phases?
23. At which phase(s) of the Moon does a solar eclipse
occur? A lunar eclipse?
The Celestial Sphere
• Imagine the sky as a hollow sphere with the
stars attached to it. This sphere rotates once
every 24 hours. This imaginary sphere is
called the celestial sphere.
• Even though we know it is not the case, it is
useful to imagine the Earth as being
stationary while the celestial sphere rotates
around it.
The Celestial Sphere
• The north celestial pole is directly above
the north pole on the Earth.
• The south celestial pole is directly above
the south pole on the Earth.
• The celestial equator is an extension of the
Earth’s equator on the sky.
• The zenith is the point directly over your
head. The horizon is the circle 90 degrees
from the zenith.
The Celestial Sphere
• The celestial poles and the celestial equator
are the same for everyone.
• The zenith and the horizon depend on where
you stand.
http://www.astronomynotes.com/nakedeye/s4.htm
Stellar Coordinates and Precession
• There are a few ways to specify the location of a
star (or planet) on the sky:
• Altitude/Azimuth:
– The altitude describes how many degrees the star is
above the horizon, the azimuth describes how far the
star is in the east-west direction from north.
– The altitude and azimuth of a star is constantly
changing owing to the motion of the star on the sky!
Stellar Coordinates and Precession
• There are a few ways to specify the location of a
star (or planet) on the sky:
• Equatorial system:
– Lines of longitude on the earth become right
ascension, measured in units of time. The RA
increases in the easterly direction.
– Lines on latitude on the earth become declination,
measured in units of degrees. DEC=90o at the north
celestial pole, 0o at the equator, and -90o at the south
celestial pole.
– http://www.astronomynotes.com/nakedeye/s6.htm
Stellar Coordinates and Precession
• The north celestial pole moves with respect to
the stars very slowly with time, taking 26,000
years to complete one full circle.
The Cycle of the Sun
• The Sun would be in different constellations
during certain times of the year, if you could see
the stars in the day. Where the Sun is depends on
the season.
The Cycle of the Sun
• The Sun would be in different constellations
during certain times of the year, if you could see
the stars in the day. Where the Sun is depends on
the season.
In Detail:
•
If we do some careful observations, we find:
1) The length of the daylight hours at a given spot
varies throughout the year: the Sun is out a longer
time when it is warmer (i.e. summer), and out a
shorter time when it is colder.
2) On a given day, the length of the daylight hours
depends on where you are on Earth, in particular
it depends on your latitude: e.g. in the summer,
the Sun is out longer and longer the further north
you go.
In Detail:
• Near the North
Pole, the Sun never
sets in the middle
of the summer (late
June).
• Likewise, the Sun
never rises in the
middle of the
winter (late
December).
In Detail:
• In most places on Earth, the weather patterns
go through distinct cycles:




Cold weather: winter, shorter daytime
Getting warmer: spring, equal daytime/nighttime
Warm weather: summer, longer daytime
Cooling off: fall, equal daytime/nighttime
• These “seasons” are associated with the
changing day/night lengths.
In Detail:
• When it is summer in the northern
hemisphere, it is winter in the southern
hemisphere, and the other way around.
What Causes the Seasons?
• Is the Earth closer to the Sun during
summer, and further away during winter?
(This was the most commonly given answer
during a poll taken at a recent Harvard
graduation).
What Causes the Seasons?
• Is the Earth closer to the Sun during
summer, and further away during winter?
(This was the most commonly given answer
during a poll taken at a recent Harvard
graduation).
• No! Otherwise the seasons would not be
opposite in the northern and southern
hemispheres.
What Causes the Seasons?
• The Earth moves around the Sun. A year is
defined as the time it takes to do this, about
365.25 solar days.
• This motion takes place in a plane in space,
called the ecliptic.
• The axis of the Earth’s rotation is inclined
from this plane by about 23.5 degrees from
the normal.
What Causes the Seasons?
• The axis of the Earth’s rotation points to
the same point in space (roughly the
location of the North Star).
What Causes the Seasons?
• The axis of the Earth’s rotation points to
the same point in space (roughly the
location of the North Star).
• The result is the illumination pattern of the
Sun changes throughout the year.
What Causes the Seasons?
• Here is an edge-on view, from the plane of the
Earth’s orbit.
What Causes the Seasons?
• Here is a view from slightly above the Earth’s
orbital plane.
What Causes the Seasons?
• A slide from Nick
Strobel.
What Causes the Seasons?
• Because of the tilt of the Earth’s axis, the
altitude the Sun reaches changes during the
year: It gets higher above the horizon
during the summer than it does during the
winter.
What Causes the Seasons?
• Because of the tilt of the Earth’s axis, the
altitude the Sun reaches changes during the
year: It gets higher above the horizon
during the summer than it does during the
winter.
• Also, the length of the daytime hours
changes during the year: the daylight hours
are longer in the summer and shorter in
winter.
What Causes the Seasons?
• The altitude of the Sun matters: when the Sun is
near the horizon, it does not heat as efficiently as
it does when it is high above the horizon.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com/).
What Causes the Seasons?
• The Sun’s daily path across the sky
depends on the time of year…
What Causes the Seasons?
• Winter: The combination of a short
daytime and a Sun that is relatively low
above the horizon leads to much less
heating in the day, plus a longer period of
cooling at night. Overall, it is colder.
What Causes the Seasons?
• Summer: The combination of a long
daytime and a Sun that is relatively high
above the horizon leads to much more
heating in the day, plus a shorter period of
cooling at night. Overall, it is warmer.
What Causes the Seasons?
• Spring and Fall: The number of hour of
daylight is about equal to the number of
nighttime hours, leading to roughly equal
times of heating and cooling.
The Phases of the Moon
• Next to the Sun, the Moon is the most noticeable
object in the sky.
• The lunar cycle is the basis of the month.
How Long is one Month?
How Long is one Month?
• It depends:
How Long is one Month?
• It depends:
 If you use the Sun as a reference, the Moon
takes 29.5 days to complete one orbit around
the Earth.
How Long is one Month?
• It depends:
 If you use the Sun as a reference, the Moon
takes 29.5 days to complete one orbit around
the Earth.
 If you use a star as a reference, the moon takes
27.3 days to go around the Earth.
How long is one Month?
• During the course of 27
days, the Earth has moved
around a substantial part of
its orbit about the Sun.
• It takes an extra 2 days for
the Moon to “catch up” with
the Sun.
How Many Months are in a Year?
• It depends:
– 365.25/29.5=12.4 if you use the Sun as the
reference.
– 365.25/27.3=13.4 if you use a star as the reference.
– 12 calendar months, with each calendar month
being slightly longer than one lunar cycle.
What Causes the Phases of the
Moon?
What Causes the Phases of the
Moon?
• The full Moon always rises just after sunset.
• The crescent Moon always points towards the Sun.
• A crescent Moon sets shortly after sunset, or rises just
before sunrise.
• The Moon is illuminated by reflected sunlight.
What Causes the Phases of the
Moon?
• The full Moon always rises just after sunset.
• A crescent Moon sets shortly after sunset.
What Causes the Phases of the
Moon?
• The full Moon always rises just after sunset.
• A crescent Moon sets shortly after sunset.
What Causes the Phases of the
Moon?
• The lit side of the
Moon always faces the
Sun.
• Because of the motion
of the Moon relative to
the Sun, we see
different amounts of lit
and dark sides over the
course of a month.
Lunar and Solar Eclipses
• But first, let’s discuss “angular size” and
“linear size”…
Angular Size
• The physical size is
measured in meters,
light-years, etc.
• The distance is
measured in the same
units.
• The angular size is
how large something
“looks” on the sky,
and is measured in
degrees.
Angular Size
• The angular size is
how large something
“looks” on the sky,
and is measured in
degrees.
• As you move the
same object further,
its angular size gets
smaller.
Angular Size
• The angular size is
how large something
“looks” on the sky,
and is measured in
degrees.
• If two objects are at
the same distance, the
larger one has the
larger angular size.
Angular Size
• Trick photography often involves playing with
different distances to create the illusion of large
or small objects:
http://www.tadbit.com/2008/03/06/top-10-holding-the-sun-pictures/
http://www.stinkyjournalism.org/latest-journalism-news-updates-45.php
Angular Size
• This figure illustrates how objects of very different
sizes can appear to have the same angular sizes. The
Sun is 400 times larger than the Moon, and 390 times
more distant.
Lunar and Solar Eclipses
• A solar eclipse is seen when the Moon
passes in front of the Sun, as seen from a
particular spot on the Earth.
• A lunar eclipse is seen then the Moon
passes into the Earth’s shadow.
Shadows
• If the light source is extended, then the shadow of an
object has two parts: the umbra is the “complete”
shadow, and the penumbra is the “partial shadow”.
Shadows
• If the light source is
extended, then the
shadow of an object has
two parts: the umbra is
the “complete” shadow,
and the penumbra is the
“partial shadow”.
Lunar Eclipses
• During a total lunar eclipse, the Moon passes through
Earth’s shadow.
Solar Eclipses
• The umbral shadow of
the Moon sweeps over
a narrow strip on the
Earth, and only people
in that shadow can see
the total solar eclipse.
Solar Eclipses
• The umbral shadow of
the Moon sweeps over
a narrow strip on the
Earth, and only people
in that shadow can see
the total solar eclipse.
Solar Eclipses
• The umbral shadow of
the Moon sweeps over
a narrow strip on the
Earth, and only people
in that shadow can see
the total solar eclipse.
• During totality the
faint outer atmosphere
of the Sun can be seen.
Annular Eclipses
• The angular sizes of
the Sun and Moon
vary slightly, so
sometimes the Moon
isn’t “big enough” to
cover the Sun
Lunar and Solar Eclipses
• Why isn’t there an eclipse every month? Because the orbit of the
Moon is inclined with respect to the orbital plane of the Earth
around the Sun.
How often do we see an Eclipse?
• Roughly every 18 months there is a total solar
eclipse visible somewhere on the Earth.
Good Review Questions, Chapter 1
7. What is the celestial sphere, and why is this ancient
concept still useful today?
8. What is the celestial equator, and how is it related to
Earth’s equator? How are the north and south celestial
poles related to Earth’s axis of rotation?
11. Why does the tilt of Earth’s axis relative to its orbit
cause the seasons as Earth revolves around the Sun?...
15. Why is it warmer in the summer than in winter?
16. Why does the Moon exhibit phases?
23. At which phase(s) of the Moon does a solar eclipse
occur? A lunar eclipse?
Good Review Questions, Chapter 2
6. How did Copernicus explain the retrograde motions of
the planets?
10. What are Kepler’s three laws? Why are they
important?
11. In what ways did the astronomical observations of
Galileo support a heliocentric cosmology?
12. How did Newton’s approach to understanding planetary
motion differ from that of his predecessors?
15. Why does an astronaut have to exert a force on a
weightless object to move it?
A Brief History of Astronomy
• By the time of the ancient Greeks (around
500 B.C.), extensive observations of the
planetary positions existed. Note, however,
the accuracy of these data were limited.
• An important philosophical issue of the
time was how to explain the motion of the
Sun, Moon, and planets.
What is a model?
• A model is an idea about how something
works.
• It contains assumptions about certain things,
and rules on how certain things behave.
• Ideally, a model will explain existing
observations and be able to predict the
outcome of future experiments.
Aristotle (385-322 B.C.)
• Aristotle was perhaps the most influential
Greek philosopher. He favored a
geocentric model for the Universe:
 The Earth is at the center of the Universe.
 The heavens are ordered, harmonious, and
perfect. The perfect shape is a sphere, and the
natural motion was rotation.
Geocentric Model
• The motion of the Sun around the Earth
accounts for the rising and setting of the
Sun.
• The motion of the Moon around the Earth
accounts for the rising and setting of the
Moon.
• You have to fiddle a bit to get the Moon
phases.
Geocentric Model
• The fixed stars were on the “Celestial
Sphere” whose rotation caused the rising
and setting of the stars.
• This is the constellation of
Orion
• The constellations rise and set each night, and individual
stars make a curved path across the sky.
• The curvature of the tracks depend on where you look.
Geocentric Model
• The fixed stars were on the “Celestial
Sphere” whose rotation caused the rising
and setting of the stars.
• However, the detailed motions of the
planets were much harder to explain…
Planetary Motion
• The motion of a planet with respect to the background
stars is not a simple curve. This shows the motion of
Mars.
• Sometimes a planet will go “backwards”, which is
called “retrograde motion.”
Planetary Motion
• Here is a plot of the path
of Mars.
• Other planets show similar
behavior.
Image from Nick Strobel Astronomy Notes (http://www.astronomynotes.com/)
Aristotle’s Model
• Aristotle’s model
had 55 nested
spheres.
• Although it did
not work well in
detail, this model
was widely
adopted for nearly
1800 years.
Better Predictions
• Although Aristotle’s ideas were commonly
accepted, there was a need for a more
accurate way to predict planetary motions.
• Claudius Ptolomy (85-165) presented a
detailed model of the Universe that
explained retrograde motion by using
complicated placement of circles.
Ptolomy’s Epicycles
• By adding epicycles, very complicated motion could be
explained.
Ptolomy’s Epicycles
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com/).
Ptolomy’s Epicycles
Ptolomy’s Epicycles
• Ptolomy’s model was considered a
computational tool only.
• Aristotle’s ideas were “true”. They
eventually became a part of Church dogma
in the Middle Ages.
The Middle Ages
• Not much happened in Astronomy in the
Middle Ages (100-1500 A.D.).
Next:
The Copernican Revolution
The Sun-Centered Model
• Nicolaus Copernicus
(1473-1543) proposed
a heliocentric model of
the Universe.
• The Sun was at the
center, and the planets
moved around it in
perfect circles.
The Sun-Centered Model
• Nicolaus Copernicus
(1473-1543) proposed
a heliocentric model of
the Universe.
• These stamps mark the
500th anniversary of
his birth.
The Sun-Centered Model
• The Sun was at the
center. Each planet
moved on a circle,
and the speed of the
planet’s motion
decreased with
increasing distance
from the Sun.
The Sun-Centered Model
• Retrograde motion
of the planets could
be explained as a
projection effect.
The Sun-Centered Model
• Retrograde motion
of the planets could
be explained as a
projection effect.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com/)
Copernican Model
• The model of Copernicus did not any better
than Ptolomy’s model in explaining the
planetary motions in detail.
• He did work out the relative distances of the
planets from the Sun.
• The philosophical shift was important (i.e.
the Earth is not at the center of the
Universe).
Johannes Kepler (1571-1630)
• Kepler was a mathematician by training.
• He believed in the Copernican view with the
Sun at the center and the motions of the
planets on perfect circles.
• Tycho hired Kepler to analyize his
observational data.
Johannes Kepler (1571-1630)
• Kepler was a mathematician by training.
• He believed in the Copernican view with
the Sun at the center and the motions of the
planets on perfect circles.
• Tycho hired Kepler to analyize his
observational data.
• After years of failure, Kepler dropped the
notion of motion on perfect circles.
Kepler’s Three Laws of
Planetary Motion
• Starting in 1609, Kepler published three
“laws” of planetary motion:
Kepler’s Three Laws of
Planetary Motion
•
Starting in 1609, Kepler published three
“laws” of planetary motion:
1. Planets orbit the Sun in ellipses, with the Sun
at one focus.
Ellipses
• An ellipse is a “flattened circle” described by a
particular mathematical equation.
• The eccentricity tells you how flat the ellipse is:
e=0 for circular, and e=1 for infinitely flat.
Ellipses
• You can draw an
ellipsed with a loop of
string and two tacks.
Kepler’s Three Laws of
Planetary Motion
•
Starting in 1609, Kepler published three
“laws” of planetary motion:
1. Planets orbit the Sun in ellipses, with the Sun
at one focus.
Kepler’s Three Laws of
Planetary Motion
•
Starting in 1609, Kepler published three
“laws” of planetary motion:
1. Planets orbit the Sun in ellipses, with the Sun
at one focus.
2. The planets sweep out equal areas in equal
times. That is, a planet moves faster when it
is closer to the Sun, and slower when it is
further away.
Kepler’s Second Law
• The time it takes for the
planet to move through
the green sector is the
same as it is to move
through the blue sector.
• Both sectors have the
same area.
Kepler’s Three Laws of
Planetary Motion
•
Starting in 1609, Kepler published three
“laws” of planetary motion:
1. Planets orbit the Sun in ellipses, with the Sun
at one focus.
2. The planets sweep out equal areas in equal
times. That is, a planet moves faster when it
is closer to the Sun, and slower when it is
further away.
Kepler’s Three Laws of
Planetary Motion
•
Starting in 1609, Kepler published three
“laws” of planetary motion:
1. Planets orbit the Sun in ellipses, with the Sun
at one focus.
2. The planets sweep out equal areas in equal
times. That is, a planet moves faster when it
is closer to the Sun, and slower when it is
further away.
3. (Period)2 = (semimajor axis)3
Kepler’s Third Law
P2
distance d3
Mercury 0.241
0.058
0.387
0.058
Venus
0.615
0.378
0.723
0.378
Earth
1.000
1.000
1.000
1.000
Mars
1.881
3.538
1.524
3.540
Jupiter
11.857
140.588 5.203
140.852
Saturn
29.424
865.772 9.537
867.432
Period
Heliocentric or Geocentric?
• The year is around 1610. The “old” school is
Aristotle and a geocentric view. The “new”
school is the heliocentric view (Copernicus and
Kepler).
• Which one is correct?
• Observational support for the heliocentric
model would come from Galileo.
• Theoretical support for the heliocentric model
would come from Isaac Newton.
Next:
Who Wins?
Galileo Galilei (1564-1642)
• Galileo was one of the
first to use a telescope
to study astronomical
objects, starting in
about 1609.
• http://www.pacifier.c
om/~tpope/index.htm
Galileo Galilei (1564-1642)
• Galileo was one of the first to use a telescope
to study astronomical objects, starting in about
1609.
• His observations of the moons of Jupiter and
the phases of Venus provided strong support
for the heliocentric model.
Jupiter’s Moons
• The 4 objects circled Jupiter, and not the Earth!
Jupiter’s Moons
• You can watch Jupiter’s moons move from one
side of Jupiter to the other in a few days.
Jupiter’s Moons
• Not all bodies go around the Earth!
Venus
• Venus, the brightest planet, is never far
from the Sun: it sets at most a few hours
after sunset, or rises at most a few hours
before sunrise.
Venus
• Venus, the brightest planet, is never far
from the Sun: it sets at most a few hours
after sunset, or rises at most a few hours
before sunrise.
• It is never out in the middle of the night.
Venus
• Galileo discovered that Venus had phases, just like the
Moon.
Venus
• Galileo discovered that Venus had phases, just like the
Moon.
• Furthermore, the crescent Venus was always larger
than the full Venus.
Venus
• Galileo discovered that Venus had phases, just like the
Moon.
• Furthermore, the crescent Venus was always larger
than the full Venus.
• Conclusion: Venus shines by reflected sunlight, and it
is closer to Earth when it is a crescent.
Venus in the Geocentric View
• Venus is always
close to the Sun on
the sky, so its
epicycle restricts its
position.
• In this view, Venus
always appears as a
crescent.
Venus in the Heliocentric View
• In the heliocentric
view, Venus orbits
the Sun closer than
the Earth does.
• We on Earth can see
a fully lit Venus
when it is on the far
side of its orbit.
Venus in the Heliocentric View
• The correlation between
the phases and the size
is accounted for in the
heliocentric view.
Isaac Newton (1642-1727)
http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Newton.html
Isaac Newton (1642-1727)
• Newton was perhaps the greatest scientist of
all time, making substantial contributions to
physics, mathematics (he invented calculus
as a college student), optics, and chemistry.
• His laws of motion and of gravity could
explain Kepler’s Laws of planetary motion.
Newton’s Laws of Motion
1.
2.
3.
A body in motion tends to stay in motion in a straight
line unless acted upon by an external force.
The force on an object is the mass times the acceleration
(F=ma).
For every action, there is an equal and opposite reaction.
(For example, a rocket is propelled by expelling hot gas
from its thrusters).
What is Gravity?
• Gravity is a force between all matter in the
Universe.
• It is difficult to say what gravity is.
However, we can describe how it works.
What is Gravity?
• Gravity is a force between all matter in the
Universe.
• It is difficult to say what gravity is.
However, we can describe how it works.
What is Gravity?
• The gravitational force between larger
bodies is greater than it is between smaller
bodies, for a fixed distance.
What is Gravity?
• As two bodies move further apart, the
gravitational force decreases. The range of
the force is infinite, although it is very small at
very large distances.
Newton’s Laws
• Using Newton’s Laws, we can…
 Derive Kepler’s Three Laws.
 Measure the mass of the Sun, the Moon, and
the Planets.
 Measure the masses of distant stars in binary
systems.
Laws of Physics
• The models of Aristotle and Ptolomy were
based mainly on beliefs (i.e. that motion should
be on perfect circles, etc.).
• Starting with Newton, we had a physical
model of how the planets moved: the laws of
motion and gravity as observed on Earth give a
model for how the planets move.
• All modern models in Astronomy are based on
the laws of Physics.
Good Review Questions, Chapter 2
6. How did Copernicus explain the retrograde motions of
the planets?
10. What are Kepler’s three laws? Why are they
important?
11. In what ways did the astronomical observations of
Galileo support a heliocentric cosmology?
12. How did Newton’s approach to understanding planetary
motion differ from that of his predecessors?
15. Why does an astronaut have to exert a force on a
weightless object to move it?
15. Describe four methods for discovering extrasolar
Good Review Questions, Chapter 3
4. What are the three major functions of a telescope?
12. Why must astronomers use satellites and Earth-orbiting
observatories to study the heavens at X-ray
wavelengths?
13. What is a blackbody? What does it mean to say that a
star appears almost like a black body? …
15. What is Wien’s Law? How could you use it to
determine the temperature of a star’s surface?
16. What is the Stefan-Boltzmann law? How do
Astronomers us it?
Good Review Questions, Chapter 3
18. What is an element? List the names of five different
elements…
20. Explain how the spectrum of hydrogen is related to the
structure of the hydrogen atom.
Telescopes
• A flat surface reflects incident light at the
same angle.
• A curved surface can focus light.
Telescopes
• Glass alters the path of light.
• A curved piece of glass can focus light.
Telescopes
• A telescope uses mirrors or lenses to
collect and focus light.
• The area of the lens or mirror can be
considerably larger than the area of the
eye’s pupil, hence much fainter objects can
be seen.
Telescopes
• A refracting telescope
uses a large lens to bring
the light to a focus, as in
Figure (a).
• A reflecting telescope
uses curved mirrors to
bring the light to a focus,
as in Figure (b).
Telescopes
• The largest lenses that can
be built have a diameter of
about 1m, and have very
long focal lengths.
• A lens must be held by its
edges, and large lenses sag
under their own weight.
Also lots of light is lost in
the glass.
• For these and more reasons,
all modern telescopes use
mirrors.
Telescopes
• Using an objective mirror, plus some additional
mirrors and lenses, light is collected and focused
to a point.
• This is a Newtonian telescope.
Telescopes
• Using an objective mirror, plus some additional
mirrors and lenses, light is collected and focused
to a point.
• This is a Cassegrain telescope.
Telescopes
• A telescope’s main job is collecting photons.
• The light gathering power is proportional to
the area of the mirror or lens. The area of a
circle is
•If you double the diameter of the mirror, the
light gathering power goes up 4 times.
Telescopes
• Modern mirrors can be made thin.
Their shapes are maintained using
pistons under computer control.
• The Gemini telescope in Hawaii has
primary mirror 8.1m in diameter.
Telescopes
• Modern mirrors can be
made thin. Their shapes
are maintained using
pistons under computer
control.
• The Gemini telescope in
Hawaii has primary mirror
8.1m in diameter.
• These thin mirrors are cast
in special rotating ovens.
Telescopes
• Mirrors can also be
made out of smaller
segments.
• The Keck telescopes
in Hawaii have
primary mirrors 10m
in diameter.
What a Telescope Does
• A Telescope is used to collect photons, so you
can see fainter objects.
Seeing Detail
• What does the next line say?
–
If you can read this, thank a teacher.
• Why is so hard to read?
• Why do binoculars help?
• It is hard to read because the angular size is
small. The binoculars magnify the angular
size.
What a Telescope Does
• A telescopes magnifies angular sizes.
What a Telescope Does
• A telescopes magnifies angular sizes and allows
you to see more detail.
Telescopes at other Wavelengths
• Recall that there other forms of “light”,
including radio waves, X-rays, UV light,
etc.
• The goal of “collect and detect” is still the
same.
Telescopes at other Wavelengths
• Recall that there other forms of “light”,
including radio waves, X-rays, UV light, etc.
• The goal of “collect and detect” is still the
same.
• However, the technologies used to collect and
detect are different at different wavelengths.
Radio Telescopes
• Radio telescopes use
“mirrors” made from
steel plates.
• Radio receivers collect
the focused radio
waves.
• The radio telescopes
are huge because of
the long wavelengths
of the radio waves.
Radio Telescopes
• Radio telescopes use
“mirrors” made from
steel plates.
• Radio receivers collect
the focused radio
waves.
• The radio telescopes
are huge because of
the long wavelengths
of the radio waves.
Radio Telescopes
• The GBT is the largest
steerable radio
telescope in the world,
with a diameter of 100
meters. It is perhaps
the largest movable
land-based object in
the world.
Radio Telescopes
• With modern
computers and
electronics, one can
combine the signals
from several radio
telescopes to
“synthesize” a much
larger telescope.
• The Earth’s atmosphere is transparent to visible light,
some infrared, and the radio.
• It is opaque to UV, X-rays, and gamma rays. To detect
these wavelengths, one must go to space.
X-ray Telescopes
• For example, X-ray light cannot be reflected like
visible light can. X-ray telescopes use “grazing
incidence” mirrors to collect X-rays.
Telescopes in Space
• The Hubble Space Telescopes observes in
the ultraviolet, visible, and infrared
Telescopes in Space
• The Hubble Space Telescopes observes in the
ultraviolet, visible, and infrared.
• It is also above the blurring atmosphere.
Telescopes in Space
• The Spitzer Space Telescopes observes in
the infrared
Telescopes in Space
• The image on the left is at optical wavelengths,
and the wavelength on the left is at infrared
wavelengths. Different features are seen.
Telescopes at other Wavelengths
• For most wavelengths,
you need to go into
space to observe.
Good Review Questions, Chapter 3
5. What are the three major functions of a telescope?
10. Compare an optical reflecting telescope to a radio
telescope. What do they have in common? How are
they different?
12. Why must astronomers use satellites and Earth-orbiting
observatories to study the heavens at X-ray
wavelengths?
14. Why did Romer’s observations of the eclipses of
Jupiter’s moons support the heliocentric, but not the
geocentric cosmology?
What is the nature of light?
The velocity of light is not infinite.
Good Review Questions, Chapter 3
16. Of the following photons, which has the lowest energy?
(a) infrared, (b) gamma rays, (c) visible light, (d)
ultraviolet, (e) X-ray.
What is the nature of light?
Light can be thought of as a
wave in an electric field
or
as discrete particles of energy…
What is the nature of light?
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Light can be thought of as a wave. The wavelength
(usually denoted with a l) is the distance from crest to
crest.
What is the nature of light?
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Light can be thought of as a wave. The frequency
(usually denoted with n) is the number of crests that pass
a given point each second.
What is the nature of light?
Light can be thought of as a wave. The frequency
(usually denoted with n) is the number of crests that pass
a given point each second.
What is the nature of light?
The velocity of the wave is the wavelength times
the frequency:
The velocity of light in vacuum is constant for
all wavelengths, regardless of the relative
velocities of the observer and the light source.
What is the nature of light?
The velocity of light is not infinite.
What is the nature of light?
Although the velocity of light is large, it is not
infinite.
c = 300,000 km/sec
or
c = 186,000 miles/sec
What is the nature of light?
Although the velocity of light is large, it is not
infinite.
c = 300,000 km/sec
or
c = 186,000 miles/sec
Ordinary matter cannot travel faster than the
speed of light.
What is the nature of light?
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
The above animation shows waves with different
wavelengths moving with the same speed. Their
frequencies are different.
What is the nature of light?
Light can be thought of as a
wave in an electric field
or
as discrete particles of energy…
What is the nature of light?
Light can also behave like discrete particles called
photons. The energy of a photon depends
on the frequency (or equivalently the
wavelength):
The value of h is constant for all situations.
What is the nature of light?
Photons of higher energy have higher frequencies
and shorter wavelengths, since
What is the nature of light?
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
The above animation shows waves with different
wavelengths moving with the same speed. Their
frequencies are different.
Intensity vs. Energy
• A photon’s energy
depends on the
frequency.
• The intensity of a source
refers to the number of
waves or photons from
that source.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Different “types” of light.
What light can tell us.
Visible light
• White light is made up of different colors
Visible light
• Different colors correspond to different
frequencies (or wavelengths).
• The colors of the rainbow are ROY G BIV:
red orange yellow green blue indigo violet.
Visible light
• In the visible,
 red has the longest wavelength, the smallest
frequency, and the lowest energy.
 violet has the shortest wavelength, the highest
frequency, and the highest energy.
The Electromagnetic Spectrum
• Visible light is only a tiny
fraction of the
Electromagnetic Spectrum.
• For example, there is invisible
radiation with wavelengths
longer than red light that heats
the thermometer.
The Electromagnetic Spectrum
• As we go to wavelengths slightly longer
than visible (i.e. smaller frequencies and
lower energies), we find infrared radiation,
which is basically perceived as heat.
The Electromagnetic Spectrum
• As we go to wavelengths slightly longer
than visible (i.e. smaller frequencies and
lower energies), we find infrared radiation,
which is basically perceived as heat.
• As we go to longer wavelengths still, we
find microwave radiation, which is often
used to pop popcorn.
The Electromagnetic Spectrum
• At the longest wavelengths, corresponding
to the smallest frequencies and the lowest
energies, we have radio waves, including
AM/FM, shortwave, TV, etc.
The Electromagnetic Spectrum
• Visible light is only a tiny fraction of the
Electromagnetic Spectrum.
• If we go to shorter wavelengths (higher
frequencies and energies), we find
ultraviolet light. With higher energies, UV
photons can damage skin cells.
The Electromagnetic Spectrum
• As we go even shorter in wavelength
(higher in frequency and energy), we get Xrays. With their high energies, X-rays can
be used to image our insides.
The Electromagnetic Spectrum
• As we go even shorter in wavelength
(higher in frequency and energy), we get Xrays. With their high energies, X-rays can
be used to image our insides.
• As the shortest wavelengths and the highest
energies, we have gamma rays. Gamma
rays are sometimes used to sterilize food.
The Electromagnetic Spectrum
• Visible light is only a tiny
fraction of the
Electromagnetic Spectrum.
The Electromagnetic Spectrum
• Gamma rays, X-rays, UV light, visible light,
infrared radiation, microwaves, and radio waves
are all different manifestations of
electromagnetic energy.
• The range in wavelengths typically encountered
span a factor of 1014.
• All forms of electromagnetic radiation travel
with the same velocity.