- The same force that holds objects to the ground, gravity, keeps
objects in orbit around others. This applies to planets orbiting the Sun,
moons orbiting planets, and artificial satellites in Earth orbit.
- The
difference between an object on Earth and one in orbit is that an
orbiting object has an initial transverse velocity. Transverse
velocity is the ``sideways'' velocity of an object. If an object
has transverse velocity, the force of gravity causes it to orbit,
even though gravity acts to pull objects towards one another. This is
because the motion of an object is a combination between its initial
velocity and the acceleration caused by gravity. If an object starts
off with zero velocity, gravity will pull it directly towards another
object. But if an object starts with some transverse velocity, gravity
acts to pull it around another object. The amount of transverse
velocity that an object has determines the type of orbit it will make.
- The laws of motion and the law of gravity can be manipulated to
derive Kepler's laws of planetary motion. They explain why these
laws apply. However, they are far more general: they apply not only to
planetary motion, but to motions of other objects as well.
- The idea of transverse velocity applies to how rockets go
into orbit. To place an object into orbit, a spacecraft must have
enough velocity along the orbit. Too little velocity and the
spacecraft will fall back to Earth; too much velocity and the
object will escape into space. The exact orbital velocity needed
depends on the mass of the planet & the orbital altitude (Law of
Gravity equation). When a rocket is launched, it must be given transverse
velocity: a rocket is never launched straight up!
- Why do astronauts appear to be ``weightless'' on the Space
Shuttle if gravity is present? This is an unfortunate use of terminology. The Space
Shuttle is really free falling toward the Earth constantly but because
of its orbital speed, it misses the edge of the Earth. Any
free-falling objects appear to be weightless (person dropped from an
airplane in an enclosed box) because both the object and the container
are falling at the same rate.
- Gravity can explain why planets orbit around the
Sun if the planets have some transverse velocity. In fact, our ideas
about how the solar system formed explain why we would expect that
planets do have some initial transverse velocity.
- We think that the solar system formed out of a large interstellar
gas and dust cloud. Such clouds are expected to have a very slight spin.
- The formation of the solar system started when one of these clouds
started to collapse because of the force of gravity pulling it together.
- As the cloud collapses, it starts to spin faster because of a principle
called the conservation of angular momentum. This is the same reason an
ice skater spins faster when he/she pulls her arms inward.
- The combination of the increased spin with the attractive force
of gravity makes the cloud flatten into a disk which is spinning relatively
fast.
- Inside this disk, the Sun forms at the center, and planets form
around it. The spinning provides the necessary transverse velocity to keep
planets from falling into the Sun. The planets will necessarily be
rotating around the Sun all in the same direction and in the same plane
- exactly as is observed.
- Collisions between particles in the protoplanetary disk are likely
responsible for making the orbits nearly circular.
Gravity as a Mass Probe
- We can use our understanding of gravity to measure masses of
astronomical objects. The principle is simple: the presence of
gravity makes objects fall towards each other or orbit each other,
and the observed motion depends on the strength of the gravitational
force. Since the gravitional force depends on the mass of the objects
and the distance between them, we can measure masses of objects if we
can measure how fast they move (or how long it takes for them to go
around each other), and how big the orbits are.
- orbit simulator
(credit: PhET Interactive Solutions, University of Colorado!)
- For example, measuring the accelaration an object dropped on the
surface of the earth can tell us the mass if the Earth if we know the
Earth's radius.
- For orbits, gravity tells us that the speed of an orbiting object
depends on the masses of the objects and the distance between them.
The speed of the orbiting object can be combined with the size of
the orbit to determine the period of the orbit. We can then derive,
using our understanding of gravity, a relation between the period of
an orbit, its size, and the masses of the two objects. This
leads to a generalization of Kepler's 3rd law which can be derived from
Newton's laws:
(M1+M2) = A3/P2
where P
is the orbital period (in years), A
is the average distance
between the bodies (in astronomical units), and M1
and M2
are
the masses of the bodies (in solar masses). For our solar system,
M1
is the mass of the Sun and M2
is the mass of a planet which
is always much less than that of the Sun; this explains why Kepler's
3rd law works for planetary orbits.
- This version of Kepler's 3rd Law can now be used for any situation
in which two objects are orbiting about each other and can be used to
determine the total mass of the system (M1 + M2
). In many cases,
one object is much more massive than the other, and the sum of the two
masses is essentially identical to the mass of the more massive object.
For example, the Galilean satellites orbit about Jupiter. We can
measure the orbital period by observing the motion of a Jovian moon over
time and we can measure the orbital radius (A
) from a photograph.
Then, plugging into Newton's version of Kepler's third law above,
we can determine the mass of Jupiter (which is much larger than that
of any of the moons,
MJupiter + Mmoon
MJupiter
).
Even when one object is not much more massive than the other, the
masses can be measured individually if one can measure the velocities.
- This formulation of Kepler's 3rd law can be applied to many astronomical
objects to determine their masses. The basic idea is that astronomical
objects move because of gravity; the strength of gravity depends on the
masses of objects, so by observing motions of objects and understanding
gravity, we infer masses of objects. When we see an orbiting object,
if we can measure its period (or speed) and the size of the orbit, we
can learn about the mass of the object that is causing it to orbit.
- Planetary masses are determined by looking at the time it takes
satellites (either natural or man-made) to orbit the planets, and
measuring the radius of the orbit. We find that the masses of planets
have a large range. In units of Earth masses, the planets have the
following masses: Mercury 0.06, Venus 0.82, Earth 1.00, Mars, 0.11,
Jupiter 317.9, Saturn 95.2, Uranus 14.5, Neptune 17.1, Pluto 0.003.
One can immediately see that there are at least two generally different
types of planets in the solar system, the inner planets and the outer
planets (except for Pluto); the inner planets are substantially less
massive than the outer planets.
- Masses of stars can also be determined by looking at motions. This
is done using binary stars which orbit each other. By measuring the
period and the sizes of the orbits, we can infer masses of the stars. We
find that not all stars have the same mass. The most massive stars
are about 100 times as massive as the Sun, while the least massive
stars are about 1/10 the mass of the Sun. So in this respect, the
Sun is roughly average. However, there are many more low mass stars
than there are high mass stars.
- We can also use our understanding of gravity to infer masses of galaxies.
The law of gravity applies to the rotation of stars around the
center of
spiral galaxies.
If most of the mass is concentrated in the centers of these galaxies,
similarly to the concentration of light, one would expect stars in
the outer regions of galaxies to be revolving with slower velocities.
- However, we observe
that stars in the outer regions of galaxies
are rotating with approximately the same velocity as stars in the inner
regions. The graph that shows the rotation speed of stars as a function
of distance from the center of the galaxy is called a rotation
curve.
- This implies that there is a large amount of mass in the outer
regions of galaxies, even though we don't see very much starlight in
those regions. The presence of this mass is inferred entirely from
gravity. This unseen matter is called dark matter. Something to
ponder - the rotation velocities imply that there may be 10 times
more dark matter than luminous, so we may be the abnormal matter!
- Dark matter only has a significant effect on the scale of
galaxies. For example, on the scale of the solar system, there is
very little dark matter, so it does not affect the orbits of
planets.
- There is other evidence for dark matter in the Universe. For
example, motions of galaxies in
galaxy clusters
imply that there is more mass in these clusters than can be accounted
for in the luminous parts of the galaxies.
- Evidence of dark matter is also provided by another gravitational
effect, namely, the effect of gravity on light. Although
Newton's laws provide a very accurate description of gravity in most
cases, they do not provide a perfect physical theory. The best modern
theory of gravitation is Einstein's theory of general relativity. For
most locations in the Universe, the prediction of Einstein's theory
is identical to those of Newton's theory, so it is fair to say
that Newton's laws are ``correct'' almost everywhere. However, there
are a few effects of gravity which occur in nature which Newton's laws
don't describe. In particular, it turns out the the motion of light
can be influenced by a strong gravitational force; Newton's laws don't
predict this because light does not have any mass (it is a form of
pure energy). However, Einstein's theory does predict that the path
of light will be altered by a strong gravitational field.
- We can observe the bending of light in what is known as
gravitational lenses.
These occur when we observe very distant
galaxies which happen to have other nearer galaxies which lie along
the same line of sight. Light from the distant galaxy goes out in all
directions. Some of the light comes directly to us on a straight path,
but we also observe other light which is directed towards us by the
gravitational bending of light by the nearer galaxies. This causes
us to see multiple images of the same galaxy.
- Measuring the properties of these gravitational lenses
allows us to infer something about the masses of the intervening
galaxies. Again, we find significant evidence for a lot more mass
in galaxies than we would infer from the observations of bright they
are. This is supporting evidence for the existence of dark matter.
- What is the dark matter made of? Currently, we
do not know. Some possibilities are:
- ``Failed'' stars; stars which don't have enough mass to start
nuclear reactions, and hence, shine. Planets could be considered to
be failed stars. However, it doesn't seem likely that there
are enough of these to make up the dark matter. Also, they'd have
to be found in galaxies in a totally different distribution than
stars are found in.
- ``Burned-out'' stars, stars which have lived their lives and
no longer shine. Also seems unlikely for same reasons as ``failed
stars''.
- Black holes.
- Einstein's theory of gravity, general relativity, allows for
a very peculiar type of object called a black hole. A black hole is
an object which has such a strong gravitational force at its
surface that even light cannot escape from the object.
- The gravity required to keep light from escaping is immense.
To get a black hole, you need to have a lot of mass concentrated into
a very small volume, so that the gravitational force at the surface
is very large.
- At a distance from a black hole, the black hole behaves no
differently that any other massive object; the force of gravity is
exceptionally strong at its surface, but not necessarily strong at
a distance. Consequently, black holes don't suck other objects into
them; objects with transverse velocities can orbit a black hole just
like they could orbit, for example, a star or the center of a galaxy.
- You cannot see a black hole directly, since by definition no
light can escape a black hole. However, we can infer their presence,
for example, in binary star systems or at the
Galactic Center
(see also here
or here),
by their gravitational effect on surrounding objects.
- Given our understanding of how black holes are likely to form,
however, it does not seem likely that there are enough of them
to make up the dark matter.
- Some other sort of matter than ``normal'' matter (i.e. protons,
neutrons, and electrons) which only weakly interact with normal matter
and which do not produce light. A strange idea, but currently this
is the leading candidate! There are some existing experiments that
are trying to detect this stuff....
- Our current understanding of what makes up the bulk of our
Universe
is
very limited! Not only do we have the existence of dark matter, we also
believe there is a large component of ``dark energy'', which, as we discussed
briefly some time ago, is suggested by observations of the expanding Universe
and the microwave background.
Light
- We have considered two basic questions: why do objects move? and
what can we learn about objects by studying their motion? We now proceed
to ask some other basic questions: Why do things shine? What can we
learn about them from studying the light they emit?
- Before we talk about this, we need to consider an underlying question:
What is light? Light is a form of energy, in particular, a form of
electromagnetic energy. Light is intimately related to the electromagnetic
force. The presence of light makes charged particles accelerate, and
the acceleration of charged particles makes light.
- How do we characterize light? Light comes in little packets called
photons. Each of these can be thought of as a little wave which moves
through space. Like any waves, you can characterize light waves with a
wavelength, a frequency, a speed, and an energy. Light waves come in all
different wavelengths. However, all wavelengths travel at the same speed,
the so-called speed of light, in empty space.
In addition, the energy of each photon
is also related to the wavelength. Photons with shorter wavelengths
have more energy than those with longer wavelengths.
- Light of different wavelengths have different names. The whole
range of different kinds of light is called the
electromagnetic spectrum.
Gamma rays (
10-12m
) have the shortest wavelengths,
followed by X rays(
10-10m)
, ultraviolet light(10-7m
), visible
light (violet, blue, green, yellow, red), infrared light (10-4m
),
microwaves (10-3m
), and radio waves (
0.1 - 104m
). All of these
are forms of light.
- How do you describe what kind of light you see from a source? You
can consider two things: how bright is an object, and what different
wavelengths are being produced by an object. The combination of these
two things, namely, measuring the brightness of each different wavelength,
is called the spectrum of an object.
- When your eye sees an object, it sees a combination of all the
different wavelengths that the object produces.
- You get a crude idea of the spectrum of an object by looking at
the color of an object: a blue object produces more blue light than
other wavelengths, a red object produces more red light than other
wavelengths, etc.
- You can measure the different wavelengths individually by using
an instrument called a spectrograph. A spectrograph takes incoming
light and sends each different wavelength in a different direction
where its intensity can be measured.
- A prism is a simple type of spectrograph. Another kind of spectrograph
uses an element called a diffraction grating, which you'll see in lab.
- When we look at objects, it is important to distinguish between light
that is emitted by the object and light that is reflected
by the object. Reflected light requires an external light source to shine
on the object before you can see it. Much of what we see around us is
reflected light.
- group question: color
- group question: color 2
- Do sources that emit light produce all kinds of light simultaneously,
or just particular wavelengths? By observation, there are three main
categories of spectra that are observed:
- continuous spectra: produce light over a range of different wavelengths
- emission-line spectra: produce light at only several distinct wavelengths
- absorption-line spectra: produce light over a range of different wavelengths,
but with light missing at several distinct wavelengths
- Group question: classes of spectra
- What determines what wavelengths are produced by a light source?
It depends on the properties of the source, as formulated
in the 1800s in some simple principles by Gustav Kirchoff, who stated that:
- dense warm substances produce continuous spectra, with some
light over a broad range of wavelengths. There are many different types
of continuous spectra, which we'll discuss in more detail later. Be aware
that the light that is produced is not necessarily light that our eyes
are sensitive too, unless the object is hot!
- low density, hot gases emit emission lines at distinct
wavelengths. There are many different types of emission line spectra.
- if a continuous source is placed behind a cooler gas, the
cooler gas produces absorption lines. There are many different
types of absorption line spectra.
- A schematic representation
- How do these apply to astronomical objects?
- Planets are dense objects, and produce continuous spectra. However, most
of this continuous light is in the infrared part of the spectrum.
The bulk of the visible light from planets which we see is not light which is
produced by the planet itself, but instead, it is light from the Sun
which is reflected by the planet.
- The inside of stars are hot, dense objects and thus produce
continuous spectra. However, the outer layers of stars are composed of
cooler gasses, so the combination of a cooler gas in front of a continuous
source make stars produce absorption line spectra.
- Some of the interstellar matter is composed of hot, low density
gasses, so these regions produce emission line spectra. Cool
regions in the interstellar matter can produce absorption lines in
background objects.
- questions
- What can we learn from studying the light which comes from
astronomical objects? First, we consider what we can learn by observing
object with continuous spectra.
- All warm dense objects produce light at all wavelengths, but they don't
produce an equal amount at all wavelengths. Inside dense objects, there
are large numbers of atoms, and photons of light don't travel far before
they interact with other atoms. As a result, the energy distribution of
the photons is closely connected with the energy distribution of the
atoms, i.e. how fast the atoms are moving. The particular kind of continuous
emission that warm objects produce is called thermal radiation
(also called blackbody radiation),
and the spectrum that such objects produce is called a thermal, or
blackbody spectrum. In a thermal spectrum, although light comes
out over a wide range of wavelengths, there is always a wavelength where
the most light is emitted, and all objects emitting thermal radiation have
spectra with the same characteristic shape.
- The wavelength where most of the light comes out depends on the
temperature
of the source. This happens because the emission of light
arises from the motions of charged particles; when particles move faster,
they produce light with typically higher energies than when particles
move slower. The energy of a photon of light is related to its wavelength;
photons of shorter wavelengths carry more energy than photons of longer
wavelengths. In addition, the motion of particles is related to the
temperature of the object; in hotter objects, particles move faster than
in cooler objects. Consequently, hotter objects produce more light at shorter
wavelengths, while cooler objects produce more light at longer wavelengths.
For objects where the peak wavelength falls around the optical part
of the spectrum, like stars, hotter objects are bluer than cooler
objects.
- Astronomers and physicists use a temperature scale called the Kelvin
scale which is directly related to the motions of atoms. Temperatures in
degrees Kelvin are very similar to temperatures in degrees Celsius:
K = C + 273
. Degrees Kelvin are directly related to the motions of atoms;
at 0 K, atoms don't move at all - this is called absolute zero. In degrees
Kelvin, the temperatures of objects on Earth are roughly 300 degrees Kelvin.
- We can measure
colors of stars,
hence we can infer temperatures.
The sun is about 5700 degrees K, and puts out most of its light at
yellow wavelengths. Hotter stars are bluer, cooler stars are redder.
Objects at ``room temperature'' put out most of their light at infrared
wavelengths; consequently, all objects around us (including us) are glowing,
but in light which are eyes cannot see.
- Light from objects around us on Earth and from planets is a bit
complicated because it arises from two sources. All objects are glowing
with continuous radiation because they are dense objects. In addition,
however, many objects also reflect light from other sources. For example,
the planets glow in infrared light, but also reflect visible light from
the Sun.
- group question: what can you learn from continuous
spectra?
- Although in principle we can measure temperatures of stars by looking
at their colors, there is a complication which makes this difficult.
The problem arises because light from a star has to travel through space
before it arrives at Earth. If there was nothing between the star and Earth,
the light would be unaffected, but sometimes, the light passes through
some interstellar matter which lies between the stars. This interstellar
matter (in particular the dust in the ISM) can affect the color of the star.
- Light can be affected by the presence of intervening matter. In the
simplest example, if you put something in front of a light source (e.g.,
a brick wall), you can block the light entirely. This occasionally happens
in space when there are very dense interstellar clouds between us and a
star.
- More commonly, light has to pass through a region of space which has
a relatively sparse number of particles. In this case, most of the light
passes through fine, but some of the light is affected. Because of the
nature of how light interacts with particles, blue light is usually more
affected than red light; more blue light is lost when travelling
through an interstellar cloud than red light. As a result, an object which
is viewed through an interstellar cloud appears redder than it would have
appeared if the cloud had not been there. This complicates the measurement
of temperature from an observation of color; a red star may be red because
it is cool, or it may be red because its light has passed through an
interstellar cloud.
- This same phenomenon is responsible for the changing color of the
Sun from yellow at midday to red at sunrise and sunset. The Sun's light
must pass through particles in the Earth's atmosphere before arriving at
the Earth's surface. During the middle of the day, the Sun's light passes
through a shorter path in the atmosphere than at sunset. Consequently,
during the middle of the day, all wavelengths from the Sun except the
shortest (bluest) make it through the Earth's atmosphere, and the Sun
appears yellow. The blue light which is removed by the Earth's atmosphere
is scattered around and can arrive at the Earth's surface from directions
other than the direction of the Sun, which makes the sky appear blue. At
sunset, the Sun's light must travel through more atmosphere, and only the
reddest wavelengths make it to the surface directly, making the Sun appear
red.
- group question: color of the Moon's sky
- group question: color of another sky
- Why do objects produced emission and absorption line spectra and
what can we learn from these? We shall see that the production of
emission and absorption lines depends on the characteristics of
individual atoms, and will find that we can measure something about
the compositions, temperatures, and motions of stars by studying
their spectra.
- In low density objects, atoms are much farther apart, and the
physics that explains light emission and absorption is closely
related to the structure and energies of individual atoms.
- Atomic structure
- At the most basic level, all matter is composed of elementary particles,
the most common of which are protons, neutrons, and electrons.
- These particles are found in groups known as atoms. Inside atoms,
protons and neutrons are found together in a nucleus, and electrons
are found orbiting around the nucleus.
- The chemical
properties of atoms are largely determined by the number of protons in the
nucleus. Because of this, the number of protons determines what the
element is. For example, hydrogen is the element with one proton in
its nucleus, helium has two protons, lithium has 3 protons, carbon has 6
protons, uranium has 92 protons, etc.
- Atoms normally have about the same number of neutrons as protons, but
they can come in different forms with different numbers of neutrons. These
different forms of an element are called isotopes.
- Atoms normally have about the same number of electrons as protons, but
they can come in different forms with different numbers of electrons. These
different forms of an element are called ions.
- Atoms can be found linked together into things called molecules.
- How do atoms produce or absorb light?
- Inside atoms, electrons orbit around the nucleus, as we have discussed.
Each electron orbit in an atom has a different energy associated with it.
However, we find that electrons do not exist at all possible energy levels.
Whenever we study a particular type of atoms, we find that
electrons are always found in one of several possible energy levels, but never
in between these levels. This is the basis for our current theory
of atoms, quantum mechanics.
- It is possible for electrons to switch from one energy level to another, and
in the process, they either emit energy (if they switch to a lower energy
orbit) or need to absorb energy (if they switch to a higher energy orbit).
The energy that they emit or absorb comes in the form of light. In an
isolated atom, the electrons will fall down to their lowest allowed
energy states.
- When electrons shift to lower energy orbits, they produce emission
lines. Emission line sources are
hot, low density gasses; in these gases, electrons are continually being
knocked up to higher orbits by collisions with other atoms, after which
the electrons fall down to lower orbits and produce emission lines.
- If there is a background light source which in shining on atoms,
absorption lines will be created at the energies which can be used by the
electrons to shift to higher energy orbits.
- The incredibly powerful thing about emission and absorption lines
is that every different element has different electron orbit energies and
consequently has
different possible emission or absorption lines.
This lets us determine the composition of any gas in which we see
lines.
- We can also use emission and absorption lines to determine the
temperature of objects. The temperature of a gas is related to the speed
at which atoms move around, and thus related to the strength of collisions
between atoms. In hotter gases, collisions are stronger and electrons
can be knocked to bigger orbits than in cooler gases. Although each element
has its own unique set of spectral fingerprints which correspond to
all possible electron transitions, in any object you will only see some
subset of these depending which orbits are populated by electrons. Since
this depends on the temperature, you can also determine the temperature
of an emission or absorption line source by seeing which of the lines
are present.
- group questions
- How does this work for astronomical objects?
- In the interstellar matter, atoms are heated by nearby stars. The
temperature of an object is related to the speed of the atoms in the
object, so when we say an object is hotter, that means its atoms are
moving around faster. When atoms move around, they can collide with
each other. These collisions can knock electrons up to higher energy
orbits. Left in the higher energy states, electrons in an atom will
always fall down to lower energy orbits; in the process they will emit
light of precisely the wavelength that corresponds to the energy change
between the two orbits. Consequently, these gas clouds will produce
emission lines, with the pattern of lines which are emitted being
determined largely by the chemical composition of the gas. However,
the lines which are produced also depend on the temperature. If the
gas is too cool, atoms won't move around fast enough so that collisions
are able to excite the electrons to higher energy orbits. If the gas
is too hot, collisions will knock the electrons entirely away from the
atoms. At temperatures in between, only a subset of the possible electron
orbits will be occupied. Thus, observations of emission lines can be
used to determine both compositions and temperatures.
- In stars, the inner denser regions produce continuous spectra, but as
this light passes through the outer layers of the star, certain
wavelengths are absorbed by whatever type of atoms happens to be in
these layers. The wavelengths which are absorbed are the photons whose
energies precisely match the energy difference between electron orbits in
the outer layers. Any photon which has an energy which does not match the
exact energy differences passes through unaffected. However, a few photons
have just the right energy to excite an electron, and these photons are
removed from the light passing out of the star. This causes the appearance
of
absorption lines in stellar spectra; these are wavelengths where
light appears to be missing. By studying which wavelengths are absorbed,
we can measure what the outer layers are made of. The energy which is
absorbed by the electrons is eventually re-emitted when the electrons
fall back to the lower orbits, but this energy is re-radiated equally
in all directions, and thus we still observe absorption lines. As with
emission lines, we can also determine the temperature of absorption lines
sources (at the layer where the absorption arises) by seeing what subset
of possible lines are present.
- In fact, in stars, one finds that all stars have very similar
compositions. We find that most of the normal matter Universe appears
to be made of hydrogen (approximately 90%. Of the remaining 10%,
about 9% is helium, and all of the other elements only make of 1% of
the total number of atoms. There is some important variations in the
abundances, but these variations are small: they range from heavy element
(everything except hydrogen and helium) abundances of nearly zero,
to about 2-3 percent of the star's mass. Of course, these fractions
do not necessarily apply to the dark matter which appears to dominate
the mass in the Universe, since we do not at this time know what this
dark matter is made of. It is possible that it is not made of protons,
neutrons, and electrons at all, but is perhaps made of some other sort
of basic particle.
- However, different stars have very different spectra from each
other because of a strong temperature dependence of absorption line
strengths. The different types of spectra from stars lead to what
astronomers call spectral classification, in which different
stars are placed into different groups depending on the appearance of the
absorption lines in their spectra. The different spectral types arise
almost entirely from the temperature effect. Originally, astronomers
didn't know this, and they just invented letter names for different
groups of stars. Now we understand that the sequence is a sequence in
temperature, and the groups can now be ordered by temperature into the
sequence: OBAFGKMLT, where O and B stars are the hottest and M,L, and
T stars are the coolest.
- Observed spectrum of the Sun
- Observed spectra of stars of different temperatures
- group question: what can we learn from absorption lines?
- What can we learn from studying the total brightness of objects?
- Up until now, we've been seeing what we can learn about objects
by studying their spectra, or the relative amount of light coming out at
different wavelengths. So far, we haven't talked about the total
brightness of stars,
partly because this is affected by several factors.
- To some extent, the brightness of stars is related
to their distance (closer stars are brighter), but stars clearly
come in a range of brightnesses
even when at the same distance, like in a
star cluster
- The total brightness of objects is affected primarily by three different
things:
- Hotter objects are brighter than cooler ones of the same size.
- Bigger objects are brighter than smaller objects of the same
temperature.
- Objects of the same size and temperature appear brighter when they
are closer to you than when they are further away.
- Group questions
- However, if you can independently measure the temperature, the brightness, and
the distance to a star, you can infer a size for the
star. We have learned that you can measure temperatures by studying the
spectra, and distances from parallax. Thus it is possible to measure
the sizes of stars.
- Of course, the simplest way to measure the size of an object is
to measure how large an area it appears to take up in the sky. This is
called the angular size. If you know the distance to the object, you
can easily calculate its true size, since the angular size is determined
from the true size and the distance. However, stars are so far away (except
for the Sun!) that
we cannot detect their angular size, hence inferring the size from the
brightness is very important.
- We find that there is an interesting relation between the
size of stars and their temperatures. A very useful tool for understanding
stars is a diagram which plots the color against the luminosity, or
intrinsic brightness (that is, after correcting for the effects of distance).
This diagram is called a color-magnitude diagram, or sometimes, a
Hertzsprung-Russell (HR) diagram
(for the people who first used it).
In such a plot, stars are only found at several locations:
- Most stars are found along a line in this diagram, known as the
main sequence. The hotter stars along this sequence are brighter,
even more than expected from their temperature: they are also bigger.
- Some stars are found which are cool but bright. The only way this
can be is if such stars are very large. Consequently these stars are
known as red giants. They are red because they are cool, and bright
because they are very large.
- Some stars are found which are hot but faint. These stars are known
as white dwarfs.
- We can also learn something about the motions of astronomical objects
by studying the light which they emit.
- We can measure whether objects are moving towards or away
from us (their radial velocity) by a
pheonomenon called the Doppler shift. The radial velocity is the part
of the velocity directed towards or away from us.
- The Doppler shift arises for objects which emit waves. Since light
behaves like a wave, we can observe the Doppler shift in the light which
is emitted from astronomical objects.
- The motion of an object affects the wavelength of the light which it
emits because if an object moves towards you, the crests of the emitted
waves will be bunched closer together than if the object is standing still
and emitting waves. In the same way, if an object is moving away from you,
the crests of the emitted waves with be spread further apart. For light,
a shorter wavelength (crests bunched closer together) means bluer light.
So if an object moves towards you, its light appears slightly bluer, and if
it moves away from you, its light appears slightly redder.
- This wavelength shift of light is usually quite small. For example,
it changes red light into slightly redder or less red light; it rarely
significantly affects the color of an object. However, for objects with
emission or absorption lines, it can clearly be detected because a
characteristic pattern of lines from some element will be noticed to
be shifted a small amount from the position where the lines are observed
in the element when it is at rest. This small shift can be used to measure
the radial velocity of astronomical objects.
- The Doppler shift applies to any sort of wave-like phenomenon. Since
sound is also a wave, the Doppler shift affects sound as well. This is
the reason why a car or train horn appears to change pitch as it passes
from coming towards you to going away from you.
- group question: doppler applications
- Astronomical applications of the Doppler shift: expansion of the
Universe, detection of dark matter in spiral galaxies, masses of binary
stars, detection of planets around other stars....
- Group questions
- The Doppler shift only allows us to measure the radial
component of an object's motion, but not the transverse
component. Transverse velocity means the part of the velocity which is
perpendicular to our line of sight. For example, if a star is moving
directly towards or away from Earth, it will not appear to move
with respect to more distant objects. For relatively nearby objects, we
can measure the transverse velocity by observing how the star appears to
move relative to background stars from night to night. However, even the
nearest stars have very tiny observed transverse velocities because they
are so far away. New space missions will be able to measure positions
to higher accuracy allowing many more measurements of full space motions
of objects.
Next: PART 5 - INTERESTING
Up: AY110 class notes
Previous: PART 3 - OVERVIEW
Jon Holtzman
2013-12-06
