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We have seen that quantum mechanical theo- quark and antiquark (which doesn™t weaken as they get far-
ries of forces require carrier particles. QCD is no ther apart). (a) We just have the normal separation. (b) We
different. In fact, the mathematical theory pre- are pulling them apart, doing work against the attractive
force. (c) We have done so much work that we have created
dicts the existence of a group of eight particles
a new quark“antiquark pair, and now have two mesons
carrying the force. These particles are called glu-
instead of two free quarks.
ons. There is a major difference between QED and
416 PART V THE UNIVERSE AT LARGE



apart, creating new combinations, but no free In the electroweak force, the photon and the W
quarks. This leads to quark confinement, and tells (or Z) are essentially the same. You might wonder
us that we should not see any free quarks. Pulling how two particles can be the same if one is very
quarks apart is like cutting a piece of string. Each massive and the other is massless. The answer to
piece will always have two ends. You can never get this question tells us what we really mean by uni-
a piece with one end. fication. In this case, the electromagnetic and
weak forces appear to be the same when we deal
21.3.5 The uni¬cation of forces with particles whose energies are much greater
Following his general theory of relativity, Einstein than the difference between the mass of the W and
spent the latter part of his life attempting to the mass of the photon (zero). At these high ener-
˜unify™ the forces of gravity and electromagnet- gies, the W mass arises from a small spontaneous
ism. By ˜unify™ we mean that we would like to symmetry breaking. However, we don™t really
explain all of the forces as really being manifes- notice the difference until the energy is so low that
tations of one larger force. The search is not new. the mass of the W can no longer be ignored. This is
After all, Maxwell unified the previously distinct another case of our maxim that nature is symmet-
forces of electricity and magnetism. Einstein™s ric as long as there is enough energy.
search for unification was not successful, and The masses of the W and Z are about 80 GeV
some thought that he was wasting his time (being expressed as equivalent energy, where the
because the problem had no solution. However, proton mass is about 1 GeV). These masses are
during the 1980s and 90s we have seen amazing barely accessible in today™s best particle accelera-
progress towards this goal. This progress is based tors. Therefore, we cannot even approach the
on mathematical theories, which are, in turn, range where particles will have energies much
based on the expectation that nature will obey greater than this in order to see a world in which
certain symmetries. The progress in the unifica- the electromagnetic and weak forces are the same.
tion of the forces is shown in Fig. 21.23. However, there must have been a brief instant in
The first of the recent successes was the unifi- the early universe when the temperature was high
cation of the electromagnetic and weak forces enough for this symmetry to be present. This is
into one force, called the electroweak force. (For this one of the important connections between parti-
work, Sheldon Glashow, Abdus Salaam and Steven cle physics and cosmology, and we will explore it
Weinberg shared the Nobel Prize for Physics in further in the next section.
1979.) A major test of that theory was the predic- The next step has been to unify the color
tion of the masses of the W and Z particles, carri- (strong) force with the electroweak force, using
ers of the weak force, before their discovery. the same mathematical tools. Theories that do
this are called grand unified theories, or GUTs. These
are still in the developmental stage. The carriers
Increasing energy
of this force are designated the X and Y particles.
There masses are estimated to be about 1014 GeV,
Electricity &
or 1012 times the mass of the W. This means that
Magnetism
the differences between the color force and the
Electroweak
electroweak force disappear when the energies
Weak
are much greater than 1014 GeV. These energies
Grand Unified
are clearly beyond the range of accelerators that
Theory
Strong we could contemplate on the Earth. However,
Theory of these conditions existed, ever so briefly, in the
Everything
big bang.
Gravity ????
One prediction of these GUTs is that the pro-
Fig 21.23. Uni¬cation of the forces. As we go from left to ton is not stable. Our normal understanding of
right in the ¬gure, we see how, at higher energies, the forces the apparent stability of the proton is that it is
become more uni¬ed.
the lowest mass baryon. The electroweak and
21 THE BIG BANG 417



color forces obey a conservation of baryons. Since section, we saw that the big bang provides a unique
a decay must always be to a lower mass particle, opportunity for testing the predictions of various
if a proton decayed the result would not be a unified theories. It is as if an experiment was
baryon. Hence the stability of the proton. However, done for us, some 15 billion years ago, and the
GUTs say that, at high enough energies, there is no data are around in coded form. We only have to
difference between the electroweak and color decode the results. For example, the current
forces. This means that the differences between abundance of helium in the universe tells us that
hadrons and leptons should be lost. According to the three neutrino types we have so far are likely
these theories, the proton would decay into a to be the only ones existing.
positron and a pion, with a half-life of about 1031 Some recent developments in particle physics
years. This doesn™t mean that half of the protons may be able to help solve some of the outstanding
wait this long, and then decay all at once. There problems in cosmology. We have already dis-
should be a steady trickle of decays. The probabil- cussed most of these in one form or another. The
ity of any proton decaying in a given year is small, problems that we would like to address include
but there are many protons on the Earth, so we the following.
could actually hope to catch some decaying. So
(1) Is the universe open or closed? If it is closed,
far, no such decays have been detected, indicating
what form does the dark matter take?
that the proton probably lives about ten times as
(2) Why is the universe so close to the boundary
long as the theory predicts. This means that there
of being open or closed?
will have to be some modification of the theory.
(3) Where did the magnetic monopoles go?
Another prediction of the GUTs is the exis-
(4) How can the background radiation be so
tence of magnetic monopoles. These are particles
smooth on large scales?
that would serve as the source of magnetic fields
(5) What caused the initial density concentrations
that are not due to the motions of charges. The
that led to galaxy formation?
magnetic field around a magnetic monopole
(6) Is there an excess of matter over antimatter?
would look like the electric field around a proton.
If so, how did it arise?
The simplest GUT theory predicts that there should
(7) For every baryon in the universe, there are
have been a large number of magnetic monopoles
approximately 1010 photons. Why is this?
made in the big bang, and they should be as
numerous as baryons. However, none have been To see how particle physics can help us answer
detected. Again, some modification of the theory these questions, we go back even farther than the
is required. epochs we have talked about already in this chap-
Even though there are still problems with ter. This is outlined in a time line, shown in Fig.
GUTs, some theoreticians are forging ahead with 21.24. As we go through this scenario, notice the
the final step, the inclusion of gravity in the uni- extremely short time scales.
We cannot say anything about the first 10 43
fied forces. These theories have been called super
seconds. This time is called the Planck time. To
GUTs, or supergravity, or theories of everything (TOE).
describe phenomena on this time scale we need a
Needless to say, they are still in the very specula-
quantum theory of gravity. It is even possible that
tive stages.
on this short time scale, the continuous fabric of
space-time breaks down.
21.4 Merging of physics of the big From 10 43 s onward, the temperature was so
and small high that GUTs are needed to describe the appli-
cable physics. Since the electroweak and color
21.4.1 Back to the earliest times forces are the same at these high energies, the
One of the most fascinating developments in the differences between quarks and leptons disap-
1990s has been the interaction between two fron- pear. (This is one reason why we think the num-
tier areas of physics and astronomy “ elementary ber of quark types should equal the number of
particle physics and cosmology. In the preceding lepton types “ currently thought to be six each.)
418 PART V THE UNIVERSE AT LARGE



Particle
E & M Freezeout
100 000 yr




Radiation
Antiparticle

3 min
Weak Freezeout
Nuclear Synthesis
1s
Leptons
Quarks
&

Quark Confinement
10“6 s
Quarks and Leptons




Electroweak (a)
10“12 s

Unmatched
Particle

10“35 s GUTs
Inflation

Planck Time
10“43 s
Fig 21.24. Time line for the early universe.This shows
Radiation
events from the Planck time through the beginning of galaxy
formation. Each magni¬cation is a factor of about one million
in time.

(b)
During this period baryon number was not con-
Fig 21.25. Matter“antimatter imbalance and the excess of
served. The breaking of symmetries involving
photons in the universe. In this ¬gure there is one extra
mirror reflection, and matter“antimatter inter-
particle of matter for every ten matter“antimatter pairs. In
change resulted in a slight excess of matter over the real universe it is one extra for ten billion! (a) The tem-
antimatter. This excess is one particle for every perature is high enough that the particles and antiparticles
1010 particle“antiparticle pairs produced. This are all present. (b) The temperature is low enough so that
tells us that our universe now has some matter, the particles and antiparticles annihilate and don™t re-sepa-
rate. For each annihilation, we get two photons.The lighter
which is not balanced by an exact amount of anti-
colored circles show the previous locations of particles and
matter. This answers question (6) listed above.
antiparticles.
This slight excess of matter over antimatter
also explains the observation that there are 1010
At the end of this period, after only 10 35 sec-
photons for every baryon in the universe. This is
illustrated in Fig. 21.25. As the universe continued onds, the universe had ˜cooled™ to the point
to cool, particles and antiparticles found each where the average energy was no greater than the
other and annihilated. For each pair that annihi- mass of the X and Y particles. This means that the
lated, two photons were produced to carry away symmetry between the electroweak and color
the energy. It was like a cosmic game of musical forces was broken. From that point on, baryon
chairs. For every 1010 particles that found a part- number was conserved.
By 10 12 seconds, the universe had cooled to a
ner, there was one particle for which there was no
antiparticle. That particle is still around, as well point where the electromagnetic and weak forces
as the 1010 photons left from that number of separate. This is because the average energy is
annihilations. This means that for every baryon comparable to the mass of the W. (Remember, we
left today, there must be 1010 photons. This solves saw in the preceding section that this symmetry
problem (7). This slight imbalance is very impor- is broken when average energy is no longer much
tant. If there were perfect balance between mat- greater than the W“photon mass difference.) At
ter and antimatter, the universe would now be all this point, the weak force was as strong as the
radiation, and we wouldn™t be here. electromagnetic force. From that point on, the
21 THE BIG BANG 419



weak force became much weaker than the elec-
tromagnetic force. However, it was still hot
enough for the quarks to move as a fluid. By 10 6
seconds, the quarks were confined in hadrons.
At 1 s, the temperature was low enough for
the weak force to have weakened to the point
where the neutrinos are rarely absorbed by mat-
ter. From that point on, the neutrinos and matter
decoupled (just as radiation and matter decou-
pled after 100 000 years). These neutrinos should
now be everywhere in the universe, just like the
cosmic background radiation. After the neutrinos
decoupled, there were still some electron“positron
annihilations that added photons to the radiation.
Thus the temperature of the neutrinos should be
less than the 3 K of the radiation. In fact, it is esti-
mated that the neutrinos are like a gas at 2 K.
These low energy neutrinos are extremely hard to
detect. However, there are so many of them that
if it turns out that neutrinos have a very small Fig 21.26. What might happen in a quantum mechanical
vacuum. Each frame is at a slightly different time.We see
rest mass, even as low as 20 eV (only about
particles/antiparticles and photons being created for brief
1/40 000 of the mass of the electron), the total
instants.
mass of neutrinos could exceed the mass of
nuclear matter by a factor of ten. That could be
enough to close the universe. It may also be that liquid water changing to water vapor. According
clumps of neutrinos formed the centers of attrac- to the theory, the rearrangement resulted in an
tion for the formation of clusters of galaxies. extremely rapid expansion of the universe. In this
We have now reached the regime that has expansion, the scale factor had a rapid exponen-
already been discussed earlier in this chapter. tial growth, as if there were a large cosmological
constant. R changed by more than 1040 in 10 32 s,
Nuclear reactions continued for the first three
minutes. By 100 000 years, the matter had cooled as indicated in Fig. 21.27. This rapid growth was
enough to become neutral, and the radiation called inflation. Once the inflation ended, the nor-
decoupled, remaining to be detected as the cos- mal expansion resumed.
mic background radiation. Though it is still a speculative theory, inflation
might explain some of our remaining cosmologi-
21.4.2 In¬‚ation cal puzzles. It solves the monopole problem (3) by
Particle physics has one more surprise for us, relat- saying that all of the monopoles were produced
ing to the nature of the vacuum during the GUT before inflation, and were carried far apart by
era. Classically, we think of the vacuum as simply inflation. Therefore, they are separated by large
being ˜nothing™. In quantum mechanics, it is not reaches of space, and we are not likely to run into
so simple. The vacuum is merely the lowest energy many.
state. It is still possible for interesting things to To see how it solves the flatness problem (2),
happen. This is illustrated in Fig. 21.26. On the let™s go back to our expanding sphere analogy.
smallest scales, we have the ongoing creation and Remember, we can only see things that are closer
destruction of particle“antiparticle pairs. to us than the distance light could have traveled
It has been proposed that, during the GUT era, in the age of the universe. If there was a large
the nature of the vacuum changed. When this inflation, our horizon doesn™t include a very
happened the universe underwent a phase large piece of the universe. Since we can only see
change, like solid ice changing to liquid water, or a small fraction of the surface, it appears flat.
420 PART V THE UNIVERSE AT LARGE



first, with the galaxies then forming out of den-
sity fluctuations within the forming cluster. In
Scale Factor

this latter scenario, calculations show that the
original large-scale structures would be flattened,
and these are referred to as pancakes.
In deciding between these scenarios, it is
important to understand the nature of the dark
Factor of
matter in the universe. Even if there is not
1035
Inflation
Jump enough dark matter to close the universe, there
must be at least enough to account for the viral
masses of clusters. Even this amount would
place the density of dark matter as being signif-
icantly greater than the density of luminous
matter. This means that the dynamics of the
Time
universe and galaxy formation is dominated by
Fig 21.27. Change of the scale factor in an in¬‚ationary dark matter.
universe.Time is plotted on the horizontal axis and scale Models of galaxy formation must also include
factor on the vertical axis. Notice that we have to put a
the effects of a non-zero cosmological constant, if
break in the scale factor axis to show the whole change.
there is one. That will affect the evolution of the
universe on the largest scales, especially affecting
the formation of the largest structures, super-
This is analogous to the Earth; when we only see
clusters. This gets around the problem, with cold
a small piece of its surface, it appears flat too.
dark matter explaining the largest structures. It
It solves the causality problem (4) by saying
now appears that we can simulate structures that
that everything within our horizon was so close
we see on all scales with cold dark matter, and
together before inflation that it could all be
0.3, 0.7. An example of one such
causally connected. MAT
stimulation is shown in Fig. 21.28.
It may even solve the galaxy formation prob-
lem (5) by saying that galaxies (or the matter to
21.4.4 Estimates of values of cosmological
form them) condensed around irregularities in
parameters
the distribution of phases as the inflation ended.
Here we summarize our current estimates of the
It must be remembered that these ideas are
values of various cosmological parameters
quite speculative. However, even if the specifics
needed to describe our big-bang universe. It
are wrong, they may have opened many new pos-
should be understood that, while a consistent pic-
sibilities in our understanding of the universe. At
ture seems to be emerging from a variety of
this point theoreticians working on cosmological
approaches, there is still a lot of work to be done,
models now include some form of inflation as
both observationally and theoretically.
part of their standard model.
Various approaches to measuring H0 are giv-
21.4.3 Galaxy formation ing consistent values near 70 km/s/Mpc. This cor-
responds to a Hubble time of 14 Gyr. The actual
As mentioned in Section 21.1, we believe that
age of the universe for the currently accepted
galaxies grew out of small fluctuations in the den-
model parameters is also 14 Gyr.
sity that were present before radiation and matter
The universe appears to be flat, as predicted
decoupled. (This is why anisotropies in the cosmic
by theories of inflation. The best observational
background radiation may tell us about the sizes
evidence for this comes from the small-scale fluc-
of these fluctuations.) As we have said in Chapter
tuations in the cosmic microwave background
18, there are two basic galaxy formation scenarios:
radiation, as shown in Fig. 21.12. Remember, this
(1) the galaxies may have formed first and then
radiation has been running through the universe
gathered into clusters; (2) the initial condensa-
back to z 1000. For any given size fluctuations,
tions may have been larger, forming protoclusters
21 THE BIG BANG 421




(a) (c)
Fig 21.28. Simulation of large-scale structure formation
and evolution in a cold dark matter universe with density
parameter MAT 0.3, cosmological constant 0.7, and
Hubble constant H 65 km/s/Mpc, inside a box of 154 Mpc
in size.The calculations were performed on a Cray SV1
supercomputer, with 2.7 million particles. (a) z 5; (b)
z 2; (c) z 0. [This simulation was produced at the Texas
Advanced Computing Center by the University of Texas
Galaxy Formation Group (Paul R. Shapiro, Hugo Martel and
Marcelo Alvarez)]




chapter that the effect of the cosmological con-
/8 G, so it acts in the opposite sense
stant is
(b) of matter. While matter wants to bring galaxies
together, the cosmological constant makes them
want to fly apart. Observations (still preliminary)
using supernovae to measure the deceleration
curvature in space-time (positive or negative)
parameter suggest that the expansion is not
would cause a distortion of how we view those
slowing down very quickly, and may be increas-
fluctuations. The fluctuations in Fig. 21.12 are
ing, consistent with a significant cosmological
those that would be expected with no distortion,
constant.
so they point to a flat universe.
If M is approximately 0.3, this is the com-
If the universe is flat, this tells us that the
bined effects of light and dark matter. From analy-
total density parameter (defined in Chapter 20),
sis of the results of big-bang nucleosynthesis, bary-
1. This doesn™t necessarily mean that
TOT
onic matter, neutrons and protons, is about 5% of
there is enough matter for this. TOT only tells
the closure density. Only one-fifth of the baryons
about the combined effects of matter ( MAT) and
(or 1% of the closure density) is in the form of
a cosmological constant ( ). So we know that
stars, galaxies, etc. It has been suggested that the
1. A number of other data suggest
M
rest is in the form of intergalactic ionized H. We
that M is approximately 0.3 and is approxi-
still don™t know the nature of the dark matter
mately 0.7. Remember, we saw in the previous
422 PART V THE UNIVERSE AT LARGE



that makes up more than 25% of the closure den- stant, suggest that cold dark matter can explain
sity, but it appears that simulations with cold most of the structures we see in the universe.
dark matter, and a non-zero cosmological con-



Chapter summary
When we work backwards to the conditions in apart would have had to communicate with each
the early universe, we find that there must have other in the first 100 000 years. This is called the
been an era in which the material was very hot causality problem.
and dense. This hot dense era is called the big One of the great successes of big-bang cos-
bang. The debris of the big bang is all around us. mologies is that they can explain the abundances
Just as the early universe was filled with hot of the light elements. For approximately the first
matter, it was also filled with hot radiation. The three minutes the universe was hot enough for
radiation and matter stayed in contact as long as nuclear reactions to take place. Those reactions
the radiation could scatter off the charged parti- produced essentially all the helium and deu-
cles. When the temperature of the universe fell terium that we see in the universe today (though
below 3000 K, the electrons and protons com- deuterium is destroyed and helium is produced
bined to form neutral atoms, and the universe in stars). The abundance of deuterium is particu-
became transparent. The radiation and matter larly sensitive to the density of the material in
decoupled. The radiation is still everywhere in the nuclear reactions. The denser the material,
the universe traveling in all directions. It is called the less deuterium there is. The density of mate-
the cosmic background radiation. As the universe rial in the first three minutes can be related to
expanded, the cosmological redshift increased the current density, and can tell us if nuclear
the wavelengths of all of the photons, and the reacting material (protons and neutrons) can
effect on the background radiation was to pro- close the universe. The best estimate is that this
duce ever cooler blackbodies. The current tem- material is only about 5% of what is needed to
perature is about 2.7 K. reach the critical density.
Following its accidental discovery, the back- When the universe was less than one second
ground radiation has been studied extensively. old, the temperature was so high that matter was
Studies of the spectrum were made difficult by stripped down into its fundamental components,
the Earth™s atmosphere. Radio observations from the elementary particles. The leptons, particles
the ground, some balloon and rocket observa- which do not feel the strong nuclear force,
tions, and some indirect measurements involving appear to be fundamental in that they have no
interstellar CN, were all employed to study the apparent internal structure. There are six of
radiation until the Cosmic Background Explorer these, with the familiar ones being the electron
Satellite was launched. COBE provided definitive and electron neutrino. The hadrons, or strongly
evidence that the spectrum is indeed that of a interacting particles, appear to be made up of var-
blackbody. These studies also showed that the radi- ious combinations of quarks. There are six known
ation is very isotropic. There is a dipole anisotropy, types (flavors) of quarks. The baryons (neutron,
due to the Earth™s motion. COBE revealed very low proton, etc.) are made up of three quarks; the
level fluctuations in intensity all over the sky. It is mesons (pion, etc.) are made up of quark“anti-
believed that these fluctuations are a snapshot of quark pairs. Each quark can come in three differ-
the small density enhancements in the early uni- ent colors, which provide for the binding of the
verse that gave rise to the clusters of galaxies that quarks.
we see today. Apart from these fluctuations, the In describing the elementary particles it is
radiation is actually too smooth. The degree of important to identify the fundamental forces. We
smoothness that we see would suggest that think that each force is carried by a particle.
points that were farther than 100 000 light years (These particles can be real or virtual, meaning
21 THE BIG BANG 423



that they violate conservation of energy but for gies are much higher than the masses of the car-
times too short to measure.) The long range elec- riers of the forces. To the best of our knowledge,
tromagnetic force is carried by massless photons, this has only occurred in the first fraction of a
as described by quantum electrodynamics (QED). second of the big bang.
The weak nuclear force is carried by the massive Applying particle physics to our study of the
W and Z particles, and the strong nuclear force is early universe has helped solve some cosmologi-
carried by the pion. We now understand that this cal problems. The excess of matter over antimat-
strong force is the residual of the color force ter, about one part in ten billion, arose from a
among the quarks. That force is carried by glu- slight asymmetry in certain weak interactions.
ons, as described by quantum chromodynamics This also explains why there are approximately
(QCD). The mass of the carriers explains the short ten billion photons for every baryon in the uni-
range of the forces. Attempts to unify the forces verse. The GUTs also suggest that, in the first frac-
have been partially successful. The electromag- tion of a second, the universe went through a
netic and weak forces appear to be manifestations rapid expansion, or inflation, in which the scale
factor increased by about 1035 almost instanta-
of the electroweak force. Theories that combine
the electroweak and QCD are called grand unified neously. This might explain why the universe
theories (GUTs). In each case, the unification appears to be flat and so isotropic. It might even
means that the forces are equivalent when ener- explain how galaxy formation started.


Questions
21.10. Does the dipole isotropy in the cosmic back-
21.1. When the temperature in the early universe
ground radiation violate the part of the cos-
fell to 3000 K, the matter recombined. Why
mological principle that states that the uni-
is this an important event?
verse should be isotropic?
21.2. How is the existence of the cosmic back-
21.11. Why is it important to find small-scale
ground radiation related to the origin of the
anisotropies in the cosmic background
light elements?
radiation?
*21.3. When the universe grows to twice its cur-
21.12. What do we mean when we say the universe
rent size, what will the temperature of the
is too isotropic?
background radiation be?
21.13. What conditions were prevalent in the first
*21.4. When the cosmic background radiation first
three minutes that allowed nuclear reac-
decoupled from the matter, in what part of
tions to take place?
the spectrum (radio, infrared, visible, ultra-
21.14. Why is the abundance of deuterium particu-
violet, etc.) did the radiation peak?
larly sensitive to the density during the time
21.5. Why is the cosmic background radiation
of nucleosynthesis?
hard to observe?
21.15. How do we know that the C, N and O
21.6. What are the similarities between CN mole-
around us were not produced in the big
cules and space probes in studying the cos-
bang?
mic background radiation?
21.16. Why is it so important to determine the rela-
21.7. What is it learned from studying the
tive abundance of deuterium in the universe?
spectrum of the cosmic background
21.17. If the deuterium measurements tell us that
radiation rather than simply measuring its
there aren™t enough protons and neutrons
intensity?
in the universe to close it, how can it be that
21.8. Why was COBE able to measure properties
the universe might still be closed?
of the cosmic background radiation that
21.18. What makes us think that the hadrons are
could not be measured in other ways?
not fundamental particles?
21.9. What is the significance of the dipole
21.19. What makes us think that the leptons might
anisotropy in the cosmic background
be fundamental particles?
radiation?
424 PART V THE UNIVERSE AT LARGE



21.20. What do we mean when we say that we only described as spontaneous symmetry
need the up and down quarks for everyday breaking?
life? 21.29. Why is it important that certain symmetries
21.21. Why are we not likely to see a free quark? were not perfect in the early universe?
21.22. What are the successes of the quark theory? 21.30. What is the difference between quantum
21.23. What are the differences between quark electrodynamics (QED) and quantum chro-
color and flavor? modynamics (QCD)?
21.24. If the quarks have fractional charges, how 21.31. Work out the different combinations of u
do the particles that we see have integral and d quarks that can make allowed parti-
charges? cles. Give their electronic charge. (Note: the
21.25. What do we mean when we say we are try- order doesn™t matter; i.e. uud is the same as
ing to unify the forces? udu.)
21.26. How is the mass of the carrier of a force 21.32. What cosmological problems can be
related to: (a) the range of the force, (b) the explained by inflation?
Why are there approximately 1010 photons
temperature at which that force might be 21.33.
unified with others? in the universe for every baryon?
21.27. How are we limited by the absence of a 21.34. Why is there an excess of matter over anti-
quantum mechanical theory of gravity? matter in the universe?
*21.28. As the universe cooled (still in the first 21.35. If neutrinos had masses only about 1/40 000
fraction of a second), previously unified that of the electron, how could they provide
forces became distinct. How can this be enough mass to close the universe?



Problems
For all problems, unless otherwise stated, use *21.5. Compare the energy density in the cosmic
H0 70 km/s/Mpc. microwave background with that in diffuse
21.1. (a) What is the present energy density in the starlight. Assume that the diffuse starlight
cosmic background radiation, and (b) what has a brightness temperature of 10 000 K
and a filling factor of 10 14.
was it when it was emitted at a temperature
of 3000 K? 21.6. In the CN experiment to study the cosmic
21.2. (a) Suppose the scale factors at times t1 and background radiation, what must the popu-
t2 are R1 and R2, and the background radia- lation ratio be for the temperature to be 2.7 K?
tion temperatures are T1 and T2. What is the (Take g2/g1 3.)
relationship between T1 and T2 in terms of 21.7. For the dipole anisotropy, the fractional
R1 and R2? (b) If we know that the back- increase in temperature, T/T, is equal to
v/c, where v is our speed. Justify this rela-
ground temperature now is 3 K, and we let
R 1, write an expression for the back- tion using Wien™s displacement law and the
ground temperature at any time when the Doppler shift relation.
scale factor is R(t). 21.8. Use the result of the previous problem to
predict T/T resulting from the Earth™s
21.3. Assume that the energy density, integrated
over all wavelengths, in the background orbital motion.
radiation is given by the Stefan“Boltzmann 21.9. (a) Assume that a force is carried by a virtual
particle of mass m. Assume that this particle
law. Assume that we know the cosmological
can exist for a time h/2 mc2, and that it trav-
redshift, and show that these lead to the
els close to c. What is the approximate range
conclusion that the temperature must scale
as 1/R. of the force? (b) If the range of the strong
force is 10 13 cm, what is the mass of the
21.4. Use the Wien displacement law to find the
peak wavelength of a blackbody for a tem- particle carrying the force? How does it com-
perature of (a) 3 K, (b) 3000 K. pare with the mass of the pion?
21 THE BIG BANG 425



21.10. If the electromagnetic force is carried by vir- 21.12. (a) What is the temperature at which the
tual photons, which can live for a time h/E, average kinetic energy is equal to the mass
explain how the first can be felt at any of the X? (b) What is the mass of the X in
range. (Hint: Think about photons of differ- grams?
ent wavelength and energy.) 21.13. If the average lifetime of the proton is
1031 yr, how much water would you have to
21.11. What is the temperature at which the
average kinetic energy is equal to the mass watch to detect 100 proton decays in one
of the W? year?


Computer problems

21.3. In the CN experiment to study the cosmic back-
21.1. Make a graph comparing blackbody curves for T
ground radiation, draw a graph of the population
2.75 and 3.00 K.
ratio, n2/n1, as a function of temperature for an
21.2. Make a graph of the wavelength at which the cos-
interesting range of temperature. (Take g2/g1 3.)
mic background radiation spectrum peaks vs. z,
for z ranging from 1 to 1000.
Part VI
The Solar System
In studying the Solar System, we ¬nd an important exception to our con-
cept of astronomical objects being so remote that we cannot hope to visit
them in the foreseeable future. People have already visited our nearest
neighbor in the Solar System, the Moon, and brought back pieces to study
in normal Earth-bound laboratories. Unmanned probes have landed on
Venus and Mars and have visited all the other planets. Clearly, the oppor-
tunity for even limited close-up viewing has had a major impact on our
understanding of the Solar System.
However, the study of the Solar System is not simply devoted to send-
ing probes when we feel like it.The spacecraft have followed literally cen-
turies of study by more traditional astronomical methods. By the time the
¬rst probe was launched to any planet, astronomers had already devel-
oped a picture of what they expected to ¬nd. Many of these pictures did
not survive the planetary encounters, but they did provide a framework
for asking questions, and for deciding what instruments were important to
place on the various probes.
We have also had the advantage of having the Earth as an example of a
planet to study. It has been possible to develop ideas about planetary sur-
faces, interiors, atmospheres and magnetospheres by studying the Earth. For
that reason, we have devoted one whole chapter of this Part to the Earth,
viewed not as our home base, but as just one planet. In studying the Earth,
we will generate ideas which we will extend to studying other planets.
We will study the other planets in two groupings of similar planets, the
inner and outer planets.Within each grouping, we don™t study all aspects
of a given planet before going on to the next planet. Instead, we study a
given aspect, e.g. atmospheres, of all the planets for the group.This allows
us to extend common ideas to similar objects, looking for similarities and
differences.
We will also see how much of the physics we have used in other
astronomical problems “ orbits, energy transport, hydrostatic equilibrium,
tidal effects, and using spectroscopy to study remote objects, to mention a
few examples “ ¬t very naturally into our study of the Solar System.
Therefore, rather than trying to give a complete list of all the facts
revealed by various probes, we emphasize the underlying physics.
Chapter 22




Overview of the Solar System

The Earth belongs to a group of nine planets, Most of the planets have moons orbiting them.
orbiting the Sun, called the Solar System. Each Of course, the most familiar is our own Moon.
object follows its own orbit about the Sun. All of Mercury and Venus are the only planets without
the planets orbit in the same direction. As large any known moons. Mars has two small moons.
as the Earth seems to us, it is small compared to Jupiter has four large moons and numerous
the distances between objects in the Solar smaller moons. Saturn has one large moon, and,
System. This is true of the other planets, even like Jupiter, a collection of smaller moons. Uranus
those much larger than the Earth. For all practi- has three modest sized moons, and several smaller
cal purposes, the Solar System is vast emptiness, ones. Neptune has one large and a number of
with a few small island oases. small moons, and, finally, Pluto has one moon
If we could look at a side view of the Solar that is relatively large compared to the size of the
System, we would notice that the orbits are not planet. All of these moons add to the diversity of
very tilted with respect to that of the Earth. So, in objects that we can study in the Solar System.
a side view from the outside, the Solar System In addition to planets and moons, there is a
would look like a very thin disk. We call the plane collection of smaller sized objects. Found mostly
of the Earth™s orbit the ecliptic. The motion of the between the orbits of Mars and Jupiter is a collec-
tion of rocky bodies, called asteroids. They are
Earth around the Sun causes the Sun to appear to
move against the background of fixed stars. That mostly between the orbits of Mars and Jupiter.
path is just the projection of the ecliptic onto the From time to time we see objects appear faintly in
sky. The Earth™s rotation axis is tilted (by 23.5 ) so our sky that then brighten, and develop a tail, as
shown in Fig. 22.2. These are comets. Occasionally
that the ecliptic does not line up with the Earth™s
equator. the Earth runs into small debris left in its orbit.
We begin a brief tour of the Solar System by The material falls through the atmosphere and is
heated. We see the glowing trail as a meteor.
looking at the planets. A photograph of each
planet is shown in Fig. 22.1. It is convenient to Occasionally the Earth suffers large impacts from
divide the planets into two groups, the inner plan- these.
ets and the outer planets. The inner four planets One of the goals in studying the Solar System
are Mercury, Venus, Earth and Mars. The giant is to find clues to its origin, and to put together a
outer planets are Jupiter, Saturn, Uranus and picture of that origin. We will defer that discus-
Neptune. The outer planets are much more mas- sion until Chapter 27, after we have discussed all
sive than the inner planets. They also have very the material in the Solar System. For now, we
different compositions. The outermost planet is note that we expect the Solar System to form as a
Pluto (though it does spend part of its orbit closer biproduct of the formation of the Sun. The Solar
to the Sun than Neptune). Pluto is small, like the System should have formed out of the disk that
inner planets. was part of the late stages of the formation of the
430 PART VI THE SOLAR SYSTEM



and disk, as discussed in Chapter 15. Differences
among the planets should be explainable by dif-
ferences in temperature, density and composition
as one goes farther out in the protosolar nebula.


22.1 Motions of the planets

When we look at the night sky, it is clear that
most of the objects maintain their relative posi-
tions. These are the stars. However, apart from
the Sun and Moon, a small number of objects
move against the background of fixed stars. These
are the planets. The study of the motions of the
planets has occupied astronomers for centuries.
These motions do not appear simple. The planets
occasionally seem to double back along their
paths, as shown in Fig. 22.3. This doubling back is
known as retrograde motion. Historically, any
explanation of the motions of the planets had to
include an explanation of this retrograde motion.
The earliest models of our planetary system
Fig 22.1. The planets. [NASA]
placed the Earth at the center. This idea was sup-
ported by Aristotle in approximately 350 BC. His
Sun. This explains why the orbits of the planets view was that the planets, the Sun and the Moon
are almost in the same plane and why the orbital move in circular orbits about the Earth. Even
motions are in the same direction, preserving the though there is now ample evidence against this
angular momentum from the molecular cloud picture, one can see how placing the Earth at the
center was a naturally simplifying assumption.
The picture was modified by Claudius Ptolemy, in
Alexandria, Egypt, around 140 AD. In order to
explain retrograde motion, he added additional




Fig 22.3. The apparent motion of Mars against the ¬xed
Fig 22.2. Photograph of Halley™s comet. [NOAO/ background of stars.The loop when it doubles back is called
AURA/NSF] retrograde motion.
22 OVERVIEW OF THE SOLAR SYSTEM 431



An opposing picture was supported by the 16th
Epicycle
P century Polish astronomer, Nicholas Copernicus. In
the Copernican system, the Sun is at the center of
the planetary system. This picture is therefore
Or
b called the heliocentric model. Copernicus showed



ita
that the retrograde motion is an artifact, caused



lM
by the motion of the Earth. This is illustrated in


otion
Fig. 22.5. The Copernican system had the planets
E in circular orbits, not ellipses. Therefore, detailed
predictions of planetary positions had small
errors. To correct those errors, epicycles had to be
added to the Copernican model, taking away
from the simplicity of the picture.
When Galileo Galilei turned his newly invented
telescope to the planets, he found that Venus
does not appear as a perfect disk. It goes through
Fig 22.4. Epicycles. In this picture, the Earth is at the cen-
ter.The planet, P, doesn™t simply orbit the Earth. It goes a series of phases, similar to those of the Moon.
around in a circle, which in turn orbits the Earth. If the The size of the disk also changes as the phase
planet™s motion along the epicycle is faster than the epicy-
cle™s motion around the Earth, then the planet can appear to
P'5 P'4 P'3 P'2 P'1
go backward for parts of each orbit. More layers of epicycles
can be added to this picture.


circles, called epicycles. As shown in Fig. 22.4, each
planet was supposed to move around its epicycle
θ4 θ2
as the center of the epicycle orbits the Earth. To
obtain a closer fit to the observed motions, higher
order epicycles were added.

θ1
θ5



P 2 P 3 P4
P1 P5
(b)
θ4 θ
θ1 θ 2 5 Fig 22.5. Retrograde motion in the heliocentric system.
E2 E 3 E 4 (a) The Sun is at the center.We consider the Earth at ¬ve
E5 positions E1 through E5 with the planet at P1 through P5 at the
E1
same times.We use the line of sight from the Sun through E3
and P3 as a reference direction.The dashed lines are all parallel
to that direction, and the angles 1 through 5 keep track of
the differences between the line of sight from Earth to the
planet and the reference direction.We see that since the Earth
Ea is moving faster than the planet, the line of sight goes from
r t h 's O r b it
being ahead of the dashed line to being behind the dashed line.
(b) The view from Earth.The apparent position of the planet
Pla n
et's O rbit
on the sky is indicated by P 1 through P 5. During this part of
their orbits the planets appears to move backward on the sky.
(a)
432 PART VI THE SOLAR SYSTEM



changes. These observations can be explained eas-
C
ily in the heliocentric model, because Venus would
not always be at the same distance from Earth.
The phases result from the fact that we see dif-
3
fering amounts of the illuminated surface. There
was no similar explanation in the Earth-centered
Sun
system. Though Galileo was persecuted for hold- 2
1 B
A
ing that the heliocentric picture is the true one,
his work had great influence on future scientific
thought. Work switched from trying to find what 3'




In
ne
bi




t
rP
was at the center of the planetary system to try- l a net' s O r
ing to understand how the planets, the Earth
Ear
th's O r bit
included, move around the Sun.
C'
Extensive observations were carried out by
O ut
er Planet's Orbit
Tycho Brahe, at Uraniborg, Denmark, late in the
16th century. Brahe moved to Prague in 1597, and
Fig 22.6. Con¬gurations of the Earth and the inner and
died four years later. His results were taken over by
outer planets. Positions of the inner planets are indicated by
an assistant, Johannes Kepler. Based on his analysis,
numbers: (1) inferior conjunction, (2) superior conjunction,
Kepler published two laws of planetary motion in (3 and 3 ) greatest elongation. Positions of the outer planets
1609, and a third law nine years later. Together, are indicated by letters: (A) opposition, (B) conjunction,
these are known as Kepler™s laws. It is important to (C) quadrature.
remember that these laws were based on observa-
tions, not on any particular theory.
Before discussing Kepler™s laws, we look briefly the morning. When it is east of the Sun, it rises
at how we survey the Solar System, measuring the and sets after the Sun, and is most easily visible
periods and sizes of orbits. We take advantage of in the evening.
certain geometric arrangements. These are shown We then look at planets that are farther from
in Fig. 22.6. We first look at planets that are closer the Sun than the Earth. Let™s start by looking at
to the Sun than the Earth. When the planet is the planet when it is farthest from Earth, on the
between the Earth and the Sun, we say that it is at far side of the Sun. We say that the planet is sim-
inferior conjunction, and it appears too close to the ply at conjunction. At that point, it would be too
Sun in the sky to observe. As the planet moves in close to the Sun in the sky to see. As it moves far-
its orbit, the angle between it and the Sun (as seen ther from that position it appears farther from
from Earth) becomes larger. The planet appears the Sun on the sky. When it reaches a point where
farther and farther from the Sun. Eventually, the Earth, Sun and planet make a right triangle,
since its orbit is smaller than the Earth™s, it with the Earth at the right angle, we say that it is
at quadrature. Notice that there is no limit on how
reaches a maximum apparent separation from
the Sun. This is called the greatest elongation. At far on the sky it can appear to get from the Sun.
that point, the Earth, the Sun and the planet Eventually, it reaches the point where it is on the
make a right triangle, with the planet at the right opposite side of the sky from the Sun. We call this
point the opposition, and it is also the closest
angle. After that the planet appears to get closer
to the Sun, and when it is on the far side it is at approach of the planet to Earth. When the planet
superior conjunction. The pattern then repeats on is at opposition, it is up at night (since it is oppo-
the other side of the line from the Earth to the site to the Sun in the sky). Therefore, when a
Sun. When the planet is on one side of the Sun it planet is favorably placed for observing, it is also
will appear east of the Sun in the sky, and when closest to Earth and can be studied in the greatest
it is on the other side it appears west of the Sun. detail.
When it is west of the Sun, it rises and sets before When we talk about the orbital period of a
the Sun, and it is therefore most easily visible in planet, we mean the period with respect to a fixed
22 OVERVIEW OF THE SOLAR SYSTEM 433



reference frame, such as that provided by the
stars. This period is called the sidereal period of
the planet. However, we most easily measure the
time it takes for the planet, Earth and Sun to
come back to a particular configuration. This is
called the synodic period. For example, the synodic d r
period might be the time from one opposition to
E
the next. How do we determine the sidereal
1 AU Sun
period from the synodic period?
Suppose we have two planets, with planet 1




t
bi
In
ne
Or
being closer to the Sun than planet 2. (For simplic- r Pl
a ne t ' s
ity, we assume circular orbits.) The angular speed
1 of planet 1 is therefore greater than that of
planet 2, 2. The relative angular speed is given by

Earth's Orbit
rel 1 2

2 P, where P is the period of the
Since Fig 22.7. Diagram for ¬nding the distance to an inner
planet, the period of the relative motion of the planet.
two planets, Prel, is related to P1 and P2 by
11 Prel 2 11 P1 2 11 P2 2 (22.1)
distance to the planet, measured in astronomical
Now we let one of the planets be the Earth, units.
and express the periods in years. First we look at Methods like this gives us distances in terms
the Earth plus an inner planet. This means that of the astronomical unit. Even if we don™t know
P1 is the period of the planet and P2 is 1 yr. how large the AU is, we can still have all of the
Equation (22.1) then becomes distances on the same scale, so we can talk about
11 Prel 2 11 P1 2
the relative separations of the planets. The cur-
1 (inner planet)
rent best measurement of the AU comes from sit-
uations like Fig. 22.7. We can now bounce radar
Similarly for the Earth and an outer planet, equa-
signals off planets, such as Venus. By measuring
tion (22.1) becomes
11 Prel 2 11 P 2
the round-trip time for the radar signal (which
1 (outer planet)
travels at the speed of light), we know very pre-
cisely how far the planet is from the Earth. The
In each case Prel is the synodic period and P is the
right triangle in Fig. 22.7 gives us
sidereal period.
We now look at how the sizes of various plan-
cos E d 1 AU
etary orbits are determined. The technique is dif-
Since E is measured and d is known from the radar
ferent for planets closer to the Sun than the
measurements, the value of the astronomical unit
Earth and farther from the Sun than the Earth.
can be found. This distance is approximately 150
Fig. 22.7 shows the situation for a planet closer to
million kilometers (93 million miles). The exact
the Sun. When the planet is at its greatest elon-
value is accurate to within a few centimeters.
gation, it appears farthest from the Sun. The
It is more complicated to find the distance to
planet is then at the vertex of a right triangle, as
an outer planet. There are two different methods.
shown in the figure. Since we can measure the
The easier one was derived by Copernicus, but is
angle E between the Sun and the planet, we can
not good for tracing out the full orbit. It just gives
use the right triangle to write
the distance of the planet from the Sun at one
sin E r 1 AU
point in its orbit. Kepler™s method of tracing the
where r is the distance from the planet to the Sun. whole orbit is shown in Fig. 22.8. We make two
This equation can be solved for r to give us the observations of the planet, one sidereal period of
434 PART VI THE SOLAR SYSTEM



Planet's Orbit


6
1
E1
5
d1
ψ1 2
x θ Sun
1
P 3
θ
r
ψ2 2 4
(a)
d2 E2
t
Ea
r t h 's O r b i



O ut
er Planet's Orbit

P2
Fig 22.8. Diagram for ¬nding distance to an outer planet. P1


the outer planet apart. The Earth is at E1 and E2,
respectively, when these are made. The angles 1
and 2 are directly determined. The angles 1 and
P'1
2 are known, as well as the distance x. (If the
Earth™s orbit were circular, then 1 2.) We then
P'2
2, and can find d1 and d2,
know 1 1 and 2
and, finally, r. The advantage of this method is
(b)
that each point in the planet™s orbit can be traced,
Fig 22.9. (a) Kepler™s second law. Each shaded triangle has
with the observations overlapping in time.
the same area. (b) Kepler™s third law. In the time the inner
We have already encountered Kepler™s laws
planet moves from P1 to P 1 the outer planet moves from P2
(Fig. 22.9) when we discussed the orbits of binary
to P 2
stars. After all, orbiting planets and orbiting stars
must obey the same laws of physics.
The first law has to do with what types of spring is less than the number of days from the
paths the planetary orbits can be: beginning of spring to the beginning of fall. This
shows up in our calendar in two ways. First, the
(1) The planets move in elliptical orbits with the Sun at
beginning of spring is usually on the 20th of
one focus.
March, while the beginning of fall is usually on the
The second law, a consequence of angular 22nd of September. Second, the shortest month,
momentum conservation, states: February, is in the middle of the winter.
The third law states:
(2) A line from the Sun to a planet sweeps out equal
areas in equal times. (3) The square of the period of an orbit (measured in
years) is equal to the cube of the semi-major axis of
The Earth™s orbit is not very eccentric, but we can
the orbit (measured in AU).
still notice the effects of the Earth moving faster
at some times than at others. By coincidence, the This follows from the inverse square law for grav-
Earth is closest to the Sun just after the begin- ity. (Actually, Newton deduced the inverse square
ning of the year. Thus, it is slightly closer during law by seeing what gravitational law was neces-
the (northern) winter than during the (northern) sary to give Kepler™s third law. See Problem 22.5.)
summer. The result is that the number of days There is nothing in Kepler™s laws which tells
from the beginning of fall to the beginning of us how far each planet should be from the Sun.
22 OVERVIEW OF THE SOLAR SYSTEM 435



However, for over 200 years it has been known Sunlight
Last Quarter
that there is a simple relationship giving, in AU,
the semi-major axes of the actual planetary
orbits. To generate this relationship, we take the
series (0, 3, 6, 12, 24, . . .) in which each term is the
double of the previous term. If we add four to
7
each number, and then divide by ten, we obtain 8 bital Motion o
f
Or 6
the approximate distances of the planets, out to




M
oo
New Full
Uranus, with an extra term giving the location of




n
the asteroid belt. Though this is known as Bode™s 5
1
law, it is not really a law, in the sense that there
is no physical basis for it. It may just be a mathe-
matical curiosity. 4
2
3

22.2 The motion of the Moon

Since the Moon orbits the Earth every 27.3 days
(sidereal period), it is always changing its posi- First Quarter
tion with respect to the fixed stars, which serve as
Fig 22.10. Lunar phases.The numbered images on the
a backdrop. It is also changing its appearance,
circle show the actual position and illumination of the Moon.
going through a full cycle of phases in the course
The outer images show that appearance of the Moon, as
of one month. The motion of the Earth around seen from Earth. (1) New moon; (2) waxing crescent;
the Sun causes the phases to cycle in 29.5 days. (3) ¬rst quarter; (4) gibbous; (5) full moon; (6) gibbous;
(This number actually varies by up to 13 hours (7) last quarter ; (8) waning crescent.
since the Earth doesn™t move at a constant rate
about the Sun.) The Moon rotates with the same
period, so we always see the same face. and will appear high up at sunset. For the next
The Moon does not give off any light of its quarter of a cycle, the visible part grows, and is
own. It shines by reflected sunlight. Therefore, called a waxing gibbous. Halfway through the
the appearance of the Moon depends on the rela- cycle, we see the full illuminated side, and we call
tive positions of the Earth, Sun and Moon. This is it a full moon. The full moon rises roughly as the
shown in Fig. 22.10. At any given time half of the Sun sets.
Moon is illuminated. The changes in appearance The second half of the cycle goes back through
are because different amounts of the illuminated similar phases. For the third quarter of the cycle,
side face the Earth. Let us follow it through one the illuminated side becomes smaller, and we
cycle. We start when the Moon is between the call it waning gibbous. Three-quarters of the way
Earth and the Sun. Only the dark side of the through the cycle we again see half of the illumi-
Moon faces the Earth, and we see nothing. This is nated face, and it is called the last quarter. For the
called the new moon. As the Moon moves over a lit- last quarter, the half the we see is on the opposite
tle, a small piece of the illuminated side faces us side from that at the first quarter. The last quarter
and we see a crescent. Since the crescent is grow- moon will be high in the sky at sunrise. Through
ing, we call it the waxing crescent. This appears to the last quarter of the cycle, we see a waning cres-
the east of the Sun (with the crescent side towards cent, getting smaller, and getting closer to the Sun.
the Sun). This means that it is visible in the west- Finally, we return to the new moon.
ern sky at sunset. One-quarter of the way through The Moon™s axis of rotation is inclined by
the cycle, half of the visible side faces us, and we 1.5 with respect to the plane of its orbit. The
call it a first quarter. By that time, the Moon will inclination contributes to an effect, known as
have moved a quarter of the way across the sky, libration, which allows us to see more than 50%
436 PART VI THE SOLAR SYSTEM



4 SOLUTION
The force on each body is proportional to its mass,
and inversely proportional to its distance from the
Rotational P
Motion of Moon. Therefore
Moon
GM r2
P FSM SM
3
1 E GME r2
FEM EM
P

rEM 2
a ba b
M
O




bi P
r




ME rSM
ta
lM
o tio n 1033 g 105 km 2
a ba b
2
of Moon 3.85
2
1027 g 108 km
6 1.50
(a)
2.2
P
This means that the Sun exerts twice as great a
force on the Moon as the Earth does. It is therefore
5o
E not really proper to talk about the Moon orbiting
the Earth. The Moon actually orbits the Sun, with
the Earth causing the curvature of the Moon™s
orbit to change. This is shown in Fig. 22.12. Notice
(b)
that the Moon™s path is always concave toward the
P
Sun. This is because the net force on the Moon is
2o
E always inward, even when it is between the Earth
and the Sun.
(c)
When the Moon passes between the Earth and
Fig 22.11. Librations, which allow us to see more than
the Sun, it is possible for it to block some of the
50% of the Moon™s surface. (a) The effect of the eccentricity
sunlight. This is called an eclipse of the Sun, or a
of the Moon™s orbit. The Moon rotates on its axis at a con-
solar eclipse. If the Moon completely blocks the Sun,
stant rate, but orbits the Earth at a variable rate, so at vari-
ous times the rotation is ahead of or behind the orbital
Moon's Path
motion, allowing us to see an extra 6 around. Point P keeps Fig 22.12. Orbit of the
track of the steady rotation of the Moon.We can see that Moon, relative to the Sun.
the line from the Earth to the Moon passes through P at The Moon™s orbit must
positions 1 and 3, but not at 2 and 4. (b) The effect of the Earth-Moon always be concave toward
inclination of the Moon™s orbit, relative to the ecliptic, by 5 , Center of Mass the Sun.
allowing us to see over and under the poles. (c) The effect of
the ¬nite size of the Earth, allowing us to look from different
directions, providing a 2 effect.



of the surface of the Moon. Another contribu-
tion to the libration comes from the fact that
the Moon is so close to the Earth that observers
on opposite sides of the Earth see the Moon to be
rotated through approximately 2 . These effects,
as shown in Fig. 22.11, allow us to see 59% of the
Moon™s surface.
Example 22.1 Forces on the Moon
Calculate the relative strength of the forces exerted
on the Moon by the Earth and by the Sun.
22 OVERVIEW OF THE SOLAR SYSTEM 437



we call it a total eclipse. In a total eclipse, the dark- below the Earth, and during most full moons the
est part of the Moon™s shadow, the umbra strikes Moon passes above or below the Earth™s shadow.
the Earth. Otherwise it is a partial eclipse, and the We can only have an eclipse when the new or full
lighter part of the shadow, or penumbra, passes moon occurs while the Moon is crossing the
over the Earth. When the Earth is between the plane of the Earth™s orbit, the ecliptic. The plane
Moon and the Sun, it can block the sunlight reach- of the Earth™s orbit intersects that of the Moon™s
ing the Moon. This is called an eclipse of the Moon or orbit in a straight line, called the line of nodes. We
a lunar eclipse. There are also total and partial can only have an eclipse when the Moon is close
lunar eclipses, depending on whether the Moon to a node. Also, we can only have an eclipse when
passes through the Earth™s umbra or penumbra. the Moon is full or new.
The relative placements of the Earth, Sun and This favorable arrangement occurs two times
a year. These are called eclipse seasons. Each season
Moon for both of these are shown in Fig. 22.13.
You might think that there would be a lunar is approximately 38 days long. Each new or full
eclipse at each full moon and a solar eclipse at moon during the eclipse seasons results in at
each new moon. If the Moon™s orbit were in the least a partial eclipse. The eclipse season is suffi-
same plane as the Earth™s orbit, this would be the ciently long that any total eclipse of one object
case. However, the Moon™s orbit is tilted by about (Moon or Sun) must mean a partial eclipse of the
5 relative to the plane of the Earth™s orbit. This is other, either two weeks before or after. The direc-
also shown in Fig. 22.13. Therefore, during most tion of the plane of the Moon™s orbit shifts around,
new moons, the Moon™s shadow passes above or going through a full cycle every 18.6 years. The
amount of tilt doesn™t change, but the direction
of the tilt does. This results in an eclipse year that
Sunlight
rbit
's O is actually 346.6 days long. Therefore, there may
n
Moo
e of be up to seven (lunar plus solar) eclipses in a cal-
Plan
Ecliptic endar year, of which two to five will be solar.
5o
In a total lunar eclipse, the whole Moon passes
through the darkest part of the Earth™s shadow,
the umbra. In some eclipses, the Moon only passes
(a)
through the lighter (outer) part of the Earth™s
shadow, the penumbra. Penumbral eclipses are
hardly noticeable. If the Moon is partly in the
umbra, we see a partial eclipse. The Moon is never
completely dark, even for a total lunar eclipse.
Sunlight
Plane of Moon's Orbit
Some sunlight is refracted (bent) by the Earth™s
Ecliptic atmosphere and illuminates the Moon. Since the
atmosphere filters out the blue light better than
the red, the Moon appears red. Particles in the
Earth™s atmosphere sometimes block sunlight
more than at other times, and different eclipses
have different amounts of light reaching the
(b) Moon. Eclipses just after major volcanic erup-
tions are particularly dark.
Fig 22.13. Eclipse geometry. Since the Moon™s orbit is
Lunar eclipses can be seen from any point on
inclined by 5 , whether or not there is an eclipse depends on
the nighttime side of the Earth. They are cur-
whether the Earth is in a part of its orbit where the new
rently of limited scientific value. They used to
and full moon are in the ecliptic. (a) The Moon is out of the
provide astronomers with information on the
ecliptic at the new and full moon and no eclipse takes place.
(b) The Moon is in the ecliptic at new and full moon and thermal properties of the lunar soil. Astronomers
eclipses can take place.The times of year when eclipses are could use radio and infrared observations to see
possible are called eclipse seasons.
how fast that soil cooled when the sunlight was
438 PART VI THE SOLAR SYSTEM



System formed, and how did it reach its current state?
removed. However, we now have samples of lunar
Related to that are the questions of: how did the
material in the laboratory. As the Earth™s shadow
Earth form and how did it reach the state where it can
passes across the Moon, its shape serves as a
support life? To answer these larger questions we
reminder of the Earth™s roundness.
must ask: what are the constituents of the Solar System
Solar eclipses are of continuing scientific value,
and what are their properties? By properties we might
as was discussed in Chapter 6, when we talked
about the Sun. As viewed from the Earth, the Sun be referring to mass, size, composition, structure.
and Moon cover almost exactly the same angle on These are the questions that we will be address-
the sky. This is just a coincidence. Since the Moon™s ing in this part of the book. To study the Solar
orbit is elliptical, it is sometimes closer and some- System, we use traditional astronomical tech-
times farther from Earth. This means that usually niques, such as those discussed in Chapter 4. In
the Moon covers a slightly larger region than the addition, we have the advantage that we can send
Sun, but occasionally the Moon is directly in line, spacecraft to many parts of the Solar System.
but doesn™t cover the Sun completely. A ring (or In studying other planets, comparisons with
annulus) of the Sun shines around the edge of the the Earth are also interesting. For example, we
Moon, so these are called annular eclipses. think that any theory of atmospheric structure
When a total solar eclipse does occur, it is quite that can explain the Earth™s atmosphere should,
spectacular. First the Moon begins to cover the with the input of the right parameters, be able to
Sun slowly, creating a partial eclipse that engulfs explain that of Mars or Jupiter.
more and more of the Sun. During any stage of a In studying the Solar System, theoretical tools
partial eclipse, there is still enough sunlight pres- now include sophisticated computer modeling of
ent to damage your eyes. You should not look various processes. The processes include accre-
directly at the partial stages of a solar eclipse. The tion of interstellar material to form the various
easiest way to follow the progress is to use a small planets, or the evolution of an atmosphere. These
telescope to project an image of the Sun on a models are a great aid in interpreting complex
screen. Special solar filters can also be used, but observations.
sunglasses, or exposed film, do not filter out the harmful We have undergone a great revolution in our
radiation. During totality it is safe to look at the observations of the Solar System. Ground-based
Sun. With the bright disk of the Sun blocked, you observations, yielding images and spectra, have
can see the outer atmosphere, or corona, of the been quite useful. However, the opportunity
Sun. During totality, the sky becomes almost as afforded by space probes to take a close-up look
dark as at night, and you can briefly see stars. has greatly added to our knowledge. Flybys have
Since the Moon barely covers the Sun, at any given us detailed pictures, and have allowed us to
instant, a total eclipse can only be seen over a study spectral bands that do not penetrate the
small section of the Earth. As the Moon™s shadow Earth™s atmosphere. They can also directly sam-
moves across the Earth, it traces out a thin band ple the environment of the object being studied.
in which a total eclipse can be seen. Along the Landings can provide even more information,
band, totality progresses from one end to the allowing us to study conditions at a site. In the
other. Since solar eclipses are only visible in lim- case of the Moon, we have had the additional lux-
ited areas, we generally have to plan to travel to ury of bringing samples back for study in our lab-
see them. Therefore, it is important to know when oratories. This has brought the Solar System into
and where you can see one. the realm of the geologist.
The Solar System actually provides us with a
unique opportunity to visit the astronomical
22.3 Studying the Solar System objects that we are studying. Throughout the chap-
ters on the Solar System, we will constantly be
What are the things that astronomers would like comparing Earth-based and space-probe images
to know about the Solar System? Probably the of the members of the Solar System. The contrast
most fundamental question is: how was the Solar is spectacular. You should remember, however, that
22 OVERVIEW OF THE SOLAR SYSTEM 439



this is not something that we can do for any of tary probes. The shortest trips, to the Moon, take
the other objects discussed in this book. a few days. The longest trips, to the outer planets,
Also, as we discuss various members of the take several years. By comparison, at the speeds of
Solar System in detail, we will see that, as spec- these probes, a trip to the nearest star would take
tacular as the close-ups are, they complement a about 20 000 years.
very active ground-based observing program. This In this section, we look at the mechanics relat-
is due, in part, to the fact that the space missions ing to space probes traveling to other planets. It is
are expensive and of short duration. So, they give important to remember that during most of the
us detailed information, but for only a short flight of a planetary probe, it is unpowered. This
period of time. Observations from the Earth can means that it is simply in an orbit about the Sun.

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