. 26
( 28)


2:1 center of
3:1 mass R
GG G Hildas
3 3
G R < d1 R > d2
Fig 26.14. Occultations of stars by asteroids tell us about
asteroid sizes.
2 2

1 1
where the gravitational forces of the Sun and
Jupiter and the pseudo-force, the centrifugal force,
0 0 sum to zero. It is thought that Phoebe, Saturn™s
2.0 5.0
outermost moon, which is only 200 km across and
Distance from Sun (AU)
quite dark (low albedo), is a captured asteroid. It
has also been suggested that the smaller moons of
Jupiter, as well as the moons of Mars, are captured
asteroids. Astronomers think that some of the
larger asteroids would have a similar appearance
to Phobos and Deimos.
Asteroids are classified according to their sur-
face types. E types have very high albedos. They
Sun are rare and are found at the inner edge of the
belt. S types have lower albedos. They are more
abundant and are found from the inner part to
the center of the belt. M types are also abundant,
being found in the middle of the belt. They have
moderate albedos. The most abundant are the C
types, which are found in the outer parts of the
belt. They are characterized by a low albedo.
There is some correspondence between asteroid
types and meteorite types.
Fig 26.13. (a) Radial distribution of asteroids.The places
The brightness of asteroids varies with time.
marked G are gaps, with the orbital period relation to
Studies of their light curves show periodic varia-
Jupiter given above.The two groups, the Hildas and Trojans,
are also indicated. (b) Locations of the Trojans, at two tions with up to a factor of three change in
Lagrangian points of the Jupiter“Sun system. brightness. This is interpreted as indicating
either an irregular shape or an irregular surface
coverage. In the latter case, the asteroid would
have a dark and a light side. In some cases, elon-
asteroid (see Problem 26.7). Albedos for asteroids
gated shapes have been detected.
fall in the range 3% to 50%.
The origin of asteroids is still not clear. For a
Not all of the asteroids are in the asteroid belt.
Some, the Apollos, cross the Earth™s orbit. Another long time, it had been speculated that the aster-
group, known as the Trojans, is found in Jupiter™s oid belt was the remainder of a planet that was
destroyed. The total mass of the asteroids, only 2%
orbit, one-sixth of an orbit ahead and behind the
planet. This is a point, called a Lagrangian point, of the mass of the Earth, would not provide a very

massive planet. However, it does seem likely that may therefore may have been debris that would
the large tidal effects of Jupiter kept a planet have formed into a planet had Jupiter not pre-
from forming too close to Jupiter. The asteroids vented it.

Chapter summary
In this chapter we looked at Pluto, as well as aster- System formed. This is because they reside well
oids, comets and meteoriods. These small objects beyond the orbit of Pluto, and only make brief
give us important clues to the history of the Solar visits to the inner Solar System. We saw how the
System. appearance of a comet changes as it approaches
Pluto was discovered in a search for a planet the Sun. We saw the processes that are important
perturbing the orbit of Neptune. (We now know to the development of the tail.
that those perturbations are not real.) As we have For the most part, meteoroids are the debris
learned more about Pluto, especially through the left behind by comets. When they fall to Earth,
discovery of a moon, whose orbital size and they provide us with information on the com-
period give us Pluto™s mass as about one-fifth that position of material in the forming Solar
of our own Moon, we have come to revise our System.
understanding of its role in the Solar System. It is We saw that most asteroids are between Mars
also the planet with the most eccentric orbit, and Jupiter, but there are a few notable excep-
spending some of its orbit inside that of Neptune. tions. Even within the asteroid belt, there are dif-
We think that comets may provide us with the ferences in composition as one moves farther
best record of material out of which the Solar from the Sun.

26.9. Why do we think that comets may preserve
26.1. How does the mass of Pluto compare with
a record of the early Solar System?
that of the larger moons in the Solar
26.10. Why are comets brightest when they are
close to the Sun?
26.2. Why was the discovery of a moon around
26.11. Draw a diagram to show how a tail going
Pluto important in telling us about Pluto™s
away from the Sun could be viewed from
Earth as pointing towards the Sun.
26.3. Why are some astronomers questioning
26.12. Why do we think that comets come from far
Pluto™s status as a planet?
out in the Solar System (i.e. the Oort cloud)?
26.4. How do we measure the size of an asteroid?
26.13. What is the relationship between mete-
26.5. If you see a bright asteroid, what might you
oroids and comets?
conclude about it?
26.14. Why are meteor showers most active
26.6. If comets have very little mass, how can
between midnight and dawn for any
they be seen so easily when they are near
the Earth?
26.15. Explain why the presence of xenon-129 in
26.7. What does the term “dirty snowball” mean
large quantities in a meteoroid means that
when applied to comets?
large quantities of iodine-129 were pro-
26.8. If you see a comet in the sky with two tails,
duced just before the formation of the
how can you tell which is the gas tail and
which is the dust tail?

26.5. Use the mass of a typical comet and the mass
26.1. What is the force on the Earth due to the
of the Oort cloud to estimate the number of
Sun™s radiation pressure? How does that com-
comets in the Oort cloud.
pare with the Sun™s gravitational force on the
26.6. (a) Estimate the kinetic energy of a 100 m
diameter object, of density 5 g/cm3, striking
26.2. It has been suggested that radiation pressure
the Earth with a speed equal to the escape
from the Sun could be used to propel a large
speed from the Earth. (b) Find one phenome-
spacecraft toward the outer Solar System.
non on Earth that has a comparable energy
How large a sail would you need to provide
an acceleration of 1 m/s2 for a 106 kg associated with it. (c) Why is the escape speed
a reasonable estimate? (Hint: Think of the
speed an object would have if it fell from far
26.3. Suppose an asteroid is a distance d from
Earth. Its center of mass is going to pass
26.7. For an asteroid of radius r and albedo a a dis-
within an angle of the star. How large does
tance d from the Earth, and a distance R from
the asteroid have to be to occult the star?
the Sun, find an expression for the amount of
26.4. How far can the center of mass of a 100 km
reflected sunlight reaching the Earth. You
radius asteroid pass from the direct line
may treat the asteroid as a disk, oriented so
between the Earth and a star and still have
the sunlight will be reflected toward the
the asteroid occult that star, if the asteroid is
3 AU from Earth?

Computer problem

radiation pressure. How fast is it moving by the
26.1. Suppose a grain 10 3 cm in extent starts at rest
time it reaches Mars?
near the Earth. It is pushed outward by the Sun™s
Chapter 27

The origin of life

Because of our present understanding of star
In this chapter we look at the steps that led up to
formation, we now think that the Solar System is
life on Earth, starting with the formation of the
the remnant of the material that collapsed to
Solar System. We then look at the possibilities of
form the Sun (Fig. 27.1). The original cloud might
finding life on other planets, both within the
have been spherical. However, it must have been
Solar System, and around other stars.
rotating, since we know that the Solar System has
angular momentum. As we saw in Chapter 15, the
27.1 Origin of the Solar System result of the rotation is that collapse perpendicu-
lar to the axis of rotation is retarded, while that
parallel to the axis of rotation continued. This
One of our goals in studying the Solar System is
means that the spherical cloud flattened to form
understanding how it formed. As we studied the
a disk. It is the disk out of which the planets prob-
planets we saw that they provide many clues to the
ably formed. Once the planets had formed, the
Solar System™s history. In this section, we briefly
debris not included in the planets was mostly
outline some of the ideas that have been proposed.
cleared away by a very strong wind from the Sun.
Any theory on the formation of the Solar System
This would have been when the Sun was going
should be able to explain such things as the fact
through a T Tauri phase, and its wind would have
that the planets™ orbits are approximately in the
been much stronger than it is today. The peak
same plane, and the fact that the planets orbit in
mass loss rate may have been 1 M 106 yr. The
the same direction. In addition, it must be able to
wind carried sufficient energy and momentum
explain the distribution of angular momentum in
to sweep out the debris and stop the infall into
the Solar System. Also, the different compositions
the solar nebula.
and appearances of the planets must be explained.
Attempts have been made to calculate the
Historically, two basic scenarios have been dis-
minimum amount of material in the solar neb-
cussed. In one, the Solar System formed as a by-
ula. This is the amount of material in the planets,
product of the Sun™s formation. The material left
plus that which escaped during the formation. In
over from the Sun™s formation is the material out
understanding how the nebula produced planets,
of which the planets formed. The idea was first
there is a problem involving angular momentum
discussed by Rene Descartes in 1644, and was elab-
distribution. The Sun has only 2% of the angular
orated upon by Immanuel Kant, and farther by
momentum in the Solar System (see Problem
Pierre Simon de Laplace, who was the first to take
27.1), but it would be expected that most of the
the effects of angular momentum into account.
angular momentum is in the central condensa-
In the other scenario, originally proposed by
tion. To explain this, it has been proposed that
Georges Leclerc de Buffon, the material to form the
the material to form the planets fell slowly into
planets was ripped from the Sun by the effects of
the cloud around the already forming Sun.
a passing object, possibly a comet.

temperatures, in excess of 2000 K. They make up
0.44% of the mass (not including the Sun) in the
Solar System. They are particularly prominent in
the inner planets, while the ices are prominent in
the outer planets. Comets provide us with the
best clues on the initial composition of the rocks
and ices.
(a) The accretion of the nebula probably took
place over 10 000 to 100 000 years. The first step in
the process was for small grains to clump together.
The grains collided, sometimes making larger
ones, and sometimes breaking into smaller ones.
The process produced many grains about 1 cm in
(c) (d)
size. These grains were large enough to settle
through the gas in the plane of the nebula. This
brought the clumps closer together, and allowed
for even more collisions. Calculations indicate that
the thin sheet of grains could then clump into
objects with sizes of a few kilometers (essentially
asteroid sized objects). About 1000 of these could
then form a group held together by their own
Fig 27.1. Formation of the Solar System. (a) A rotating
gravity. At that point, the groups were spinning
interstellar cloud. (b) The cloud begins to contract. Since the
too fast to collapse completely. Eventually these
angular momentum is conserved, the rotation becomes
groups served as the cores for farther condensa-
faster. (c) The rotation is fast enough to slow the collapse
tion of bodies orbiting at the same distance from
perpendicular to the axis of rotation, so a disk forms.The
the Sun.
center is collapsing fastest, forming a denser concentration
that will eventually become the Sun. (d) When the rotation Different parts of the Solar System then
prevents farther collapse of the disk, it breaks up into evolved differently because of the fall-off in solar
smaller clumps, so that some of the angular momentum is radiation with distance from the Sun. The col-
taken up by the orbital motion of the clumps.The clumps
lapsing nebula had a higher temperature in the
can then collapse. (e) Clumps of material gather together,
center (near the forming Sun) than at the edge.
forming planets, as the proto-Sun begins to radiate, and
In equation (23.4) we found the equilibrium tem-
generate a large wind. (f) The wind clears debris from the
perature of a planet as a function of the solar
Solar System.
luminosity and its distance from the Sun. This
expression works as well for dust particles.
In following the evolution of the solar nebula, (Indeed, the calculation that led to equation (23.4)
we must keep track of three types of materials: was essentially the same as that which we used to
gases, ices and rocks. Most of the mass was in the calculate the temperature of interstellar grains, in
gas (as most of the mass of the interstellar Chapter 14.) So, from equation (23.4), we see that
medium is in gas). However, gas cannot be held to the temperature falls off as the square root of the
a growing planet by gravity, so it escapes from all distance from the Sun. When the temperature
but the largest objects. The ices are water (H2O), was about 3000 K near the center, it was a few
carbon dioxide (CO2) and nitrogen (N2), along hundred kelvin in the regions of planetary forma-
with some ammonia (NH3) and methane (CH4). tion. It also falls by a factor of about five between
These make up 1.4% of the mass of the Solar the orbits of Venus and Neptune. Therefore, dif-
System. The rocks are iron oxides and silicates of ferent materials condensed at different distances
magnesium, aluminum and calcium. Some of the from the center.
iron was metallic and some of it was in iron sul- Another factor affecting the nature of forming
fide (FeS). They can only be destroyed at high planets was a fall-off in the density of material as

one goes farther from the Sun. As we saw in several Moon-sized objects should have appeared.
Chapter 15, when even a uniform interstellar After about ten million years, these objects col-
cloud collapses, it develops a higher density in lected to form most of the four terrestrial planets,
the center than at the outside. In fact, ultimately though these planets probably continued to
the highest density center becomes the star. In sweep up planitesimals for 100 million years.
the higher density regions near the center, the These collisions were constantly reforming the
material is also moving faster, as a result of infall, surfaces of the planets through violent events.
converting gravitational potential energy into The outer edge of the inner zone is the aster-
kinetic energy. The higher density and higher oid belt. There is a large gap between Mars and
speeds near the center meant that collisions also Jupiter suggesting that there was room for
played an important role in shaping the gas. As a another planet to form. It is the one gap in Bode™s
result of the temperature and density variations, law (discussed in Chapter 22). We don™t expect a
we can think of planetary formation as occurring gap, since we expect that the material in the solar
in three zones: (1) the terrestrial planets, (2) the nebula would have been falling off gradually in
giant planets, and (3) comets. abundance, and we know there was enough mate-
Near the Sun, the temperature was too high rial farther out to form the giant planets. The
for most of the gas (especially the H2 ) to have sur- most likely explanation is that the early forma-
vived the star formation process. So solid materi- tion of the very massive Jupiter prevented the for-
als had to be involved. We think that the original mation of a planet. This could have been either by
building blocks for the terrestrial planets where Jupiter somehow preventing the formation of the
chondrules (discussed in Chapters 23 and 26). more massive planitesimals, or by Jupiter some-
These were heated to temperatures of 1500 to how removing them after they had formed. We
1900 K, and then cooled. Chondrules that we can do know that Jupiter has been effective at remov-
study in meteors suggest that, to give their par- ing objects from certain resonant orbits, e.g. the
ticular structure, the heating and cooling took Kirkwood gaps discussed in Chapter 26.
place very quickly, possibly over a few hours. This In the second zone, material was far enough
would mean that the early solar nebula was rocked out for water ice to exist. Since O is more abun-
with energetic events. These chondrules would dant than the elements that are important in
have had a range of sizes, but typical sizes might dust grains (e.g. Si, Mg, Fe), particles of water ice
have been a few millimeters. There were so many (essentially snowflakes) would have been more
of these chondrules, and their relative speeds abundant than dust particles in the second zone.
were so low (about 1 m/s), that they eventually It is thought that Jupiter and Saturn formed ini-
began to stick together. We don™t know what pro- tially from planitesimals made up primarily of
vided the attractive force. It has been speculated water ice. These planitesimals would have formed
that the so-called van der Waals force could have in a manner similar to those for the rocky plani-
been involved. This is a very weak electrical tesimals that formed the terrestrial planets.
attraction between neutral objects when the However, once Jupiter and Saturn had enough
charges can move so that the centers of positive material to exert strong gravitational forces, then
and negative charge are in different places. This they would have collected all of the interstellar
created small aggregates of chondrules, which material (mostly gas and a little dust) that was
could also grow by sweeping up dust. Eventually near them. This resulted in two very massive
they grew to sizes of about 1 km. At that point, we planets. Also, the planets had compositions
call them planitesimals. reflected in the interstellar medium 4.5 billion
Even though there were many planitesimals, years ago. So the compositions of Jupiter and
they were distributed over a large volume of Saturn are essentially the same as that of the
space, so encounters between planitesimals were Sun, meaning that they have primarily hydrogen.
rare, maybe once per thousand years. Computer Uranus and Neptune formed in the outer
simulations show that these collisions eventually parts of the second zone. The icy planitesimals
made larger objects, and after about 20 000 years would have filled a larger volume of space,

meaning fewer collisions, and less chance for Solar System. The momentum carried by the light
growth than the ones that started Jupiter and is the energy, divided by the speed of light. That is,
Saturn. There would therefore have been less
p Ec
gravity to hold interstellar gas in. Furthermore,
the density of interstellar gas was lower the far- h
ther one got from the center of the solar nebula.
The radiation would have been able to sweep
So, Uranus and Neptune are just the result of the
out small dust particles, and also carry away the
buildup of icy planitesimals, and are dominated
orbital angular momentum of the dust. Finally,
by ices. Their compositions are therefore differ-
some of the collisions could also reduce the
ent from those of Jupiter and Saturn. (Fig. 25.13
orbital energy of the dust, allowing it to fall into
illustrates some of the differences in composi-
the Sun. This is known as the Poynting“Robertson
tion between Jupiter and Saturn and Uranus and
effect. In these collisions, aberration of light, dis-
cussed in Chapter 7, makes it appear to the dust
Most of the satellite systems probably grew
particle that the light from the Sun is coming
from a disk forming around the planet. This
from slightly ahead in the orbit. Thus, the parti-
process repeated the formation of the rocky plan-
cles lose energy, and eventually spiral into the
ets on a smaller scale. The satellites whose orbits
are close to the ecliptic and are not too eccentric
were probably made in this way. Satellites with
very inclined or eccentric orbits may have been
27.2 Chemistry on the early Earth
In the third zone, beyond Neptune, ice/rock
planitesimals were formed. However, they fill It is very likely that the atmosphere, surface and
such a large volume of space that gravitational oceans of the early Earth were very different from
encounters are very rare. This means that they their present condition. We have very little direct
cannot collect into a planet. The ones from evidence, and this has been an area of consider-
Neptune™s orbit out to 50 AU formed the Kuiper able disagreement.
Belt. Those farther out formed the Oort cloud. As As the Earth was forming, there was still a lot
we discussed in Chapter 26, occasionally one of of debris in the Solar System, so the Earth was
these objects has its orbit perturbed, and enters subjected to a much greater rate of bombardment
the inner Solar System as a visible comet. than it is today. As the conditions became less vio-
The scenario that we have discussed probably lent, the Earth cooled enough for water to form
left a large amount of debris around the planets. on the surface. The continents were beginning to
However, the Solar System is now relatively form. There was considerable volcanic activity,
clean. Where did the leftover material go? We which introduced large quantities of hydrogen
sulfide (H2S) into the atmosphere.
think that the Sun went through a stage when its
There was no free oxygen, O2. The oxygen in
wind was much stronger than it is now, much
today™s atmosphere is the result of plant life.
like the winds in T Tauri stars. The peak mass
loss rate may have been 1 M 106 yr. The wind (Remember, there is a symbiotic relationship
between animal and plant life. Plants consume
carried sufficient energy and momentum to
CO2, which is given off by animals, and through
sweep out the debris and stop the infall into the
photosynthesis convert sunlight into energy, and
solar nebula.
give off O2 as a by-product. The O2 is then used by
Collisions among the particles also helped to
the animals.) The absence of free oxygen also
clear the Solar System. Some of the debris
meant that there could be free iron (Fe) on the
crashed directly into planets, leaving the craters
surface. Today any free Fe would react with O to
that we still see on Mercury, Mars and the Moon.
make iron oxide (rust).
Other collisions led to ejection of bodies from the
For a long time it was thought that the atmos-
Solar System. Finally, the momentum carried by
phere contained a lot of hydrogen in various forms,
the sunlight itself may have helped clear the

especially molecular hydrogen (H2), methane More recently, it has been suggested that mol-
(CH4), ammonia (NH3) and water vapor (H2O). More ecules like those that came out of the Miller“Urey
recently, it has been suggested that there was experiments could have been formed in the inter-
more carbon monoxide (CO) and carbon dioxide stellar medium as part of the molecular cloud
(CO2) than methane, and more nitrogen (N2) than from which the Sun (and Solar System) formed.
ammonia. These more recent ideas also suggest As we saw in Chapter 14, a rich collection of inter-
that there was not very much molecular hydro- stellar molecules has been found, including some
gen. There is some disagreement over how much simple prebiotic molecules. It had been thought
phosphorous was available. We will see below that, even if these molecules were made in inter-
that P is an important component in some biotic stellar space, they would not survive the process
molecules. of star formation, at least not in the inner Solar
There is also some disagreement over what System. However, we know that some of this inter-
the temperature was on the early Earth. stellar material has been preserved, as comets in
Estimates range from freezing to boiling. The Sun the Oort cloud or the Kuiper belt. Some comets
gave off 25% less energy 4 Gyr ago than it does that passed close to the early Earth could have left
now. However, there was no ozone layer to absorb some of this material behind, for it to sink into
solar ultraviolet, so a larger fraction would have the atmosphere, and then eventually find its way
penetrated to the surface. to the surface.
There may have been frequent lightning in There is some evidence that such materials
the early Earth™s atmosphere. The effects of such might survive a meteoritic impact. Remember,
lightning were simulated in a laboratory at the meteors are the debris of comets, left in their
University of Chicago, in the early 1950s, by a orbits. The most famous example is the Murchison
graduate student, Stanley L. Miller, under the meteorite (mentioned in Chapter 26), which fell
supervision of his advisor Harold Urey. (Urey had in 1969, in Murchison, Australia. It was found to
won the 1934 Nobel Prize in Chemistry for his dis- contain a number of amino acids which are not
covery of deuterium.) The Miller“Urey experiments likely to have been made on Earth.
helped chemists understand how the first prebi-
otic molecules may have formed in the Earth™s
27.3 Origin of life on Earth
atmosphere. To simulate the effects of lightning,
they carried out their experiment in a sealed
Whether as a result of conditions like those sim-
glass tube with electrodes and produced repeated
ulated by the Miller“Urey experiments, or as a
electrical discharges.
result of deposition from comets, it is possible
Miller and Urey started with a mixture of
that the early atmosphere was enhanced in these
methane, ammonia and hydrogen. The effects of
prebiotic organic molecules. So the question is
evaporation and condensation of the early oceans
how we go from these simple organic molecules
were simulated by recycling water through the
to the life that is around us now. Evidence sug-
system. They ran the experiment for a few days at
gests that there was a gap of almost 1 Gyr
a time and then analyzed what had been pro-
between the formation of the Earth and the
duced. After some runs they found simple
appearance of the first multicell organisms.
organic molecules important as building blocks
At the molecular and cellular level, a funda-
of life, including amino acids. At the time they
mental tenet of life is the ability to replicate
did these experiments, it was thought that the
itself. That replication allows for the develop-
early atmosphere contained large amounts of
ment of multicell organisms. It also allows for
methane, ammonia and hydrogen. As we said
generations of organisms. Imperfect replications
above, there is now some disagreement over how
are called mutations. Mutations can have no
abundant those molecules actually were.
effect, provide a change for the better (more able
Alternative means have been investigated in
to survive), or provide a change for the worse (less
which the simple amino acids formed in various
able to survive). According to Darwin™s theory of
clay deposits.

evolution, the increased survival rate of the bene- show that the likelihood of random formation is
ficial mutations means that the better trait is very small.
passed on to future generations. Most organic chemists working on this prob-
At the molecular level, for most life as we lem have decided that it is more likely that the
know it, the replication is carried out by a very DNA we have today is the end product of a series
large molecule, deoxyribose nucleic acid (DNA). It is of well defined steps, building up more complex
shaped like a ladder twisted into a double helix classes of molecules. While each of these steps
structure. This structure was first worked out in may have taken some time, none was as improba-
1953 by James Crick (England) and William Watson ble as the direct formation of DNA, and even the
(USA), and they won the Nobel Prize in sequence of events is much more likely than the
Chemistry for their work. There are four possible direct formation. Of course, there is no agree-
parts, called nucleotides, for each position of the ment on what those steps were. This is in part due
ladder. The nucleotides are made of subunits, to the fact that the initial conditions are not well
called base, sugar and phosphate. In assembling known. Also, the current state is so far removed
a chain of nucleotides, sugars link to phosphates, from the initial conditions that there are many
so they alternate in the chain. The bases dangle equally plausible ways of getting here. We will
off to the side. Each base can only have a partic- just briefly note some of the more prevalent
ular base partner on the other side of its ladder ideas.
rung. These partners are called base pairs. The It is generally agreed by those looking at the
sequence of bases determines the genetic infor- possible large steps that would lead from simple
mation that is carried in the DNA, and governs amino acids to DNA, that RNA is an important
the replication. intermediary. In fact, one might be tempted to
There is another nucleic acid, ribonucleic acid note that amino acids are the constituents of pro-
(RNA) . The current purpose of RNA is to facilitate teins, and proteins are the constituents of RNA,
the replication of the DNA by transferring infor- so the amino acids could have formed into pro-
mation from the DNA to proteins. RNA consists of teins and the proteins formed into RNA. However,
chains of up to a few thousand nucleotides. Each those studying how RNA works today have
nucleotide has a phosphate, ribose (which is a noted that RNA is a catalyst for the synthesis of
five-carbon sugar), and one of four bases (ade- proteins. This means that the RNA would have
nine, guanine, cytosine and utracil). All four had to form first.
bases have a flat ringlike structure. By compari- The formation of RNA without making pro-
son, the sugar in DNA is deoxyribose (ribose with- teins first is quite difficult (given the complexity
out an oxygen), and one of the bases, utracil, is of RNA). Chemists working on the problem have
replaced by thymine (utracil to which a methyl focused on the idea of finding enzymes that
group, CH3, has been added). So you see there is a might serve as catalysts for this process.
very close relationship between DNA and RNA. It Remember, a catalyst is something that helps
is possible that historically RNA played a role in promote some reaction but is not changed in
the development of DNA. the process. Some catalytic reactions have been
So, the question is, how do you go from a pre- proposed which may have created RNA on a time
biotic soup to the complex DNA in less than 1 Gyr? scale of less than a year. Once the RNA formed,
One suggestion is that, once the simple amino it could begin the process of replication.
acids formed, they would have had so many Furthermore, one by-product of such a process
chances to react over half a billion years, that it was was the formation of certain proteins.
possible to form DNA molecules by random Once the chemicals are available, the develop-
chance. One argument in favor of this is that since ment of life requires the formation of cells. Cells
there was no life, there were no predators. are the basis of all life we know now, and one of
Therefore, once formed, simple amino acids could the questions that is still being addressed is when
stay for hundreds of millions of years without the cells first developed. In the first RNA that
being destroyed. However, realistic calculations developed, replications that directly produced

surviving molecules were favored. With the devel- visually connecting unconnected features. The
opment of cells, a replication (and some variation) color changes are real, but are due to dust storms,
could be favored because it produced something which vary with season. So, we must look for life
which could help the cell survive. There are two in much more subtle ways. The life we find may
different views on when cell walls began to be microscopic, or it may be extinct, having left
appear. One is early in the process, and the other fossils. So we use remote sensing to select likely
is late, about 3.8 Gyr ago. Different processes for sites of current or former microscopic life, and
the formation of RNA favor one or the other then inspect those sites with various landing
picture. equipment. That landing equipment must have
Cell walls are made of a lipid bilayer (double instruments capable of detecting the life or some
10 7 cm thick.
molecular level). It is about 5 by-product of its existence. For example, we may
The molecules that make up these typically have look for the results of respiration. Such searches
two ends, one that attracts water and the other may be limited in the sense that they are looking
that attracts fat. Membranes grow by adding for some particular organism or by-product.
more material to a pre-existing membrane. Lunar soil samples, returned to Earth by
Apollo astronauts, have been extensively studied
in the laboratory, with no evidence for extrater-
27.4 Life in the rest of the
restrial life. For the first few missions, astronauts
Solar System? were kept in a quarantine for an extended period
of time, because of the fear that they might carry
If the development of life on Earth did not some form of previously unknown contagion.
require a special set of circumstances, then we That practice was limited when the first few mis-
expect life to have started elsewhere in the sions revealed no signs of microbial life. Not find-
galaxy. It is therefore of interest to search for life ing life on the Moon should not be surprising, as
elsewhere, and the obvious starting place is our the Moon lacks both an atmosphere and water.
Solar System. Finding even primitive life else- Mars is potentially an interesting place to look
where in the Solar System would indicate that for life, either current or fossil. That is because
the Earth is not just one lucky case, and would we think that prior to 3.5 Gyr ago, when life was
give us hope of finding it widespread in the emerging on Earth, conditions on Mars were sim-
galaxy. Also, finding certain types of life else- ilar to those on Earth. There is evidence for abun-
where in the Solar System would give us insights dant liquid water on Mars, in the form of rivers,
into how life actually formed on the Earth. When lakes and possibly larger bodies, like oceans. We
we talk about searches for life, we generally mean might ask how far the early, prebiotic, chemistry
“life as we know it”. That is, life based on carbon proceeded on Mars. Did such a chemistry develop
bearing (organic) molecules. (Science fiction writ- so far as to lead to life “ replicating molecules? If
ers have speculated on other forms of life, such as such early life started, how did it evolve? Is it still
silicon based, but there is no current evidence to present or did it die off? If it is still present, we
suggest that searching for such life forms would can look for it directly. If it died off, we can still
be fruitful.) Development of carbon based life look for fossil evidence.
generally requires water, so in choosing places to The first attempts to answer these questions
search for life, we would look at places with evi- were made by the Viking landers. In designing
dence for water, at least in the past. Such life experiments to look for chemical signs of life, e.g.
would also require the presence of an atmosphere. respiration or photosynthesis, you have to make a
Let us think about how we might look for life decision about what chemicals you will look for.
elsewhere in the Solar System. Some used to sug- This requires making assumptions about the
gest that “canals” on Mars were evidence for intel- kind of life we are looking for. So, as a starting
ligent life, or that changing colors with seasons point, the Viking experiments were designed to
suggested vegetation. We now know that those look for microbial life with a chemistry similar to
canals don™t really exist. They are artifacts of that on Earth. These experiments did not yield

evidence for existing life “as we know it” at either of interesting consequences. One is that, if plane-
site. A more extensive analysis of this data sug- tary systems are a natural by-product of star for-
gests that there is some evidence for organic mation, we should be able to find many other
chemical activity, but Martian life is not the only planetary systems in our galaxy. As you might
possible explanation. This shows some of the dif- suspect, looking for planets around a distant star
ficulties in designing and interpreting remote is a formidable observational challenge for a
experiments to answer such subtle questions. number of reasons. Any radiation given off by the
We are now early in the next phase of this planets (either by reflected starlight or emitted
search on Mars. From orbital mapping, we look far infrared and radio emission) would be very
for places that show evidence for an abundance of weak, especially at large distances. This is compli-
water in the past, as well as temperate weather cated by the fact that it is much weaker than the
conditions to promote chemical activity. (It has radiation from the star in that system. The linear
even been suggested that Mars had sources of separation between a planet and the star it orbits
heated water, like geothermal springs on Earth.) is not very large, so the angular separation is
From these orbital missions landing sites have small, even for relatively nearby systems (a few
been chosen for current and future landers. These parsec away). The masses of the planets are much
landers will use increasingly sophisticated experi- less than the stars they orbit, so the recoil motion
ments to explore the chemistry of the terrain sur- of the star is also very small.
rounding the landing sites. Eventually, material To illustrate the problem, consider Example
from promising sites will be returned to Earth on 27.1.
unmanned spacecraft. These samples will be stud-
Example 27.1 Appearance of the Solar System
ied extensively in terrestrial laboratories.
Assume we are observing the Solar System from a
There is already a small source of Mars surface
distance of 10 pc. (a) What is the angular separa-
material on Earth. These are rocks that were
tion between Jupiter and the Sun? (b) Estimate
thrown off the surface of Mars by meteoritic
Jupiter™s apparent magnitude. (c) What is the angu-
impact, and then happened to strike the Earth,
lar amplitude of the Sun™s motion in response to
like other meteors that the Earth encounters. The
the gravitational force exerted on it by Jupiter?
hard part is to distinguish rocks from Mars from
(d) By how much will a spectral line from the Sun
those that come from normal meteor showers. If
be Doppler-shifted due to Jupiter™s orbital motion?
we can study them in the laboratory, we find that
their chemistry is generally like that at the
Viking lander site. This strongly suggests that
(a) We can generalize equation (2.17) to tell us that
they are from Mars. One meteor “observatory” on
if an object is a distance D(pc) from us, and has a
Earth is in Antarctica, as it is easy to pick out
linear separation R(AU), then its angular separation
rocks against the white snow/ice background.
(in arc sec) is
One object found in 1984 was not classified as
¢ 1arc sec 2 R1AU2 D1pc 2
Martian until 1993. It was studied extensively for
the next two years, and the researchers found
So for Jupiter (5.2 AU from the Sun),
microscopic fossils, which they concluded may
¢ 1arc sec 2
have come from Mars. However, other groups 5.2 10
studying this meteor suggested that these fossils
0.5 arc sec
may have been contamination from Earth. This
shows how difficult these experiments can be. (b) To estimate the brightness of Jupiter, we first
calculate how much sunlight hits it. The fraction, f,
27.5 Other planetary systems? of sunlight hitting Jupiter is the ratio of the solid
angle of Jupiter as viewed from the Sun 1 R2 d2 2
divided by the solid angle of a full sphere (4 ), so
The notion that the Solar System formed as a by-
1R2 4 d2 2 9
product of the formation of the Sun has a number f 8 10

If the albedo of Jupiter is 0.5, then half of this is Solving for the speed of Jupiter, we have
reflected, meaning that Jupiter is 4 10 9 as 2
v1 1.3 10 km s 13 m s
bright as the Sun. This makes its absolute magni-
So v c 4.3 10 8.
tude 2.5log10(4 10 9) 21 mag fainter than the
For comparison, remember that the Doppler shifts
Sun. The absolute mag of the Sun is 4.8, so the
and broadening of typical interstellar lines were a
absolute mag of Jupiter is approximately 26,
few kilometers per second, so the recoil of the Sun
and at a distance of 10 pc, the apparent magni-
due to Jupiter™s motion is much less than that. The
tude equals the absolute magnitude, so the
Doppler shift is independent of the distance.
apparent magnitude is 26, barely at the limit of
However, the farther away the object, the fainter
our sensitivity, and it must be seen next to the
the signal, so the harder it is to measure the
Sun, which is 21 mag brighter and only 0.5 arc
Doppler shift.
sec away.
(c) The ratio of the radii of the orbit of Jupiter and This illustrates the difficulty of detecting
that of the Sun about the Sun/Jupiter center of planets around other stars. Shining by reflected
mass is just the ratio of the masses: sunlight, Jupiter would appear just at our detec-
tion threshold, even if it wasn™t swamped by the
r2 r1 m1 m2
direct light from the Sun which would be less
11.9 10 2 12 10 2
30 33
than an arc second away. This does suggest, how-
ever, that if you were going to detect direct radi-
10 3
ation from a planet, you might do better in the
infrared where the blackbody radiation from
So the radius of the Sun™s orbit about the center of
the planet peaks. The Sun still gives off much
mass is

r2 110 3 2 15.2 AU2
more radiation, but the imbalance is less (see
Problem 27.4).
5.2 10 3 AU Directly seeing the motion of the Sun about
the center of mass would also be very difficult.
At a distance of 10 pc, the angular size is
The best hope is to look for the Doppler shift
¢ 1arc sec 2 caused by that motion. As we discussed for binary
5.2 10 3 10
stars (Chapter 5), that motion is best observed if
5.2 10 4 arc sec
we are in the plane of the orbit. We would
observe a variation in the star™s Doppler shift that
(d) To find the orbital velocities, we use equation
looked like a sine wave with a period equal to the
(5.23) and solve for the sum of the speeds:

2 G1m1 m2 2
orbital period of the planet. Just as for binary
1v1 v2 2 3 stars, if the orbit is inclined, you still see periodic
P motion, but the range of Doppler shifts is
2 16.67 10 8 dyn cm2 g2 2 12.0 1033 g 2 reduced by the sine of the inclination angle. If
111.9 yr 2 13.16 107 s yr2 more than one planet is present (e.g. Jupiter and
Saturn) you would see a more complicated pat-
12.2 10 cm s2
18 3
tern that comes from adding two sine waves with
different periods, amplitudes and phases (see
Taking the cube root gives
Problem 27.5).
v1 v2 1.3 10 cm s 13 km s The technique which has proved most suc-
cessful has been looking for the variations in the
The ratio of the speeds is equal to the ratio of the
Doppler shifts of nearby stars. A group headed by
masses (equation 5.12),
Geoffrey Marcy and R. Paul Butler has studied a large
number of potential systems. Other groups have
v 2 v 1 m1 m2

11.9 1030 2 12 1033 2
also made independent measurements, giving
more confidence, as the measurements are diffi-
10 cult. These groups have studied more than 1000

HD 46375
stars. This comprises a nearly complete sample of
Sun-like stars within 30 pc of us. They have found P = 3.023 day
Mass = 0.24 MJUP /sini
evidence for a planet in more than 90 systems (so K = 34.9 ms’1
e = 0.03
far). More recently, they have found a few systems 40
with evidence for more than one planet.

Velocity (ms’1)
Marcy and Butler™s observations are done at
Lick Observatory using a 3 m telescope, and on
Mauna Kea, using the 10 m Keck-I telescope (dis-
cussed in Chapter 4). Because the variations in ’20
the Doppler shifts are so small, very accurate
spectrometers had to be used. Before the starlight
enters the spectrometer, it passes through a tube RMS = 4.61 ms’1 Keck
of iodine gas. The iodine produces a series of nar-
0.0 0.6 1.0
row absorption lines superimposed on the stellar
spectrum, providing a very accurate calibration,
HD 217107
and making it easier to detect variations in
Doppler shifts. The spectra are also corrected for P = 7.126 day
Mass = 1.23 MJUP /sini
K = 133 ms’1
things like the motion of the Earth around the 200
e = 0.14
Sun, the motion of the observatory about the cen-
ter of the Earth, and perturbations on the Earth™s
Velocity (ms’1)

motion due to the other planets. Once a variation
consistent with a planet is detected, its period is 0
measured. The central stars of these systems are
nearby and are well studied, so their properties ’100
are well known. If the mass of the central star is
known, then the period and Kepler™s third law ’200
RMS = 12.8 ms’1
can be used to determine the semi-major axis of
0.0 0.6 1.0
the planet™s orbit. By measuring the amplitude of
Orbital Phase
the Doppler shift, we can tell how much the star is
moving about the center of mass, so we can deter-
HD 210277
mine the mass of the planet, assuming that we are
P = 1.18 yr
in the plane of its orbit. If we are not in the plane Mass = 1.29 MJUP /sini
K = 39.3 ms’1
of its orbit then the derived mass is a lower limit. e = 0.45
Some sample data are shown in Fig. 27.2 The
Velocity (ms’1)

dots show the data points, with error bars to 20
indicate the uncertainties in the measure-
ments. The dashed lines show the best fit to the 0
data. The masses are expressed as MJUP/sin(i),
since we don™t know the inclination angle. So,
these numbers are lower limits to the true ’40
mass. They are expressed as MJUP, since that is a
RMS = 4.18 ms’1 Keck
convenient reference.
0.0 0.5 1.0
The orbital periods range from 3 to 15 yr. and
Orbital Phase
the Doppler shift variations range from 11 to
1800 m/s. The orbital semi-major axes range from Fig 27.2. Radial velocity variations of three stars with
0.038 to 6.0 AU. Orbits range from almost circular evidence for planets.The horizontal axis is phase within the
orbit, relative the listed period. Observations over many
to eccentricities of 0.93. M/sin(i) ranges from 0.22
periods are combined in this way. [Geoffrey Marcy,
to 14.7 Jupiter masses. The distribution of masses
University of California at Berkeley]
is shown in Fig. 27.3.

more radiation in the infrared than in the visible.
All Known Companions
25 Also, since they are often deep inside molecular
0“15 MJUP
clouds, with tens of magnitudes of visual extinc-
Number of Planets

20 tion, they are hard to see in the visual. Of course,
since they are small, we must use infrared obser-
vations with very good angular resolution. HST
has provided the opportunity to carry out these
observations, and a few samples are shown in
Fig. 15.26.
These disks are important because they allow
us to study the stage between the collapse of a
0 2 4 6 8 10 12 14 molecular cloud to form a star and the formation
M sini (MJUP) of a planetary system. Of course, in order to study
these disks in detail, we would like to be able to
Fig 27.3. Mass distribution for extrasolar planets.
do high resolution spectral line observations, so
[Geoffrey Marcy, University of California at Berkeley]
we can trace the velocity structure of the disks.
This is something that will be most easily done
This small sample has already raised a num- on the Atacama Large Millimeter Array (ALMA,
ber of questions. For example, 5MJUP planets are Fig. 4.32) when it is finished.
found closer to their stars than Mercury is to the
Sun. There are also very few very massive plan- 27.6 Searches for extraterrestrial
ets, even though these would have been very
easy to detect. Also compared to our Solar
System, a number of very eccentric orbits have
A number of recent discoveries suggest that life
been found.
may be more common in the galaxy than many
There is also a way to look for systems that
had thought. It appears that organic molecules
might be forming planets. We saw earlier in this
can form and survive in even the hostile envi-
chapter that we think that planetary systems
ronment of interstellar space. It also appears
form from the disks that are a by-product of the
that planetary systems form as a natural by-prod-
star formation process. In Chapter 15, we saw
uct of star formation, so there might be a large
how the presence of these disks could be inferred
number of potential hosts to life. It is natural to
from the existence of bipolar outflows. That is,
suggest that if life has had sufficient time to
the disks collimate the outflow. Remember, for
evolve on a planet, then it might lead to intelli-
the bipolar flows, the presence of the disks has
gent life at some point. Such intelligent life
only been inferred in most cases, though there
might, knowingly or accidentally, give off evi-
are a few examples where we see objects that
dence of its existence. These thoughts have
could be the collimating disks. Even those disks
fueled the push for searches for extraterrestrial intel-
are hard to see because they are small and sub-
ligence (SETI).
tend small angles. The disks that will form plan-
The important issues in SETI are (1) what is
ets around a solar mass star are even smaller. For
the likelihood that detectable extraterrestrial civ-
example, a 1000 AU disk at the 500 pc distance of
ilizations exist (or how many exist), and (2) what
the Orion Nebula, the nearest extensive star
is the best strategy for detecting them. We look
forming region, would subtend an angle of 2 arc
briefly at both issues.
sec. Of course, this is large compared to the size
The development (and survival) of a detectable
of Jupiter, so it would be much easier to see than
extraterrestrial civilization depends on a number
even a giant planet.
of factors. The important factors were first put
These disks are best seen in the infrared for a
down by Frank Drake (Cornell) in the famous Drake
number of reasons. They are cooler than the pro-
equation, which gives the number of civilizations
tostars they surround, so they give off relatively

survive 100 yr. So, let™s try an average lifetime of
in our galaxy that would be able to contact each
105. Putting all these together gives N 50.
other as
Obviously, the uncertainties are large, but this
N R*fPne f/ fi fC L (27.1)
discussion gives us a feel for what the considera-
where R* the rate at which stars are forming, tions are.
fP the fraction of stars that have planets, ne the If 50 civilizations are uniformly spread over
number of planets per planetary system with the disk of the galaxy (Problem 27.6) then the
conditions suitable for life to develop, f/ the frac- mean separation between civilizations is 1 kpc, or
tion on which life actually exists, fi the fraction 30 000 ly. This means that any radiation takes
of life forms that develop intelligence, fC the 30 000 yr to get from one civilization to the next.
This number depends on N1/2, so it does not
fraction of intelligent species that choose to com-
municate and L the average lifetime of the civ- depend very strongly on your assumptions that
ilization after they reach a technological state. went into N. Spacecraft travel much slower than
We can estimate some of these quantities and the speed of light. Even at 0.1 c (a pretty ambi-
make guesses at others. The low mass star forma- tious speed) it would take 300 000 yr to get from
tion rate in the galaxy is about 10/yr. Theoretical civilization to civilization. This is way too long to
considerations involving angular momentum make it useful. This is why even astronomers who
suggest that all stars should form either as mul- think that there may be abundant life in the
tiple stars (binaries etc.) or have planets (or both). galaxy do not believe that we are being visited by
Since roughly half the stars are binaries, we alien spacecraft.
might suggest that at least the other half should The most obvious form of communication is
have planets. As a more conservative estimate, electromagnetic radiation. Only moderate wave-
initial searches have revealed planets in roughly length (1 to 30 cm) radio waves pass through
10% of the systems searched, so we take this fac- interstellar space with little attenuation. This
tor as 0.1. The number of planets per system with physical fact doesn™t change with position in the
conditions suitable for life is hard to estimate. It galaxy, so we can presume that a civilization
can also include large moons, like Titan or would use radio waves in that range for such com-
Europa, so for our Solar System it might be five munication. As we saw in Chapter 4, radio trans-
(Earth, Venus, Mars, Titan, Europa). Let™s be opti- mitters and receivers are relatively narrow band,
mistic and take this number to be one. The frac- typically covering 100 MHz at a time (see
tion on which life exists might be 0.1, and the Problem 27.7). We must therefore make some
fraction of those on which intelligent life exists, guess, then retune the receiver and repeat the
could be 0.01. We can guess that half of intelli- observations at nearby frequencies, so we cover a
gent civilizations would choose to communicate. reasonable frequency range. We would want to
The final step is the lifetime of the civilization avoid strong interstellar lines (like the 21 cm line)
during which communication is possible. For us, because we could not distinguish a natural from
communication has only been possible for the an artificial signal. Some have suggested between
last 50 years (since the development of radar in 21 cm and 18 cm (the OH line), far enough away
WW II). It is very possible that a civilization does from either line so that you would not see it red-
not live long after developing technology, either or blueshifted into your search window.
because it might kill itself off in a nuclear war (or You must also decide where to look. This is
accident) or might simply pollute the planet or because radio telescopes have beams that only
use up its natural resources. If a civilization sur- look at a small fraction of the sky. One strategy of
vived long enough to develop space travel, then SETI projects has been to look in great detail in the
they might be able to relocate when they made directions of nearby stars that may have planetary
their home planet uninhabitable. Such a civiliza- systems and have environments like our Solar
tion might be more outward looking and more System. Less time per location could be expended
interested in communication. Such a civilization in looking systematically over large parts of the sky.
might survive 106 yr, but many others might only So this is one of the great technological problems

of SETI. You must search over two spatial dimen- light. They pass through interstellar space virtu-
sions (on the sky) and frequency. Sensitive searches ally unattenuated. Detectors don™t have to be
are being carried out at Aricebo, taking advantage tuned to a narrow energy (frequency) range to
of the large surface (now upgraded), and the detect them. Their energy can be deduced after
ability to use a number of receivers simultaneously, they are detected. The same is true for direction.
so we can cover more frequency ranges. More Detectors for neutrinos from natural extrater-
continuous coverage is being done using smaller restrial sources (e.g. supernovae) are just large
telescopes. tanks of water (or part of the ocean). They don™t
Another problem is how to recognize a signal have to be pointed. They will detect neutrinos
from an extraterrestrial intelligent source. The from any direction. After it is detected, the direc-
recent development of fast relatively inexpensive tion can be inferred. Of course, as we have seen,
computers has made it possible to search signals generating and detecting neutrinos is very hard.
for regular patterns or variations that could not On the other hand our neutrino technology is
be natural. Remember, when pulsars were first 100 years behind our radio technology. (Who
discovered, some thought that they might be sig- would have predicted 100 years ago where our
nals from extraterrestrial civilizations. radio technology is today ?) On the time scale of
There is one other possibility that has been the evolution of civilizations 100 years is not
suggested “ neutrinos. They travel at the speed of very much.

Chapter summary
Solar System. The presence of water would have
In this chapter we looked at the steps that led to
been important in that formation. We think that
the origin of life, starting with the formation of
early Mars had conditions much like the early
the Solar System.
Earth, including large amounts of water, so it is
We think that the Solar System formed as a
possible that life may have formed on early Mars
by-product of the formation of the Sun, from the
in much the same way as it did on Earth.
material left behind in a disk orbiting the proto-
Searches for traces of that life are in their early
Sun. A decrease in temperature and density of the
stages. There has been some suggestion that a
material led to different formation scenarios for
rock from Mars, found in Antarctica, may have
the inner planets, the outer planets and the
signs of microbial life, though there is also a pos-
comets. The final stages of formation must have
sibility of contamination from the Earth.
included a strong solar wind to clear out the
In looking for life beyond the Solar System,
debris that was not part of the planets.
the first step is to find other planetary systems.
Because of abundant water and a reasonable
We saw how difficult it is to detect planets orbit-
temperature range, we think that prebiotic
ing even a nearby star. The angular separations
organic molecules formed on the early Earth.
are very small. The planets are much fainter than
There are still uncertainties about the mecha-
their host stars. They are also much less massive,
nisms, including the relative importance of elec-
so it is hard to measure the Doppler shift in the
trical activity (as analyzed in the Miller“Urey
stars as they move in response to the orbital
experiments) and seeding from early comets. It is
motion of the planets. We described some experi-
also not clear how one gets from these prebiotic
ments which are just beginning to yield evidence
molecules to DNA, which is the basis for our repli-
for such Doppler shifts in a few nearby systems.
cating life. Despite the large amount of time
The final question we looked at is the possibil-
available, it is not likely that a random set of reac-
ity of detecting extraterrestrial intelligence. We
tions would have led to DNA. It is more likely that
first looked at the factors affecting the number of
a series of well defined steps was involved.
such civilizations that we might detect. The fac-
We think that conditions may have been right
tors are very uncertain, but there may be of the
for the formation of life in other parts of the

order of tens of such systems in our galaxy. This waves. Searching for such signals requires map-
means that they are probably too far apart to visit ping the sky a little bit at a time, and also cover-
with spacecraft, but we can detect them by radio ing a reasonable frequency range for detection.

27.1. If a planet had formed in the asteroid belt, do 27.3. Looking at each term in the Drake equation
you think it would have been more like Mars (27.1), make an argument why it might be
or Jupiter? Justify your answer. higher or lower than taken for the calculation
27.2. It appears that some planets come in twinlike in this chapter.
pairs, Earth“Venus, Jupiter“Saturn, Uranus“
Neptune. Do you think this is an accident?

27.1. Calculate the angular momentum of the Sun, 27.5. For an extrasolar planet, using dv (the varia-
tion in the Doppler shift), the period, P, and
and compare it with that of the rest of the
the mass of the star M, find the radius of the
Solar System.
27.2. How many Moon-mass objects would it take planet orbit, and the mass of the planet (a) if
to form each of the inner planets? we are in the plane of the orbit, (b) if the
27.3. (a) How much would the Sun move (angular orbit is tilted.
27.6. If there are N civilizations uniformly spread
motion) in response to the orbital motion of
a planet with ten Jupiter masses, orbiting over the disk of our galaxy (with a radius of
50 AU from the Sun, as viewed from 10 pc 15 kpc), what is the mean separation between
away? (b) What would the Doppler shift be? civilizations (ignore the thickness of the plane)?
27.4. What are the relative brightnesses of Jupiter 27.7. How many 100 MHz slices would it take to
and the Sun at the wavelength where cover the whole spectrum from 1 cm to
Jupiter™s blackbody spectrum peaks? 30 cm?

Computer problems

27.3. Use the data in Fig. 27.2 to derive masses for the
27.1. Calculate the far IR luminosity of Jupiter and com-
three planets whose data are given.
pare it with that of the Sun.
27.2. Make a graph of the Doppler shift for two planets
(e.g. Jupiter and Saturn).
Appendix A Glossary of symbols

a albedo H2 molecular hydrogen
semi-major axis of ellipse
i inclination of orbit
a acceleration
A angle to convergent point of moving
I moment of inertia
area angular momentum
atomic mass number angular momentum quantum number
k Boltzmann constant
b bottom quark constant, giving curvature of universe
distance at which a trajectory would pass an kinetic energy
object if there were no deflection kinetic energy
semi-minor axis of ellipse
galactic longitude
B blue filter
path length for absorption
Bv(T) Planck function at temperature T
L luminosity
B magnetic field
mean free path
BC bolometric correction
L solar luminosity
c charm quark angular momentum
speed of light
m magnitude
d distance from Earth to astronomical object mass
down quark order of interference maximum
telescope diameter electron mass
d deuteron gravitational mass
d0 mi
reference distance for absolute magnitudes inertial mass
dM mass of thin shell Jeans mass
mn neutron mass
e charge of electron
mp proton mass
charge of proton
mr reduced mass
eccentricity of ellipse
M absolute magnitude
e positron
M(r) mass interior to radius r
e electron
M solar mass
E energy
E n
electric field density
index of refraction
f energy flux
principal quantum number
focal length
n neutron
fraction of radiation absorbed
ni level population (i can be any index)
F force
N column density
g acceleration of gravity number of lines on a grating
gi statistical weight of the ith state number of neutrons in a nucleus
G universal gravitation constant
p parallax angle
h Planck™s constant p proton
H Hubble parameter momentum
H0 P
current value of Hubble parameter period of orbit
H hydrogen power
HI atomic hydrogen pressure
HII ionized hydrogen probability
H first Balmer line potential energy

q z
deceleration parameter zenith distance (angle away from zenith)
electric charge redshift ( / 0)
q0 Z
current value of deceleration parameter number of protons in a nucleus (atomic
r radius
R distance from center of galaxy alpha particle, or helium nucleus
radius beta particle (electron or positron)
ratio of total-to-selective extinction gamma-ray
resolving power of prism or grating photon
Rydberg constant ratio of specific heats
) 1/2
scale factor in cosmology special relativistic factor (1
RJ Jeans length increment
RS Schwarzschild radius increment
R s
solar radius space-time interval
v velocity spread
s strange quark
wavelength shift or spread
t time frequency shift or spread
top quark telescope angular resolution due to
tff free-fall time diffraction
trel relaxation time rate of energy generation, per unit mass
T temperature magnetic flux
Ti ionization temperature opacity
Tk kinetic temperature wavelength
Tx excitation temperature wavelength at which spectrum peaks
rest wavelength
u up quark
cosmological constant
proper motion
U potential energy
ultraviolet filter
v speed antineutrino
va orbital speed at aphelion or apastron rest frequency
vesc escape velocity density
vp orbital speed at perihelion or periastron density to close the universe
vr radial velocity cross section
vrms root-mean-square speed Stefan“Boltzmann constant
vT tangential velocity optical depth
v velocity lifetime to fall to 1/e of initial value
V visible filter half-life
volume angular speed
angular speed
W W particle
ratio, / crit, for the universe
x position
Xr rth ionization state of element X
Appendix B Physical and astronomical constants

Physical constants

2.99792456 1010 cm/s
speed of light
2.99792456 105 km/s
6.6732 10 8 dyne cm2g2
gravitation constant
1.3806 10 16 erg/K
Boltzmann constant
6.6262 10 27 erg s
Planck™s constant
5.6696 10 5 erg/cm2 K4 s
Wien displacement 2.89789 10 cm K
R 1.097373 105/cm
Rydberg constant
NA 6.022169 1023/mol
Avogadro™s number
u 1.66053 10 24 g
atomic mass unit
mp 1.6726 10 24 g
mass of proton
mn 1.6749 10 24 g
mass of neutron
me 9.1096 10 28 g
mass of electron
mH 1.6735 10 24 g
mass of hydrogen
e 4.8033 10 10 esu
charge of proton
a0 5.29177 10 9 cm
Bohr radius

Astronomical constants

1.4959789 1013 cm
astronomical unit 1 AU
1.4959789 108 km
1 pc 3.0856 1018 cm
3.0856 1013 km
3.2615 ly
1 ly 9.4605 1017 cm
light year
1.9891 1033 g
solar mass
6.9598 1010 cm
solar radius
6.9598 105 km
3.83 1033 erg/s
solar luminosity
ME 5.977 1027 g
Earth mass
RE 6.37817 108 cm
Earth radius
6.37817 103 km
REM 3.84403 1010 cm


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