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I
The Sun and Solar Energy
there contained the other known elements in an
abundance generally decreasing with the mass
of the element. These additional elements were
produced inside a very massive star (or stars)
and then hurled out into space in the cataclysmic explosion of a star known as a supernova.
One of the most important forces behind global
change on Earth is over 90 million miles distant
from the planet. The Sun is the ultimate,
original source of the energy that drives the
Earth’s climate system and nurtures life itself. It
provides essentially all the energy the Earth
and its atmosphere receive. If we are to understand global warming and climate change we
should examine the source of the energy that is
responsible for producing the environment we
enjoy on Earth, how this solar energy interacts
with the Earth and its atmosphere, and how the
composition of the atmosphere determines the
ultimate temperature of Earth.
Gravity
Space is not a total vacuum; even in the vast
reaches between stars there are tenuous wisps
of gas. Stars are born where the interstellar
matter is denser than average. The closer together particles are, the greater the gravitational
force between them. Gravity, the same familiar
force that keeps the Earth in orbit around the
Sun and holds us on the surface of the Earth, is
one of the major forces in the universe. It is
always attractive, tending to draw things together, and the attraction between two objects
increases faster than the distance between them
decreases: as the distance halves, the force of
gravity increases by a factor of four.1
Formation of the Sun
Throughout the universe, for more than 10
billion years, stars have been forming continuously. Galaxies—huge aggregates containing
stars, groups of stars, and interstellar (literally,
“between-star”) matter—may contain hundreds
of billions of stars, and there are billions of
galaxies.
Our Sun, a fairly ordinary star, was born
over 4.5 billion years ago in an outlying region
of the Milky Way galaxy. The Sun formed
where there was a higher than average concentration of hydrogen and helium, the two elements that have been present since early in the
evolution of the universe. The interstellar space
Kinetic Energy
Counteracting the tendency for particles to
be pulled together—in interstellar space or anywhere in the universe—is their random motion.
The energy associated with this motion is called
kinetic energy, and it depends on the temperature of the particles: the higher the temperature,
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Mathematically, the gravitational force between two particles is proportional to one over the square of the distance between
them. This is an instance of the “inverse-square law” (see p. 5).
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THE SUN-EARTH SYSTEM
particles of opposite charge attract. Two protons—subatomic particles with a positive
charge—repel each other with a greater and
greater force as they get closer together.
The electrical force is also much stronger
than the gravitational force—1038 times as great
for two protons a given distance apart. The
nuclear strong force is even stronger than the
electrical force (at close range, anyway), and it
is always attractive. The nuclear force does not
depend on charge, and although its exact relation to the distance between particles is not
known, it is known that the force only operates
within a distance of 3 x 10-15 meters (3 femtometers, or fm).
the greater the kinetic energy. If the particles
become close enough or their temperature low
enough, gravity can overcome the energy of
motion. When the number density of particles
in a particular region of space becomes great
enough, and when the gases in this region are
compressed even more, perhaps by the shock
wave from a supernova, the particles collapse
on themselves and are on their way to becoming a star.
If a forming star, or protostar, is to become
stable, however, something must happen to halt
this collapse. What happens is that the compression raises the temperature of the protostar
by the same physical process that heats the
gases in the cylinder during the compression
phase in a combustion engine. Eventually the
temperature in the central region, or core, of the
protostar becomes so high that nuclear fusion
begins.
The Proton-Proton Chain
Imagine two protons moving toward each
other. The closer they approach, the greater the
electrical force trying to push them apart. But if
they are able to move close enough, the nuclear
force takes hold and rapidly overwhelms the
electrical force. What determines whether the
protons can get close enough for the strong
force to predominate? Their speed. It’s as if you
were trying to kick a soccer ball into a hole at
the top of a steep hill. If you don’t kick the ball
hard enough it will go only part way up the hill
and then roll back down. The harder you kick,
the higher it goes, and if you kick it hard
enough, giving it enough initial speed (and if
your aim is good), you can sink it into the hole
at the top.
Protons, of course, aren’t being kicked. Temperature determines how fast they move. The
higher the temperature, the faster, on the average, they go. As the core of a star is compressed
by its collapse, its temperature rises. If it gets up
to about 10 million kelvins (kelvin, K, is a unit
of temperature equal to Celsius plus 273), the
particles are moving fast enough for protons to
collide and bond together to produce three
other subatomic particles, a deuteron, a
positron, and a neutrino. This is the first step of
the proton-proton chain, (see Table 1).
Fusion
The energy released by nuclear fusion in the
core of the protostar produces an outward pressure that eventually equals the inward pressure
from gravity. When a balance between outward
and inward pressure is reached, the protostar
becomes a star. This is how our Sun formed.
Nuclear fusion not only provided the energy to
halt its collapse, it also provides almost all the
energy the Earth receives.
Electrical and Nuclear Strong Forces
Two forces are involved in fusion: the electrical and nuclear strong forces. The electrical
force, like the gravitational force, increases as
the distance between two particles decreases.
But unlike gravity, it is not always attractive; it
may be repulsive, tending to separate the particles, depending on their charge. Charge is a
basic property of elementary particles of matter.
It may be positive, negative, or zero. Two particles with the same charge repel each other;
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THE SUN AND SOLAR ENERGY
Table 1
Particles Involved in the Proton-Proton Chain
Step 1 (The particles’ charges are noted
above their symbols.)
+ +
+ + 0
p + p ———> d + e+ + ν
Proton. Symbol: p; charge: +. Subatomic,
positively charged particle that is one of
the two principal particles comprising the
nucleus.
Step 2. The deuteron is bound to a proton to
produce helium 3 and a high-energy photon, g.
+ +
++
0
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d + p ———> He + γ
Neutron. Symbol: n; charge: 0. Subatomic,
uncharged particle found as the other
principal particle making up the nucleus.
Steps 1 and 2 occur again, so that there are
available two He3 nuclei. Then, in step 3, two
He3 nuclei collide to produce He4 and two protons.
Deuteron. Symbol: d; charge: +. One form
of “heavy hydrogen.” The nucleus of an
ordinary hydrogen atom consists of a
single proton. Deuteron contains a neutron in addition to the proton.
++ ++
++ ++
He3 + He3 ———> He4 + 2p
When the chain is complete, the two protons
are free to begin again. The complete chain,
steps 1 and 2 occurring twice and step 3 once,
converts a total of four protons (six protons are
used and two are returned) into one nucleus of
He4. Note that the charge is conserved at each
step; it is the same before the collision (left side
of the arrow) and after it (right side). Figure 1
illustrates the processes involved in the protonproton chain.
Electron. Symbol: e; charge: –. Subatomic
particle that orbits around the nucleus.
Positron. Symbol: e+; charge: +. An
“antielectron,” the same as an electron but
with a positive rather than negative
charge.
Helium 3 nucleus. Symbol: He3; charge
++. An isotope of ordinary helium containing two protons and only one neutron
instead of two.
Helium 4 nucleus. Symbol: He4; charge:
++. “Ordinary” helium nucleus containing
two protons and two neutrons.
Neutrino. Symbol: n; charge: 0. A
chargeless particle having little, if any,
mass. Important in many nuclear processes.
Photon (gamma ray). Symbol: g; charge: 0.
A chargeless “particle,” or packet, of
electromagnetic energy.
Figure 1. In the proton-proton chain, four protons combine
to form one helium nucleus and emit energy.
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THE SUN-EARTH SYSTEM
INVERSE-SQUARE LAW AND THE SOLAR CONSTANT
Because we know how much energy leaves
the Sun each second, we can calculate how
much energy the Earth receives. The
amount of radiative energy that reaches
the top of the Earth’s atmosphere when the
Earth is at its average distance from the Sun
is called the solar constant. It is also the
amount that would strike each square
meter of the surface if there were no
atmosphere.
The amount of radiative energy per unit
area arriving at a particular point each second from a source like a star decreases as
one over the square of the distance from the
source. This is an instance of the inversesquare law, and is illustrated in Figure 2.
Assume the energy leaving the star moves
out uniformly in all directions and the total
amount leaving per second is a quantity L.
Suppose we are at a distance R from the
star. The amount of energy reaching us
each second can be determined by considering a hollow sphere whose center is the
star’s center and whose radius—the distance from the center to the outer shell—is
R, our distance. The total amount of energy
passing through the shell each second has
to be the same amount that leaves the star
each second. To find out how much energy
falls on a square meter, calculate the surface
area of the imaginary spherical shell. The
formula for the surface area of a sphere is
When the source is the Sun and the distance is the distance from the Sun to the
Earth, E is called the solar constant.
Appendix IV describes a simple experiment you may do to measure the solar constant using water, black ink, a thermometer,
and a few other easily obtainable items.
We know that the amount of energy
leaving the Sun is 3.83 x 1026 joules per second, and the average distance between the
Earth and the Sun is about 1.496 x 1011
meters (this distance is defined as one astronomical unit, 1 AU), so we can calculate the
actual value of the solar constant to be 1.36
x 103 joules per second per square meter.
4πR2
where R is the radius and π is a constant.
The amount of energy per second falling on
a unit area of a surface is called the irradiance (E); we derive it by dividing the total
amount of energy leaving the Sun each second (L, the total amount passing through
the shell) by the surface area of the shell:
Figure 2. Illustration of the inverse-square law. L is
the total energy per second leaving the distant body
equally in all directions. R is the distance from the
body to the point of measurement, and E is the
amount of energy per second striking each unit area
at a distance R from the body. From the text, E = L/
4πR2.
E = L/4πR2
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THE SUN AND SOLAR ENERGY
Figure 3 is a cross section of the Sun. The
temperature of the Sun decreases drastically
and rapidly from the core outward. The surface
temperature, the temperature we measure from
Earth, is only about 5,800 K. About 70% of the
way from the center to the surface, the temperature becomes low enough for atoms to exist.
Atoms are very effective in absorbing radiation,
so they themselves take over the job of energy
transport. Heated by absorbing the radiation
from below, they begin to rise in the same way
that warm air in a room rises. When the atoms
reach the surface of the Sun, the photosphere,
their energy is radiated to space, they cool, and
begin to fall. This is energy transport by the
actual movement of matter, or convection.
Energy moves outward from the surface of
the Sun, once again in the form of electromagnetic radiation, travelling unimpeded and uniformly in all directions. Moving at the speed of
light, it strikes the Earth about eight minutes
later. It is this energy, coupled with the Earth’s
rotation, that drives our weather and establishes the Earth’s climate.
At each step a small amount of mass is converted into energy. Einstein’s law of mass-energy equivalence says that E = mc2. The m in
this case is the difference in mass before and
after the collision. E is the energy produced,
and c is the speed of light, which is a constant:
about 3 x 108 meters per second.
Each chain produces only a tiny amount of
energy, about 4.4 x 10-12 joules. (A joule is a unit
of energy.) But in the solar core, each second
there are enough chains to generate the enormous total of 3.9 x 1026 joules. About 0.7% of the
mass of the four protons is converted to energy.
This means that when 1,000 kilograms of hydrogen undergo fusion, 993 show up as helium
and 7 as energy.
It is obvious from all this that the number of
protons in the Sun’s core is steadily decreasing.
Each second about 600 billion (6 x 1011) kilograms of hydrogen are converted to helium.
When it’s all gone, in a mere 4 billion years, the
Sun will die.
Energy Transport
All this energy is produced in the Sun’s core.
Before it can be radiated to Earth, it has to get to
the surface. It makes the first part of the journey
from the core to the surface in the form of electromagnetic radiation, radiant energy that travels through space and matter.
The heat that we feel when when we hold a
hand over an electric light bulb or lie on a beach
on a hot, sunny day is produced by electromagnetic radiation. In the Sun’s core the temperature is around 15 million K. Atoms cannot exist
at the extremely high temperatures in the inner
regions of the Sun. They are moving so fast
that, if they form, collisions between them immediately break them apart again. Subatomic
particles such as protons and electrons deflect,
or scatter, electromagnetic radiation, but do not
remove much of its energy. So most of the energy created by fusion moves outward from the
core in this form.
Figure 3. Cross section of the sun’s interior, showing the
radiative and convective zones. Also shown are the sun’s
atmospheric regions, called the chromosphere and corona.
From Robert Jastrow, Astronomy: Fundamentals and
Frontiers. John Wiley & Sons. Reprinted by permission.
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THE SUN-EARTH SYSTEM
Problems
4. When Voyager II encountered Neptune on
August 24, 1989, what was the ratio of the
tug of the Sun’s gravity on it compared to
when it was launched? (Neptune is about 30
AU from the Sun.)
1. Calculate how long it takes light leaving the
surface of the sun to reach the Earth.
2. How much mass has the Sun lost, in terms of
equivalent Earth masses, in its 4.5-billionyear life?
5. We learned how much energy is produced
each second in the solar core and how much
energy each p–p chain produces. How many
p–p chains are occurring each second in the
Sun’s core?
3. What is the average mass density (mass per
unit volume) of the Sun?
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