EAS 105 – THE PLANETS
Prof. Robert L.
Nowack
Lecture 6
The Sun
We
live next to a star. The Sun is about
150 million kilometers away from the Earth or about 109 Sun diameters. The next closest star to the Earth, Proxima
Centauri, is 270,000 times farther away.
If the Sun and Earth are 1 foot apart, Proxima would be 50 miles
away. Earth’s close proximity to the Sun
is no accident. All life on Earth
depends on solar radiation for our very existence. In early cultures the Sun was a God bringing
warmth and life. In ancient
For the Greeks - The God Helios
For the Romans - Apollo
For the Persians - Mithras
The
Greek Philosopher, Anaxagoras, in 500 B. C. dared to claim that the Sun was no
God, but merely a ball of fire - for this he was exiled. Indeed, today we know that the Sun is a
sphere of incandescent gases.
Nevertheless
the Sun is an average star. Its mass,
chemical composition, size and energy output are quite
"standard". We are fortunate
that by studying the Sun, we can understand a lot about stars in general. There are "billions" of stars in
our galaxy and neighboring galaxies.
Sun's Vital Statistics:
Average Distance
from Earth 1.00 Au (1.495979 x 108
km)
Mass 1.989
x 1030 kg
Diameter 1.39 x 106
km (109 times Earth's diameter)
Average density 1409 kg/m3
Surface
temperature 5770 K
(Kelvin)
Luminosity 4.0 x 1026
watts (energy/sec)
Age Greater
than 4 ˝ billion years (Age of the Earth)
99.9% of the mass of the Solar
System is contained in the Sun. Yet, its
density of 1409 kg/m3 is much less than the Earth's at 5515 kg/m3
and is principally in a dense gaseous state.
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Aside: There are 3
common Temperature Scales:
1) Fahrenheit (F) -- Water
freezes at 32°F and boils at 212°F.
2) Celsius (or centigrade) (C) --
Water freezes at 0°C and boils at 100°C
3) Kelvin (or absolute) (K)
-- Water freezes at 273.15K and boils at
373.15K
All molecular motion stops at 0 K
(-273.15°C, - 459°F)
Conversions (rounding 273.15 to
273 K):
T° (C) = 5/9
(T° (F) - 32° )
T (K) = T° (C)
+ 273°
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(Ex.) 68°F ----- > 5/9 (68 - 32)
----- > 20°C, 293 K
37°C ----- > 9/5 (37) + 32
----- > 98.6°F, 310 K
5770 K ----- > 5497°C,
9927°F
Luminosity
of the Sun is the total outpouring of energy on its total surface every
second. This energy is the equivalent of
billions of hydrogen bombs exploding every second. But, before looking at the largest thing in
the solar system, we need to look at some of the smallest objects in the solar
system (i.e. the atoms that make up the elements and isotopes of matter).
An
atom consists of a nucleus where most of the mass is concentrated surrounded by
a cloud of electrons. The nucleus is
made up of neutrons and protons. Protons
have a positive electrical charge.
Electrons have a negative electrical charge, and neutrons are
neutral. Neutrons and protons have
roughly equal mass while electrons are 1/1800 times as massive. An atom is called neutral if the sum of the
negative charges of the electrons equals the sum of the positive charges in the
nucleus. Atoms are extremely small with
a diameter of about 10-10 meters.
Ex.) If 10 million atoms are aligned side by side,
it would measure ~ 1 millimeter.
Ex.) A human body weighting 80 kilograms contains
~ 3.4 x 1027 atoms.
The nucleus of an atom has a
diameter of about 10-15 meters (100,000 times smaller
than atom itself).
Ex.) If the nucleus were the size of a pinhead,
then the electron cloud would be 200 meters across. Yet, most of mass would be
in the nucleus.
The diameter of the atom is
determined by the electron cloud where the electrons spend most of their
time. The term “element” is used to describe any set of atoms that have the same
number of protons. The number of protons
is the “atomic number” of the
element. There are 92 naturally
occurring elements in nature (however, there are more that have been made in
the laboratory) where:
Hydrogen has 1 proton
Carbon has 6 protons
Uranium has 92 protons in the
nucleus
Nonetheless, atoms of a given
element can have a variable number of neutrons without significantly changing
the basic electrical and chemical properties.
Isotopes of a given element can have
different numbers of neutrons.
Ex.) Oxygen has 8 protons and has 3 commonly
occurring isotopes: 16O, 17O
and 18O. 16O is
the most common.
In the 16O atom, the
"16" is called the Mass Number
or the total number of nucleons in nucleus.
1 Atomic Mass unit (u) is
defined to be 1/12 the mass of 12C ("Carbon 12"). In these units:
the proton mass is 1.00728 u
the neutron mass is 1.00866 u
the electron mass is 0.00055 u
where
1 u = 1.660565 x 10-27
kilogram
Why are 12 u (1 u =
1/12 of the mass of the carbon atom ) less than the mass of 6 protons and 6
neutrons? In order to build the larger
nucleus, mass has been converted to energy and radiated away.
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Aside:
E = mc2 This is Einstein's famous relation between
energy and mass where, c = the speed of light
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Of course, to break apart a
nucleus, you would have to inject the same amount of energy in order to pry
loose the protons or neutrons (except for large unwieldy atoms like
uranium). Electrons can come and go much
more easily than nucleons. Ions are charged atoms with unequal
numbers of protons and surrounding electrons.
Two
or more atoms sharing electrons form molecules. These types of matter are called compounds.
Common Molecules
H2 Hydrogen
gas NH3 Ammonia
O2 Oxygen
gas CO Carbon Monoxide
O3 Ozone CO2 Carbon Dioxide
H2O Water SO2 Sulfur Dioxide
CH4 Methane
The H2 molecule
consists of two hydrogen atoms with the two orbitals overlapping to provide the
bond. Molecules can be disassociated by
inputing energy to break the electrical bonds.
In the Sun, temperatures are so high that we only need to deal with the
basic elements.
Nuclear Fusion
Nuclear
fusion is the basic energy source for all stars, where conditions are right for
the element Hydrogen to convert to Helium.
A helium nucleus (4He) stripped of its electrons, is called
an alpha particle and has 2 protons and 2 neutrons. The basic process in solar fusion is when 4
protons or hydrogen nuclei are successively fused into one "alpha" particle
or Helium nucleus. As this cycle continues,
energy is released. In fact, 1 alpha
particle is about 0.7% less massive than 4 protons. This mass has been converted to energy
according to Einstein's equation E = mc2.
A
hydrogen bomb uses the same thermonuclear physics as the Sun to produce energy. The former
E = mc2
2.4 x 1017 = m[3 x 108 m/s]2
or m = (2.4 x 1017)/(9 x 1016)
= 2.7 kg
Thus, this giant Soviet bomb used
up only 2.7 kilograms of matter.
The
Sun's nuclear furnace inside the core processes about 700 million tons per
second of hydrogen into helium "ashes". In the process, 0.7% of this matter, or about
5 million tons, is converted to energy.
Nuclear fusion occurs in the interior core of the Sun where temperatures
can exceed 15 million Kelvins. This is
the only region in the Sun where the temperatures and pressures are high enough
to sustain nuclear fusion. How does this
energy get to the surface? It is
theorized that the middle shell of the Sun is too cool to sustain fusion. But, the middle shell of the Sun should be
hot enough to have material be transparent enough for the principle form of
heat transfer to be high energy light radiation called Gamma Rays.
Finally,
in the outer third of the Sun, the temperature is low enough so that the
principle form of heat transfer is massive convection
as the hot material rises and cool material sinks. This is much like boiling water in a pot
heated from below. The glowing surface
of the Sun is called the photosphere.
Diagram of the Sun
Granulation is a specific hexagonal pattern
of outer convection visible at the surface.
These are the tops of individual convection cells where hot material
rises at the center. As it cools, it
gets darker and descends at the edges.
The
chromosphere is a tenuous layer of
gases extending above the photosphere to about 2000 km. Spicules
are jets of hot gases 1000 km across that surge up from the lower
chromosphere. They last 10-20
minutes before falling back and redeveloping.
The
Photograph of Solar Eclipse of
(original from http://laps.fsl.noaa.gov/cgi/albers.homepage.cgi)
One problem with internal models of the Sun based
on theoretical considerations is the number of detected subatomic particles
called neutrinos.
Neutrinos are
particles with no charge or mass. They
only rarely interact with matter, but they do.
They are predicted to be produced by nuclear fusion. Since the 1970's, a detector buried in a
One
recent theory is that neutrinos can oscillate between three different types or
"flavors" and one type was being recorded by this experiment. However, more data is needed to understand
how the Sun's nuclear furnace works. On
one front, this has led to more direct methods of mapping the interior of the
Sun.
The
use of sound waves transmitted in the Sun to infer the internal structure.
Helioseismology
Solar
prominences and convection cause the Sun to vibrate and ring like a bell. Large scale undulations on the photosphere
can be seen from the Earth. These can be
charted and used to study the extent of the convection zone, internal
composition, and the variable spin rate of the Sun. For example, helioseismology can be used to
study the variable rotation of the Sun.
The
Sun has a variable rotation rate ranging from about 25.4 days at equator to
about 36 days at the poles. This is
quite different from the Earth.
Differential rotation of the earth would cause colossal earthquakes.
Sound wave images of the interior of the SUN
Along
with granulation on the surface of the Sun, we can see large dark spots where
the temperature is cooler (~ 4500 K).
These sunspots often occur in
pairs forming about 40° in latitude above and below the
Sun's equator. Over several weeks, the
positions of the spots move, drifting toward the Sun's equator.
Individual
sunspots last a few weeks. However,
there appears to be an 11-year cycle in terms of sunspots
dating back to the 1700's. During the 17th
century, there was a definite minimum in sunspot activity - the
Maunder Minimum. These variations have
caused a great deal of interest by climatologists who have attempted to
correlate sunspot activity with variations in the Earth's climate.
(Ex) Earth had a time of cooler temperatures
during the 17th century. This
was called the Little Ice Age".
The
Sun may be slightly brighter during a sunspot maximum. It is speculated that sunspots are correlated
with the Sun's variable rotation and its magnetic field. Since the outer gases of the Sun are
electrically conducting, sunspots appear to correlate with strong fluctuations
in the magnetic fields. The gases follow
the magnetic field lines. The 11-year sunspot cycle is part of a
greater 22 year cycle in which the magnetic polarity reverses. However, further study is needed.
Magnetic
field variations can also cause solar flares and giant arching
prominences. These can create
"coronal holes" which jettison large quantities of electrified gases
out into space, forming the Solar Wind.
Photograph of the Sun
With the Sun's rotation at the
equator, it creates a spiral shape to the solar wind generated by more active
areas on the Sun. When the Sun is
active, the solar wind can become much stronger. This can cause bright
Aurora Borealis Over
Formation of the Solar System
The
planetary system and the Sun are thought to have formed from a primordial solar
nebula about 4˝ billion years ago. As
this solar nebula collapsed, the center of this gas cloud heated. The shrinking nebula began to spin faster and
the outer areas flattened into a disk.
The schematic diagram below represents the simplified idea.
The Sun accumulated most of the
mass at the center and the disk gave rise to the planets.
An Example of a Gas Forming Nebula in Orion
The disk will develop a temperature
difference with the outer parts cool and the inner parts heated by the
Proto-Sun.
Solid
grains will begin to condense from the nebula depending on temperature. At distances greater than about 5 Au from the
Proto-Sun, water ice can condense. At
about 1 Au, silicate rocks can condense.
Inside about 0.2 Au no solids formed and the material remained
gaseous. A distinct chemical sequence of
grains formed in this way at different distances from the center. This chemical condensation sequence related
to temperature provides an explanation of some of the chemical differences in
the solar system seen today.
The
next step in development of the planetary system required the grains to
coalesce creating larger aggregates by accretion. The first ones form in terms of planetesmals
and then in terms of protoplanets.
Two
of the larger planets became Jupiter and Saturn. Gas and dust were eliminated from the solar
nebula by planet formation, accretion, and later impacts, and also by an early
more active Proto-Sun which swept away much of the remaining nebula gas.
Theories
of the solar furnace suggest that about ˝ of the hydrogen in the core has been
converted to helium in 4˝ billion years.
Aside from sunspot variations, the Sun has stayed fairly constant with a
slight increase in luminosity as the Sun ages (300 K warmer on the surface in
4˝ billion years and a 6% increase in radius)
The trend is likely to continue for another 4˝ billion years until all
the hydrogen has been "burned" to helium. At this time the Sun will be about twice as
luminous than now and 40% larger.
Over the next 1˝ billion years,
the core will contract on itself and the outer surface will expand by a factor
of about 3.3. The Sun will then look
like a bloated orange-red disk from on Earth.
The surface of the Earth would be 100 K warmer than present with all
water boiled away. (We probably wouldn't
be here at this point!). Sun would
become "red giant" 100 times its present size. Helium would start to "burn"
creating carbon and oxygen. The Sun's
outer surface would blow off to expose a core no bigger than Earth, but with ˝
the Sun's mass - White Dwarf. Sun dies
as a "Black Dwarf" (at least in theory!)