Download Dr Conor Nixon Fall 2006

ASTR 330: The Solar System
Announcements 9/7/06
• Yellow forms - any more?
• Wait list.
• New materials on website: syllabus, Lecture 2, HW #1.
• Homework #1 due by Tuesday, September 12.
• Ignore the last part of Q4! “Which of these mechanisms…”
But instead you may want to think about: “What heat transport
processes occur in the Sun?”
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Lecture 3:
The Sun
Image: SOHO EIT
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Discussion
• Which form of life on Earth rely on the Sun for food?
• Green plants
• Other plants, fungii.
• Herbivores
• Carnivores
• Humans
• Which forms or energy come from the Sun?
• Solar power
• Fossil fuels
• Wind power
• Wave power
• Nuclear power
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Are all the stars suns?
• To begin to answer this question, we should be able to say
how luminous the star really is.
• The apparent luminosity or brightness of the body is a
reflection both of its actual or absolute brightness, and also
its distance.
• If we can only find the distance to the stars, then we know
the absolute brightness, and whether they are similar to the
Sun or not!
• But how to find the distance?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Stellar Parallax
• The notion of parallax was used to
measure stellar distances.
• Parallax measures the change in
position of a ‘nearby’ object against
the more distant background objects,
when viewed from two different
positions.
• This is the same principle as
binocular vision! Try it!
• Astronomers used the Earth’s
position on either side of the Sun, six
months apart as the two viewpoints.
Figure credit: James Schombert, Univ. Oregon
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Distances and masses
• Bessel in 1838 made the first successful measurement of stellar
parallax, for the star 61 Cygni. He determined its parallax as around
1/12000 of a degree giving a distance of over 600,000 AU.
• The parallax of other stars was
soon determined and all were found
to be over 250,000 AU distant,
implying luminosities similar to the
Sun.
• Stellar masses were also first
measured in the 19th century, by
applying Newton’s laws to binary
stars, once the period and
separation was measured.
Picture: St. Andrews University
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
So, stars are like the Sun..
… a huge ball of
hot, incandescent
gas.
Image: SOHO EIT
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Sun By The Numbers:
MASS:
2.0 x 1030 kg = 333,000 Earth masses
more than 100x rest of solar system!
DIAMETER:
1.4 x 109 m = 109 Earth diameters
= 10 Jupiter diameters
LUMINOSITY:
4 x 1026 watts
= 4 million million million million, 100-watt light bulbs!
TEMPERATURE:
DISTANCE:
15 million Kelvin (core)
5800 K (surface)
1.5 x 1011 m = 1 AU
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Kelvin Temperature Scale
• Throughout this course we shall refer to
temperatures in degrees Kelvin, named after Lord
Kelvin, its originator (a Belfast-man like myself!)
•The Kelvin scale has the same size of degrees as
the Celsius scale.
• BUT, whereas the zero of the Celsius scale is the freezing point of
water, the zero point of the Kelvin scale is absolute zero, the point
where atoms have no motion at all.
• Absolute zero is -273° C = 0 K (Kelvin), therefore 0° C = 273 K.
There are no negative temperatures in the Kelvin scale!
• What is the boiling temperature of water in the Kelvin scale?
Picture: St. Andrews University
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
What is the Sun?
•
OK, so the Sun is a star, and the stars are suns. But what
is the Sun? We want to know:
• What is the Sun made of?
• How does the Sun shine?
• How old is it, and how did it form?
• How long will its energy last?
• But first, we need to review our knowledge of matter…
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Atomic Ideas
• Democritus of Abdera (460-370 BC)
was an early proponent of the atomic
theory of matter.
• This theory held that matter was not
infinitely divisible, but was ultimately
composed of basic, granular,
indivisible units called atoms.
• The theory was confirmed in the 19th century, when
John Dalton, Dmitri Mendeleev and others clarified the
nature of the different chemical elements.
Picture: St. Andrews University
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Atoms
• An atom is composed of a positively charged nucleus, surrounded by a
‘cloud’ of one or more negatively charged electrons. The overall atom
has a zero net charge.
• The nucleus contains almost all the mass of the atom, but is very small
compared to the size of the electron ‘cloud’ (think of a pea in a football
field). Hence, most of the atom is empty space!
Figure credit: Philip Grandinetti, Ohio State
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Dr Conor Nixon Fall 2006
The Atomic Nucleus
• The nucleus of the atom is composed of very small but ‘heavy’
particles:
• protons, which are positively charged
• neutrons, which have no charge.
• The simplest stable atom has one proton and zero neutrons in the
nucleus (and one orbiting electron). This atom is hydrogen.
• Isotopes of hydrogen have the same number of protons, but varying
numbers of neutrons:
Figure credit: Philip Grandinetti, Ohio State
ASTR 330: The Solar System
Elements
• Adding further protons and neutrons builds up different
atoms.
• Atoms which have different numbers of protons are
chemically distinct, and known as elements.
• For example, carbon-12 has 6 protons and 6 neutrons.
Figure credit: Philip Grandinetti, Ohio State
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Quick quiz
1. Are there likely to be more:
(a) elements, or
(b) isotopes in nature?
2. How many neutrons are in:
(a)16O
(b) 18O
(c) 13CO2
(d) D2O?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Periodic Table
• There are 92 naturally occurring elements in nature:
•The heaviest is
Uranium, with 92
protons and typically
143 or 146 neutrons.
• Heavier elements
have been created
artificially and are
unstable.
• Unstable heavy
atoms undergo
‘fission’ (splitting) to
become smaller and
hence stable.
Figure credit: L. Gardiner, UCAR
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Molecules and Compounds
• Atoms may join together to form molecules, such as water.
• Water forms when two hydrogen atoms bond with one oxygen atom,
hence the symbol H2O (below, left).
• In turn, water molecules
may also join together by a
weaker bond to form solid
water ice (right).
• These inter-molecular
bonds are easily broken
when the ice warms to 273
Kelvin (0° C) and melts.
Figure credit: M. Pidwirny, Okanagan U Coll
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Light, photons and radiation
•
The colors of the rainbow are the visible types of electromagnetic
(EM) radiation.
•
EM radiation can be imagined in two ways, which are both valid:
•
•
•
as a wave of electric and magnetic fields
as a stream of particles, called photons.
Photons have:
1. No mass
2. Travel at the speed of light
3. Have a corresponding wavelength: the shorter the wavelength the
more energetic the photon.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Electromagnetic Spectrum
• Visible light is just one type of EM radiation: there are also radio waves,
microwaves, infrared, ultraviolet, X-rays and gamma rays.
Figure credit: GSU
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
EM Spectrum Continued
• The wavelength and frequency of the radiation are inversely
proportional to one another; the frequency and energy are directly
proportional.
Figure credit: LBL Laurence Berkeley
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Spectroscopy
• When light is passed through a
glass prism it becomes dispersed
into the separate component
colors (wavelengths).
• This is the same process as in
a raindrop, forming a rainbow.
• Scientists use a prism, or a
diffraction grating, to disperse the
light from stars and planets, a
technique called spectroscopy.
• This analysis provides
information on the composition
and physical state of the object.
Picture: Andrew Davidhazy, RIT
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Solar Spectrum
• When light from the sun was passed through a prism, as well as the
different colors, a pattern of dark, sharp line features was seen:
• Top left is an early
sketch drawing (1817) of
the solar spectral lines
and intensity.
• Bottom left is a modern
photograph of the same
spectrum.
Figure credit: Jose Wudka, UC Riverside
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Emission and Absorption Lines
• Both emission (bright) and absorption
(dark) lines are seen in astronomy, and
were explained in the 20th century by
quantum theory.
• Lines form when an atom or molecule
emits or absorbs a photon of a
particular wavelength, corresponding to
the difference between two energy
levels.
• Emission lines form when a bright
(hot) object is seen directly: absorption
lines occur when a dark (cold) object
comes between the bright object and
the viewer, ‘subtracting’ certain
wavelengths.
Figure credit: Jose Wudka, UC Riverside
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Composition of the Sun
• Many of the dark lines on the solar spectrum were identified with spectrum of
atoms seen in the laboratory, e.g. the bright ‘D’ lines at 589 and 590 nm due to
atomic sodium.
• In 1868, Norman Lockyer observed a bright yellow line in the spectrum of solar
prominences, and proposed that it was due to a new element, unseen on Earth.
He named it helium, after the Greek word for Sun.
• In 1895 the gas was separated from minerals on the Earth and the existence of
helium, the second lightest element, and second most abundant in the universe,
was confirmed.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Cosmic Abundances of the Major Elements
Element
Symbol
Hydrogen
Helium
Carbon
Nitrogen
Oxygen
Neon
Sodium
Magnesium
Aluminum
Silicon
Sulfur
Argon
Calcium
Iron
Nickel
H
He
C
N
O
Ne
Na
Mg
Al
Si
S
Ar
Ca
Fe
Ni
Atomic
No. of atoms
Number per million H atoms
1
1,000,000
2
97,000
6
360
7
110
8
850
10
120
11
2
12
40
13
3
14
40
16
20
18
4
20
2
26
32
28
2
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
How does the Sun shine?
• The Sun currently radiates 4x1026 joules of energy per second (or
watts) to space: it must generate the same amount of energy internally.
• What about chemical reactions, i.e. oxidation (burning)?
No: the energy released from a material such as coal is far too small
per unit mass: the entire Sun would be ‘burned up’ in just a few
thousand years.
• A likely explanation was gravitational contraction, proposed by Kelvin
and Helmholtz. This mechanism proposed that energy due to gravity
(potential energy) is converted to energy of motion (kinetic energy) and
finally to heat (thermal energy) – imagine a meteor falling to the Earth
and producing a huge fireball.
 A small contraction of only 40 m per year would be enough to
power the Sun, or 400 km over human history. The entire Sun could
shine by this mechanism for a predicted 100 million years.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
But …
• By the beginning of the 20th century, evidence was
mounting that the Earth was 100s of millions of
years, perhaps a billion years old.
• But, all theories of Solar System formation agreed
that the Earth formed at the same time or later than
the Sun.
 How could the Earth then be older than the
Sun?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
A New Source of Energy
• The answer came from an completely new concept, mass-energy
equivalence, from a completely unknown (in 1905) scientist…
… Albert Einstein.
• Einstein’s Theory of Special Relativity
has a number of consequences, including
the constancy of the speed of light in a
vacuum, and the famous formula:
E = mc2
When converting mass to energy, we
multiply by a very large number, the speed
of light squared, so a small mass becomes
a huge amount of energy.
Picture: St. Andrews Univ.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Energy from mass
• A simple calculation shows that by converting 4 million tons of matter
per second to energy, the 4x1026 watts needed to power the Sun is
released. This is miniscule compared to the mass of the Sun!
• Working out the details took several more decades of work…
• The Sun is 99% composed of hydrogen and helium, so the source was
probably in those materials.
• The crucial observation was that a helium atom has a mass just a bit
less than four hydrogen atoms combined – if four hydrogen atoms were
fused together, they would release a tiny bit of mass, converted into
energy, every time!
• It takes enormous temperatures and pressures to overcome the mutual
repulsion of the positive nucleii, but those conditions do occur in the
interior of the Sun.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Proton-proton chain
This figure shows how the Sun shines!
Graphic: Univ Tenn. Knoxville
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Energy from Thermonuclear Fusion
• The
net effect of this chain is take 4 hydrogen nucleii
(protons) and convert to:
• 1 helium nucleus (most of the original mass-energy)
• gamma rays – energy!
• 2 anti-electrons, or positrons (anti-matter), which
annihilate with 2 electrons to make more gamma rays.
•2 neutrinos, neutral, nearly mass-less subatomic
particles.
• Neutrinos travel close to the speed of light and hardly
interact at all with normal matter, the Earth and Sun are
almost transparent to them!
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Announcements 9/12/06
• Homework #1 due TODAY, September 12.
• Yellow forms - any more?
(Missing from students: Gilkey, Kim, Kneib, Moffitt, Snyder, Wallick, Wrieden).
• Test e-mail(s). Who didn’t get one?
• New materials on website: Lectures 3 (Sun) & 4 (Planets)
• Course evaluation.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Questions from last time
• Elements not found naturally on Earth (Technetium?)
• Technetium was the first element to be artificially produced, in
1937.
• All isotopes are radioactive, and have t1/2< 4.2 Myr.
• However, Tc was later discovered to occur naturally in miniscule
quantities, as a by-product of natural Uranium fission.
• Atomic mass and relative atomic mass?
• The atomic mass is the mass of the atom relative to carbon-12.
• On your periodic tables, the number in the top right is the relative
atomic mass, or the abundance-weighted average of all the
common isotopes on Earth.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Revision Quiz
1. What is meant by parallax, and why is it useful to
astronomers?
2. What is the diameter of the Sun, in terms of Earth
diameters, closer to: (a) 10x, (b) 100x, (c) 1000x ?
3. What is the temperature of solar photosphere closer to:
(a) 6000 K, (b) 8000 K, (c) 10000 K?
4. Describe the main properties of an atom. Of what three
types of sub-atomic particle is an atom composed?
5. Name 3 types of electromagnetic radiation.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Energy Transport Mechanisms
•
OK, so we know how the energy is made deep in the core of the Sun,
but somehow the energy has to escape to the surface.
•
There are three mechanisms to transport heat:
1. CONDUCTION: a microscopic process which conveys heat in
solids. Molecules vibrate and bang into one another, causing the
next one to vibrate and so on.
2. CONVECTION: a macroscopic process, when whole parts of a
liquid or gas heat up, expand and move under gravity. Hot, less
dense parts move upwards, conveying heat to cooler regions.
3. RADIATION: is the primary mechanism for heat transport in a
vacuum, and occurs when matter releases some heat energy as
a photon (EM wave) which travels at the speed of light.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Examples
• Examples of these three mechanisms in action can be found in an
everyday setting - boiling water on the kitchen stove:
CONDUCTION occurs when the bottom of the saucepan heats up
and warms the water in contact with it.
CONVECTION occurs in the water when hot ‘blobs’ of water rise and
cooler ones sink.
RADIATION occurs in the glowing hot metal element of an electric
stove, or the incandescent gas of a gas range.
• Can you think of other examples?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Heat Transport in the Sun
• Different energy transport processes dominate at different distances
from the center:
• A core where the
thermonuclear reactions
take place.
• A radiative zone where
photons carry energy
upwards.
• A convective zone in
the outer third of the Sun,
where columns of warm
gas rise and hot gas
sinks.
Graphic: Derek Homeier, Univ. Georgia
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Solar Evolution
• One
of the questions we set for ourselves was:
how long will the Sun last?
• If the Sun was able to convert all its hydrogen completely to helium,
it would take about 100 billion years to burn out.
• The Sun is about 5 billion years old, so it has 95 billion years left…
right?
• Wrong! As the Sun fuses more and more hydrogen, its internal
structure changes; it becomes hotter and hotter, eventually swelling
up into a red giant star which will envelop the inner solar system.
This is predicted to happen in about 5 billion years from now.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Helium burning in the Sun?
• After a long period of stable hydrogen burning (1010)
temperatures in the center of the Sun (and similar stars M>0.8
MS) reach ~108 K - sufficient to begin helium burning in the core.
• At these temperatures, three helium nuclei can participate in a
three-way collision, to form a 12C nucleus.
• The onset of helium burning results in a ‘helium flash’ - the star
expands rapidly and becomes a cooler red giant.
• The star then enters a stable helium burning phase for about 108
years, before exhausting fuel and shrinking to Wolf-Rayet stars
(small but very hot), and then into long-lived white dwarves which
cool slowly over 1010 years.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Appearance of the Sun: The Photosphere
• The photosphere is the visible ‘surface’ of the Sun, about 5800 Kelvin.
•
The solar photosphere shows
several interesting features:
1. Sunspots – the irregular dark
patches which come and go.
2. Granulation – a speckled
appearance which always
covers the whole surface.
3. Limb darkening – the
darkening seen towards the
edges.
Picture: Derek Homeier, Univ. Georgia
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Granulation:
Close-Up!
Image from the Swedish Solar Telescope (SST),
24 July 2002. Large ticks are 1000 km apart.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Explanation of photosphere
• Limb darkening is explained as follows. As we look towards the edges of
the Sun we are looking higher up in the photosphere. This shows us that
the higher photosphere is cooler (4400 K), and hence darker.
• Granulation (below left) is simply the visible appearance of the convection
cells in the atmosphere.
• Below right is schematic cross-section through
the top of the photosphere. At the top of an
ascending convection cell, hotter gas is brighter.
• At the edges of a
cell, cooler,
descending gas is
relatively darker.
Graphics: Derek Homeier, Univ. Georgia
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Sunspots
• Sunspots have been observed since ancient times. The amount of
sunspots is quite variable, but follows an 11-year cycle of minimum and
maximum activity, first noted by Heinrich Schwabe (1843).
Solar maximum
Images: Derek Homeier, Univ. Georgia
Solar Minimum
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
What is a sunspot?
• The sunspot mechanism is complex and still debated, but basically
sunspots are caused by loops in the Sun’s internal magnetic field, which
push hot, electrically charged gas (plasma) upwards.
• The plasma cools to around 4300
Kelvin in the center (umbra) of the
spot, hence the dark appearance.
• This cooler material is still
electrically charged and hence
trapped in the magnetic field, which
leads to the persistence of individual
spots, up to 2 months or 2 solar
rotations.
Image: T. Rimmele, M. Hanna/NOAO/AURA/NSF
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Sunspot Cycle: ‘Butterfly’ Diagram
• At the start of the 11-year activity cycle, spots appear around 35° north
and south latitude. As the number of spots increase, they gradually
‘migrate’ towards the equator, eventually disappearing as new spots
arrive at the mid-latitudes.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Solar Flares
• Flares are massive eruptions from the Sun, when magnetic energy
that has built up is suddenly released.
Image: Yohkoh Soft X-Ray Satellite
• Energy is released right across
the EM spectrum: from radio waves
through to X-rays, as in the image
(right).
• Charged particles: protons,
electrons and heavy nucleii are
accelerated outwards at great
speeds.
• Temperatures can rise within
minutes to 5 million K, releasing a
total 1030 J of energy...
= equivalent to 100 million million
1-megaton H-bombs!
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Chromosphere
• Above the photosphere lies the chromosphere (‘sphere of color’).
• The chromosphere is normally visible only during an eclipse, as a
pinkish fringe around the moon, due to hydrogen emission of red light.
• Temperatures rise through the
chromosphere, which is only a
few thousand km thick, reaching
25,000 K at the top.
• The chromosphere has an
irregular appearance, with many
small gas jets called spicules,
and larger features called
prominences and filaments.
Image: Derek Homeier, Univ. Georgia
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Chromosphere: prominences
• Solar prominences can get very large…
… such as this “Grand Daddy of June 4th, 1946”!
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Corona
• The corona (‘crown’) is the outermost part of the Sun, reaching out
several million km to the start of the solar wind. It is composed of very thin
but hot gas: up to 4 million K! The gas is ionized (positively charged).
• Due to its thinness, the
corona is several million
times fainter than the
photosphere, and usually
visible only during a solar
eclipse.
• The corona has a very
irregular appearance.
• Much of the energy is
emitted as X-rays.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Solar
Cycle
• 12 X-ray images of the Sun from
the Yohkoh spacecraft SXT
instrument.
• The images, 120 days apart from
1991 to 1995, show the change in
the corona during the waning part
of the solar activity cycle.
Images: Derek Homeier, Univ. Georgia
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Solar Wind
• The solar corona does not have a sharp boundary: the hot gases in the
corona are barely affected by the Sun’s gravitational pull, and flow
outwards in a stream known as the solar wind.
• Although the solar wind is always present, it varies greatly in strength,
as massive CME events periodically erupt.
• The solar wind is responsible
for the glorious aurora borealis
(northern) and aurora australis
(southern), as charged particles
from the solar wind follow the
Earth’s magnetic field lines
around to the poles, where they
crash into the upper atmosphere
(more in a later lecture).
Image: NASA GSFC “Living With A Star”
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Coronal Mass Ejections (CMEs)
• CMEs are sudden violent events when 1012 kg of matter is thrown into
space at speeds of 200-2000 kilometers per second (km/s).
• This movie clip from the LASCO
instrument onboard the SOHO
spacecraft shows a CME event.
• CMEs are related to solar flares,
which occur later. The mechanism
seems to involve the breaking of
initially closed magnetic field lines.
• These particles can cause havoc
when they reach the Earth, disrupting
communications, and crippling
satellites!
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Numerical Examples
• Given that the solar luminosity is 4x1026 watts, 1 AU = 1.5x1011 meters,
and the area of a sphere is 4πr2 (r=radius), calculate the amount of solar
luminosity reaching a solar panel on the Earth which is 1 m2 in area,
when the Sun is directly overhead (assume no clouds).
The solar luminosity Lsun spreads out into a spherical area around the Sun. The
area of a sphere is 4πr2, and so, the amount of sunlight per square meter is
Lsun/4πr2.
At the distance of the Earth, r=1 AU. So, the amount of solar luminosity per
square meter = 4x1026/(4π x (1.5 x 1011)2) = 1415 watts.
• What is the corresponding value for a solar panel carried by a
spacecraft at the orbit of (i) Mars (1.5 AU), (ii) Saturn (9.5 AU), (iii) Pluto
(39.5 AU)?
• Answers: (i) 629 W (ii) 16 W (iii) 0.9 W.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Numerical Examples (continued)
• If a spacecraft requires 500 watts of power and uses solar panels with
10% efficiency of converting sunlight into electrical power, what size of
solar array is needed (i) in Earth orbit, (ii) at Mars, (iii) Saturn, (iv) Pluto.
The solar intensity at the Earth is 1415 watts per m2. Therefore 500/1415 = 0.35
m2 would be needed if all the solar energy could be converted to electrical
power.
BUT, the solar array is only 10% efficient, so we need 10x as much area, or
3.5 m2.
Mars: (500/629) x10 = 7.9 m2
Saturn: (500/16) x10 = 313 m2
Pluto: (500/0.9) x10 = 5555 m2
• Comment on the practicality of such arrays. What other sources of
power might be used?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Final Quiz
1. What is the name given to the study of the composition of EM
radiation, in terms of its different constituent colors or wavelengths?
2. Name one astronomical use for the technique in Q1.
3. How old is the Sun, and what is the name of the mechanism which
powers it?
4. What is the fuel for the Sun?
5. Name the three visible layers of the Sun’s atmosphere, and give an
approximate temperature for each.
6. Name three transient features of the Sun, with a brief explanation of
each.
Dr Conor Nixon Fall 2006