OVERVIEW OF THE SOLAR SYSTEM - Department of Physics and Astronomy
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9/3/18
WELCOME TO AST 111! The Solar System and its Origins
4 September 2018 ASTRONOMY 111, FALL 2018 1
OVERVIEW OF THE SOLAR
SYSTEM
Contents of the Solar System
What can we measure and what can we
infer about the contents?
How do we know? Initial explanations of
four of the most important facts about
the solar system
The basic collection of solar system facts
The eight planets and a moon (NASA, Palomar Observatory, Lowell Observatory)
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INVENTORY OF THE SOLAR SYSTEM
Q: What would an outside observer see if they
were looking at our Solar System?
A: The Sun. And that’s pretty much it.
The luminosity (total power output in the form of light)
of the Sun is 3.8x1026 watts – 4x108 times as luminous
as the second brightest object, Jupiter.
The mass of the Sun is about 1027 metric tons – about
500 times the total mass of everything else in the Solar
System.
The Solar System is the Sun, plus a little debris.
Image by Robert Gendler
4 September 2018 ASTRONOMY 111, FALL 2018 3
ASIDE –
OBSERVATIONS OF OTHER PLANETARY SYSTEMS
In most other stellar (extrasolar) systems, all we know about are
the stars, because they are overwhelmingly bright.
But planets have been detected around other stars recently, with surprising
properties (high eccentricity, small radii from star). This is mostly done by
observing the motion of the central star, as we will learn this semester.
Our understanding of the Solar System has helped us understand the formation
and evolution of planetary and stellar systems.
However, what we are finding about extrasolar systems is challenging previous
views of solar system formation and evolution.
4 September 2018 ASTRONOMY 111, FALL 2018 4
Artist’s conception of AEgir around its star Ran
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COMPONENTS OF THE
“DEBRIS”
The Giant planets: mostly gas and liquid
The Terrestrial (Earthlike) planets and
other planetesimals, some quite small:
mostly rock and ice
The Heliosphere: widespread, very
diffuse plasma
Io and Jupiter, seen from Cassini (NASA-JPL)
4 September 2018 ASTRONOMY 111, FALL 2018 5
GIANT PLANETS
Jupiter dominates with a mass of 10-3 times that of the Sun (10-3 M⊙ ), or 318 times that of the
Earth (318 M⊕ )
Saturn’s mass is 3x10-4 M⊙ , or 100 M⊕
Neptune and Uranus are about 1/6 the mass of Saturn
Giant planets are 5, 10, 20, and 30 times further from the Sun than Earth (a = 5, 10, 20, 30 AU; a
is commonly used to denote semi-major axis, covering the possibility of an elliptical orbit)
Saturn and Jupiter have roughly Solar type abundances (composition), which means mostly
hydrogen and helium. Saturn probably has a rocky core; Jupiter might not.
Neptune and Uranus are dominated by water (H2O), ammonia (NH3), and methane (CH4) and have
a larger percentage of their mass in rocky/icy cores.
Jupiter and Saturn are called gas giants
Neptune and Uranus are called ice giants
Jupiter, seen from Cassini (NASA-JPL)
4 September 2018 ASTRONOMY 111, FALL 2018 6
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TERRESTRIAL PLANETS AND OTHER ROCKY
DEBRIS
Mercury: R ∼ 2500 km, a = 0.4 AU
Venus and Earth: radius R ∼ 6000 km, a = 0.7, 1.0
AU, respectively
Mars: R ∼ 3500 km, a = 1.5 AU
Asteroid belt: a ∼ 2-5 AU
Kuiper Belt, including Pluto, at a > 30 AU
Oort Cloud, including Sedna, at a ∼ 104 AU
Interplanetary dust
Moons and satellites
Planetary rings Images from Galileo (NASA-JPL)
4 September 2018 ASTRONOMY 111, FALL 2018 7
THE HELIOSPHERE
All planets orbit within the heliosphere, which
contains magnetic fields and plasma primarily of
solar origin. (Plasma: an ionized gas with
electrical conductivity and magnetization much
larger than an ideal gas.)
The solar wind is a plasma traveling at supersonic
speeds.
Where the solar wind interacts or merges with the
interstellar medium is called the heliopause.
Cosmic rays (high energy particles) are affected
by the magnetic fields in the heliosphere.
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PLANETARY PROPERTIES THAT CAN BE
DETERMINED DIRECTLY FROM OBSERVATIONS
Orbit Magnetic field
Age Surface composition
Mass, mass Surface structure
distribution
Atmospheric
Size structure and
composition
Rotation rate and
spin axis
Shape
Temperature Saturn, Venus, and Mercury, with the European Southern Observatory in the
foreground (Stephane Guisard)
4 September 2018 ASTRONOMY 111, FALL 2018 9
OTHER PLANETARY PROPERTIES THAT CAN BE
INFERRED OR MODELED FROM OBSERVATIONS
Density and temperature of the atmosphere and
interior as functions of position
Formation
Geological history
Dynamical history
These will be discussed in context with the
observations and astrophysical processes as part
of this course.
Cut-away view of the Sun’s convective zone
(Elmo Schreder, Aarhus University, Denmark)
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HOW DO WE KNOW…
Note that most of what we will say about the planets this semester is founded upon a lot of
very direct evidence, rather than theory or reason-aided handwaving. For example:
…that the Earth is approximately spherical?
Direct observation, of course, and known since
about 500 BC.
Lunar phases indicate that it shines by reflected sunlight.
Therefore, the full moon is nearly on the opposite side of
the sky from the Sun.
Therefore, lunar eclipses are the Earth’s shadow cast on
the Moon.
The edge of this shadow is always circular; thus, the Earth
must be a sphere. Lunar eclipse (16 Aug 2008) sequence
photographed by Anthony Ayiomamitis
4 September 2018 ASTRONOMY 111, FALL 2018 11
HOW DO WE KNOW…
…that the planets orbit the Sun, nearly all in the same plane?
Also direct observation.
The planets and the Sun always lie in a narrow band across the sky: the zodiac. This is a
plane, seen edge-on.
Distant stars that lie in the direction of the zodiac exhibit narrow features in their spectrum
that shift back and forth in wavelength by ±0.01% with periods of one year. No such shift is
seen in the stars toward the perpendicular direction, or in the Sun. The shift is a Doppler
effect, from which one can infer a periodic velocity change of Earth with respect to the stars
in the zodiac by ±30 km/s. Thus, the Earth travels in an approximately circular path at 30
km/s, centered on the Sun.
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THE DOPPLER EFFECT
Suppose two observers had light emitters and detectors that can measure wavelength
very accurately, and move with respect to each other at speed v along the direction
between them. If one emits light with a pre-arranged wavelength λ0, the other one
will detect the light at wavelength
&
! = !# 1 +
'
That is,
! − !#
&='
!#
where c = 2.99792458x1010 cm/s is the speed of light. You will learn why this is in
your E&M classes.
4 September 2018 ASTRONOMY 111, FALL 2018 13
HOW DO WE KNOW…
…that the Sun lies precisely 1.5x1013 cm (1 AU) from Earth?
Direct observation: It follows from the previous example, but we can measure
the same thing more precisely these days by reflecting radar pulses off the
Sun or the inner planets, measuring the time between sending the pulse and
receiving the reflection, and multiplying by the speed of light.
Note that knowing the AU enables one to measure the sizes of everything else one can see in
the Solar System.
Using Venus or Mercury gives the most accurate results, as the Sun itself does not have a very
sharp edge at which the radar pulse is reflected. It works with Venus or Mercury as follows:
4 September 2018 ASTRONOMY 111, FALL 2018 14
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MEASURING THE ASTRONOMICAL UNIT (AU)
Sun
Suppose you were to send a radar pulse at Venus
when it appeared to have a first- or third-quarter
phase, so that the line-of-sight is perpendicular to
the Venus-Sun line. Then
#$%
!= 1 AU
&
! Venus
1 AU =
cos +
= 1.4959787069 3 ×1067 cm
d
(corrected for planet size and averaged over the θ
orbit)
Earth
4 September 2018 ASTRONOMY 111, FALL 2018 15
HOW DO WE KNOW…
…that the Solar System is precisely 4.6 billion years old?
Direct observation, again, on terrestrial rocks, lunar rocks, and meteorites, nearly all
of which originate in the asteroid belt. We will study this in great detail:
When rocks melt, the contents homogenize pretty thoroughly.
When they cool off, they usually recrystallize into a mixture of several minerals. Each different mineral
will incorporate a certain fraction of trace impurities.
Those trace impurities that are radioactive will vanish in times that are accurately measured in the lab.
Thus, the ratio of the amounts of radioactive trace impurities tell how much of that tracer the rock had
when it cooled off, and how long ago that was.
The oldest rocks in the Solar System are all 4.567 billion years old, independent of where they came
from, so that’s how long ago the Solar System solidified.
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THE BASIC FACTS
Gravitational constant G = 6.674x10-8 dyn cm2 g-2 Astronomical unit AU = 1.496x1013 cm
= 6.674x10-11 m3 kg-1 s-2
Solar mass M⊙ = 1.989x1033 g
Boltzmann’s constant k = 1.380650x10-16 erg K-1
= 1.380650x10-23 J K-1 Solar radius R⊙ = 6.96x1010 cm
Stefan-Boltzmann constant σ= 5.6704x10-5erg s-1 cm-2 K-4 Solar temperature T⊙ = 5800 K
= 5.6704x10-8 J s-1 m-2 K-4
Planck’s constant h= 6.626069x10-27 erg s Solar luminosity L⊙ = 3.827x1033 erg s-1
= 6.626069x10-34 J s
Solar apparent magnitude m⊙ = -26.72
Speed of light c = 2.997925x1010 cm s-1
= 2.997925x108 m s-1 Light year ly = 9.4605x1017 cm
Earth mass M⊕ = 5.976x1027 g Parsec pc = 3.086x1018 cm = 3.2616 ly
Earth radius R⊕ = 6.378x108 cm Densities (in g cm-3) Water ice: 0.94
Water: 1.0000000
Solar day Day = 86400 s Carbonaceous minerals: ∼2.5
Silicate minerals: ∼3.5
Sidereal year P⊕ = yr = 3.155815x107 s
Iron sulfide: 4.8
Iron: 7.9
4 September 2018 ASTRONOMY 111, FALL 2018 17
THE SUN AND OTHER
BLACKBODIES
A few salient facts about the Sun
Nucleosynthesis
Blackbody radiation and temperatures of
stars
The spectrum of blackbodies, and solid angle
Wien’s Law
Three-color X-ray mosaic image of the Sun, made by the NASA TRACE satellite (J. Covington, LMMS)
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THE SUN: BASIC FACTS
Mass 1.98892x1033 grams
Luminosity 3.826x1033 erg sec-1
Radius 6.96x1010 cm
Surface rotation period, sidereal, at 2.193x106 sec (25.38 days)
equator
Surface temperature 5800 K Sun, sunspots, and Mercury
transit, May 2003, by
Surface pressure 10 dyne cm-2 (10-5 atmospheres) Dominique Dierick
Central temperature 1.58x107 K
Central pressure 2.50x1017 dyne cm-2
Surface composition, by mass H (70.4%), He (28.0%), O (0.76%), C
(0.28%), Ne (0.17%), N (0.08%), others
(0.32%)
4 September 2018 ASTRONOMY 111, FALL 2018 21
MUCH MORE LATER
One learns a lot more about the Sun and
other stars, including the reasons why the
Sun has the set of properties that it does,
in AST 142 and AST 241.
For our purposes, it will suffice to discuss
only three of its properties now: its
composition, its surface temperature, and
its luminosity.
UV movie of loop prominence on the Sun’s surface, from the NASA SDO satellite
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THE SUN’S COMPOSITION AND NUCLEOSYNTHESIS
The Sun is a sphere of hot ionized gas, obviously boiling at the surface, so one might
think that it is well mixed. It is not.
The Sun’s size is determined by the balance of its weight and its internal pressure.
The heat that provides the pressure would leak away (in the form of sunshine) within
a few million years if it were not somehow replenished.
The replenishment of heat is provided by nuclear fusion reactions taking place at the
very center.
When atomic nuclei fuse to produce a nucleus light than that of iron (Fe, Z = 26, A = 56), kinetic
energy is liberated (the reaction is exothermic) and added as heat to the energy of the surroundings.
By the same token, this means that the contents of stars continuously transmute
themselves from light elements to heavy elements.
4 September 2018 ASTRONOMY 111, FALL 2018 23
NUCLEOSYNTHESIS
Models of the Sun’s interior indicate that the composition at the very center is 33.6%
H and 64.3% He by mass. Much of the H there has been burned to He, mostly due to
the proton-proton reaction chains.
The interior of the Sun is so hot that the enough collisions occur to ionize H, resulting in a plasma
Individual protons collide, fusing together to form deuterium (fusion); deuterium continues to fuse with
other protons in a chain reaction to form He.
The alpha particle (He) is less massive than the four protons that combined to make it, so the proton-
proton chain releases energy equal to the mass difference via ! = #$ %
In hotter, denser stellar cores, fusion of He (by the “triple alpha” reaction), C, O, Ne,
and even heavier elements can take place at respectable rates…
…and elements heavier than Fe can be made in small quantities in such stars by the
endothermic (opposite of exothermic) s-process reactions.
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NUCLEOSYNTHESIS
The Universe was born (in a fireball we can see, which we call the Big Bang) with
hardly any elements heavier than helium.
This is because fusion of two normal helium nuclei ( "!He) produces an isotope of beryllium ( %"Be) that is
quite unstable, dissolving back into helium within 10-16 sec.
Fusion of three normal helium nuclei produces a stable result:
3 "!He → *!)C + - Triple-α process
But very high density and temperature are necessary in order to make three He nuclei
collide simultaneously, energetically enough to fuse. And by the time the Universe
cooled enough for nuclei to condense, the density was too low.
4 September 2018 ASTRONOMY 111, FALL 2018 25
NUCLEOSYNTHESIS
In the cores of some stars, temperatures and densities can both be large enough for
the triple-α process to proceed.
And the carbon produced thereby can react to form other heavier nuclei.
Thus the heavy elements that the planets – and you – are made of were synthesized by nuclear
reactions in the cores of stars that lived and died billions of years ago.
Stars die before they burn more than about 10% of their total H into He, so the
Universe will take a very long time to run out of hydrogen.
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THE NUCLEAR-
1.0E+00
CHEMICAL EVOLUTION 1.0E-01
Interstellar gas
OF THE MILKY WAY Sun
Number of atoms per hydrogen atom
1.0E-02
O Pop I stars
1.0E-03 C
Ne Pop II stars
1.0E-04 Mg Si Fe
S
New stars 1.0E-05 N Ar
Ca Ni
Younger stars 1.0E-06
Na Al Ti
Older stars 1.0E-07 P
1.0E-08
1.0E-09
1.0E-10
1.0E-11
0 10 20 30 40
Atomic number, Z
4 September 2018 ASTRONOMY 111, FALL 2018 27
THE TEMPERATURE OF THE SUN’S SURFACE
The Sun is a ball of hot gas; it has no sharp, solid surface. So what do we mean by the
“surface” of the Sun?
Usually, we mean the deepest place we can see in the Sun’s atmosphere; this is called the photosphere.
The absorption of light in the Sun varies with wavelength, though, so the position of the photosphere is different
for different parts of the spectrum.
The temperature varies with depth within the Sun’s atmosphere and interior, so the physical temperature of the
surface that we see is different for different wavelengths.
So, it is more convenient to characterize the Sun’s “surface” temperature in a way that
depends upon the luminosity (total power output), which of course is wavelength-dependent.
Effective temperature of the Sun: the temperature that would produce the Sun’s observed luminosity, if the Sun
were a spherical blackbody with the same radius.
You will learn all about blackbodies in PHY 143/123 and PHY 227. We will only list the properties and
equations pertaining to blackbodies that we will need to use this semester, and defer the detailed explanations
to those courses.
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BLACKBODIES AND BLACKBODY RADIATION
A blackbody is a body that is perfectly opaque: it absorbs all of the light incident on it.
If such a body has a constant temperature, it must therefore also emit light at exactly the same
rate as it absorbs light. This is called blackbody radiation.
The flux – total power emitted in all directions by a blackbody at temperature T per unit area
– of a blackbody is given by
! = #$ % Stefan’s Law
# = 5.67051×10-. erg sec -4 cm-6 K -%
Stefan-Boltzmann constant
= 5.67051×10-8 J sec -4 m-6 K -%
4 September 2018 ASTRONOMY 111, FALL 2018 29
DEFINITIONS: LUMINOSITY AND FLUX
Luminosity is the total power output (in the form of light) emitted in all directions by
an object. Units = erg sec-1
The Sun’s luminosity, as we listed before, is
!⨀ = 3.83×10** erg sec 01
Flux is the total power (in the form of light) per unit area that passes through a
(sometimes imaginary) surface. Units = erg sec-1 cm-2
The flux of sunlight at the Sun’s surface is
!
2 = ⨀3 1;
7 = 6.29×10 erg sec
01 cm07
456⨀
The flux of sunlight at Earth’s orbit (the solar constant) is
!
2 = ⨀3 = 1.36×10? erg sec 01 cm07
45 1 AU 7
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THE SUN’S EFFECTIVE TEMPERATURE
If the Sun were a blackbody with radius equal to that of its visible photosphere (R⊙
= 6.96x1010 cm) and luminosity as observed (L⊙ = 3.83x1033 erg/s), then its
(effective) temperature Te would be given by
.
"⨀ = %& = '()* 4,-⨀ or
5⁄ 5⁄
/⨀ 6 7.97×;5 6
() = 3 = = 5770 K
*012⨀ *0 ?.@A×;B erg sec>5 cm>3 K>6 @.C@×;9/3/18
BLACKBODY SPECTRUM
The spectrum of blackbody radiation is given by the Planck function:
2ℎ& ' 1
!" = )
( -.,"/0
+ −1
where
ℎ = 6.626×106'7 erg sec Planck’s constant
= = 1.381×106@A erg K 6@ Boltzmann’s constant
The dimensions of the Planck function may seem confusing at first: they are power per unit
area, per unit solid angle, per unit wavelength interval; for example, erg sec-1 cm-2 ster-1 μm-1
4 September 2018 ASTRONOMY 111, FALL 2018 33
SOLID ANGLE?
Solid angle is to area what angle is to length. It is usually defined by a differential
element in spherical coordinates:
!Ω = sin ' !' !(
!'
!( Angles in radians
Unit of solid angle = steradian
For small angles, the solid angle is calculated from the angular widths of the “patch”
in the same manner as plane-geometrical areas. For a rectangle, the two angles
ΔΩ = Δ( sin ' Δ'
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!, +, , ' #, ', *
, #= !- + +- + ,-
! = # sin ' cos * !- + +-
#
+ = # sin ' sin * ' = tan12
,
, = # cos ' +
12
! * = tan
!
+ *
REMINDER: THE SPHERICAL
COORDINATES r, θ, φ
4 September 2018 ASTRONOMY 111, FALL 2018 35
SIMPLE EXAMPLE
What is the solid angle of a square patch of sky 15.4 arcminutes on a side? (This
is the solid angle covered by the CCD camera you will use on the Mees 24-inch
telescope.)
15.4 arcminutes is a small angle (9/3/18
COMPUTING SOLID ANGLES
When the angles are not small, one must integrate the differential element over the range of θ
and φ. You will not be doing that in AST 111, but just so you can see how it works…
The solid angle of the entre sky:
%& & &
Ω = # '( # sin , ', = −2/ cos ,0 = −2/ −2
$ $ $
Ω = 4/ steradians
The solid angle of a cone with an angular radius of π/8 radians:
%& &9 &9
: :
Ω = # '( # sin , ', = −2/ cos ,0 = 2/ 1 − 0.924
$ $ $
Ω = 0.478 steradians
4 September 2018 ASTRONOMY 111, FALL 2018 37
BLACKBODY SPECTRUM
The reason for the funny dimensions of the Planck function is that it has to be
integrated over wavelength, solid angle, and area in order to produce a luminosity:
( (
! = # %Ω # %) *+ , = # %. # %Ω # %) *+
' '
$ - $
In PHY 227 or AST 241, you will learn how to prove that the power per unit area
emitted in all directions by a blackbody is
/0 02 (
/ 28 9 : ; ;
! = # %1 # %3 cos 3 # %) *+ = / ℎ@
A ≡ CA ;
' ' ' 15>
that is, Stefan’s Law follows from the Planck function.
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16
1 . 10
15
THE PLANCK FUNCTION 1 . 10
ul(T) (erg sec-1 cm-3 ster-1)
14
1 . 10
13
1 . 10
Note that the higher the temperature, the
shorter the wavelength at which the peak 12
1 . 10
occurs.
11
1 . 10
Note also that visible wavelengths do not
include much of the luminosity, whatever the 10
1 . 10
temperature.
9
1 . 10
8
1 . 10
0.01 0.1 1 10 100
10000 K Wavelength (µm)
5000 K
2000 K
1000 K Visible light
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WIEN’S LAW
We will not be using the Planck function much, and we certainly will not be integrating it. It
appears now because of a useful consequence of the shape of the function.
It is fairly easy to convince oneself – as you will, in Problem Set 1 – that there is a simple
relation between the temperature of a blackbody and the wavelength at which it is brightest:
!"#$ % = 0.2897756 cm K
Wien’s law
= 2.897756×1045 m K
The shape of the spectrum tells one what the effective temperature is. This shape is easier
to measure accurately than luminosity is.
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EXAMPLES
At what wavelength do you (T = 98.6°F = 37°C = 310 K) emit the most blackbody radiation?
0.29 cm K 0.29 cm K
!"#$ = =
- 310 K
= 9.4×1023 cm = 9.4 4m Infrared light
Gamma-ray bursters emit most of their light at a wavelength of about 10-10 cm. If this
emission were blackbody radiation, what would be the temperature of the burster?
0.29 cm K 0.29 cm K
-= = 256 = 2.9×107 K Pretty hot
!"#$ 10 cm
4 September 2018 ASTRONOMY 111, FALL 2018 41
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