Download planets from a distance

1/13/2014
PLANETS FROM A DISTANCE
GLG‐190 ‐ The Planets
Chapter 1
LECTURE OUTLINE
 Planetary temperatures
 Electromagnetic spectrum and composition
 Planetary sizes, masses, and densities
 Differentiation, moment of inertia, planetary interiors
Textbook web site: http://ase.tufts.edu/cosmos/
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PLANETARY TEMPERATURES
Temperature of planet controlled by distance from Sun
 Amount of solar radiation hitting distant planets is much less than for inner planets
 Intensity of solar radiation striking given area (flux) decreases moving away from Sun (falls off as 1/r2)
 Internal heat and greenhouse effect can change planet’s temperature

TEMPERATURE SCALES

Fahrenheit (used in USA)


Centigrade (used in rest of world)


Water freezes at 32 F and boils at 212 F
Water freezes at 0 C and boils at 100 C
Kelvin (scientific usage)
Size of degree same as for Centigrade scale
 Water freezes at 273.15 K and boils at 373.15 K
 All molecular motion stops at 0 K
 Very little difference between Centigrade and Kelvin at very high temperatures

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ELECTROMAGNETIC SPECTRUM
Electromagnetic radiation can be considered either particles (photons) or waves
 Classified by…

Energy
Wavelength



Inverse relationship between wavelength and energy

Shorter wavelength 
more energy

Longer wavelength  less
energy
COMPOSITION OF SUN



Prism spreads “white” light into color spectrum (right)
Sun’s light has same range of colors but with thousands of superimposed black lines
Lines catalogued by Joseph von Fraunhofer
(1787‐1826)
Solar spectrum for visible light showing dark Fraunhofer
absorption lines (spectrum wraps around edges of image: each row is part of total spectrum)
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SPECTROMETRY
Use prism or diffraction grating to spread white light into constituent colors, revealing dark lines
 Spectroscopy is only way to learn composition of something from distance

FORMATION OF SPECTRAL LINES
 Interaction of light (photons) with electrons of atoms and molecules
 Absorption lines

Wavelengths where energy is removed from spectrum
 Emission lines

Wavelengths where energy is added to spectrum
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ATOMIC ABSORPTION LINES
Photons strike atoms kicking electrons into higher energy orbitals
 Only certain photon energies will work
 Photon energy used up  absorption spectrum
 Electron is higher orbitals fall back and emit energy 
emission spectrum

MOLECULAR ABSORPTION LINES
Light (photons) also interacts with molecules
 Molecules respond by changing…

Vibrational modes (movement of atoms within molecule)
 Rotational modes (movement of molecule in space)


Photon energy used up 
dark lines in spectrum
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DETERMINING SOLAR COMPOSITION
Solar abundances determined by spectroscopy
 Match spectral lines of Sun’s photosphere with those determined in lab
 Intensity of lines is function of abundance (larger darker lines  higher abundances)

SOLAR COMPOSITION

Why do we care?


Sun contains almost all mass in solar system  representative of starting composition from which planets formed
Differences between composition of Sun and planets result from processes that formed and modified planets

Most planets have compositions very different from the Sun (exceptions: Jupiter and Saturn)
Z
Element
Atoms per
million H
1
Hydrogen (H)
1,000,000
2
Helium (He)
97,000
6
Carbon (C)
360
7
Nitrogen (N)
110
8
Oxygen (O)
850
10
Neon (Ne)
120
12 Magnesium (Mg)
40
14
Silicon (Si)
40
16
Sulfur (S)
20
26
Iron (Fe)
32
All others
<5
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TYPES OF PLANETS

Terrestrial






Giant
Mercury, Venus, Earth, Mars
Closest to Sun
Rocky (like Earth) with high densities
Few or no moons
Solid surfaces





Jupiter, Saturn, Uranus, Neptune
Far from Sun
Large, gaseous, low densities
Many moons and rings
No solid surfaces
PLANETARY SIZES

Direct observation of planet’s disk



Measure angular size
Angular size combined with distance  actual size
Occultation




Result of syzygy (alignment of three astronomical bodies)
Useful for bodies too small to directly observe disk
Body blocks star’s light when it passes in front of it
Duration of occultation combined with orbital information yields angular size and actual size
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Sun
COMPARISON OF
PLANETARY SIZES
PLANETARY MASSES
Mass determined by observing gravitation force body exerts on other bodies
 For example, orbits of planets can be used to determine mass of Sun
 Using data for Earth





107
P = 1 year = 3.156 
s
a = 1.496  1011 m
G = 6.67300  10‐11 m3 kg‐1 s‐2
MSun = 1.9886  1030 kg
M
4 2 a 3
GP 2
P = orbital period
a = semi‐major axis of planet
G = Newton’s gravitational constant
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planet
M planet 
4 2 D 3
GP 2
moon
 Use same method for planets and their moons



Know distance, d  determine orbital radius, D
Observe period, P
Calculate mass of planet
 Mass of Jupiter using Ganymede’s orbit



D = 1,070,400 km = 1.070  109 m
P = 7.15455296 d = 6.181  105 s
MJupiter = 1.8967  1027 kg (1/1000 of Msun)
PLANETARY DENSITIES

Density () is mass (m) divided by volume (V), which is determined from size…


m
V
Usually expressed as grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3)

1 g/cm3 = 1000 kg/m3
Density
(g/cm3)
Density
(kg/m3)
Water
1.00
1000
Ice
0.92
920
Air (at 0 C)
0.00129
1.29
Granite
2.75
2750
Basalt
3.0
3000
Iron
7.87
7870
Material
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UNCOMPRESSED DENSITY


Compression increases density of material
Gravity of massive objects like planets will squeeze materials in interior  increasing density
Less squeezed 
less dense
Image pile of mattresses; bottom ones will be flatter than those on top
 Flatter ones have higher density (more flat ones 
higher overall density)
 Thus, larger of two piles has higher density, even though both contain same mattresses




Planetary materials like mattresses  more squeezed at bottom (in center)
Need to account for this effect 
uncompressed density Studying uncompressed density allows comparison of the compositions of planets
More squeezed 
more dense
DENSITIES OF PLANETS
Planet

Density
(g/cm3)
Uncompressed Density
Mercury
0.06
5.44
5.4
Venus
0.85
5.24
3.97
Earth
1.00
5.52
4.03
Moon
0.012
3.34
3.3
Mars
0.11
3.93
3.71
Jupiter
318
1.3
0.3
Saturn
95
0.7
0.3
Uranus
15
1.3
0.5
Neptune
17
1.6
0.5
Terrestrial Planets
Giant Planets
Mercury, Venus and Earth have very similar observed densities


Mass
(Earth 1)
Densities of larger terrestrial planets (Venus and Earth) significantly increased by compression
Giant planets have total densities doubled or tripled by pressure
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DIFFERENTIATION

Planets not made of just one material

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Planetary bodies heated in early history



Contain metal, rock, ice, gas
These materials have different densities (complicates problem of determining uncompressed density)
Heat from accretion and impacts
Radioactive heat
Hot accretion  melting  magma ocean
Density separation of materials
Metal sinks to form core (generates additional heat)
 Metal‐rock‐ice layers on icy moons



Large planets retain heat better
Volume  R3, heat generation
 Surface area  R2, heat loss

Ganymede
PLANETARY INTERIORS
 Difficult to determine thickness of layers inside planet
 Possible to estimate types and thicknesses of layers if planet’s original composition is known


Original compositions estimated by starting with solar composition
Account for effects of various processes such as gas loss to get theoretical starting composition
 Composition estimates can be combined with moment of inertia to better constrain the distribution of mass inside a planet
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MOMENT OF INERTIA
Measure of an object's resistance to changes in rotation rate
 Depends upon mass distribution inside planet
 Measured by observing how planet interacts gravitationally with other bodies (moons, spacecraft)
 Coefficient of moment of inertia, k, reflects distribution of mass, regardless of total mass or radius

MOMENTS OF INERTIA
Object
k
Implication
Mercury
0.33
large dense core
Venus
0.33
large dense core
Earth
0.33
large dense core
Moon
0.393
Homogeneous interior; almost no core
Mars
0.366
small dense core
0.254
dense core; extended gas shell (rotationally distorted)
0.210
small dense core; extended gas shell (rotationally distorted)
Uranus
0.23
small dense core; extended gas shell
Neptune
0.29
larger dense core; extended gas shell
0.06
very dense core; extended gas shell (rotationally distorted)
Jupiter
Saturn
Sun
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SUMMARY
Kepler’s and Newton’s discoveries allowed scientific study of planets
 Developments in spectroscopy allowed determination of solar composition
 Establishing distances allowed determination of many planetary and solar characteristics



Density, in turn allowed estimates of composition


Size, mass, density
Internal layering, differentiation
Moment of inertia (determined largely by spacecraft interactions with planets) confirmed layering inside planets
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