Space Science I : Planetary Atmospheres

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Space Science I Planetary
Atmospheres Introduction A principal
reason for studying planetary atmospheres is to
try to understand the origin and evolution of the
earths atmosphere. Of course, in trying to
understand the workings of our solar system or
even the evolution of the earth as a body, the
earths atmosphere is essentially irrelevant
since its mass is negligible. For that matter,
the mass of the earth is only a small fraction
of the mass of the sun. So we are considering a
thin skin of gravitationally bound gas attached
to a speck of matter in a dynamic and, in the
past, violent, system. Therefore, it is a
formidable problem. However, it is in that thin
skin of gas and on that speck of matter that we
live, and therefore, it is interesting to us.
It is also clear now that the earths gaseous
envelope is changing and has changed. In fact it
is abundantly clear that the present atmosphere
barely resembles the original residual gas left
when the earth formed. Because of this it is
also important to study the other atmospheres in
the solar system, since they are either
different end states or in different stages of
atmospheric evolution. They may all have had
roughly similar materials as sources, but either
these atmospheres are on objects of a very
different size or at a very different distance
from the sun. Since, we can not carry out many
experiments to see how the earths atmosphere is
evolving, Interpreting the data on other
atmospheres, given to us by Spacecraft and
telescope data, is crucial and is one goal
of this course..
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Outline Overview of Solar
System Basic Properties of Atmospheres
Composition Size
Equilibrium T Scale Height
Adiabatic Lapse Role
Mixing in Troposphere Radiation Absorption
Absorption Cross Section
Heating by Absorption Chapman
Layer Ozone Production
Stratosphere Thermospheric
Structure Ionospheres
Green House Effect Atmospheric Evolution
Water Venus, Earth, Mars
Loss by Escape Isotope Ratios
CO2 cycle Earth, Venus,
Mars Atmospheric Circulation
Coriolis Effect Local Circulation
Boundary Layer
Global Circulation Zonal Belts
Cloud Formation Topical Problems in
Planetary Atmospheres
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Space Science IAtmospheres Books on Reserve

• Theory of Planetary Atmospheres Chamberlain
  Hunten
• Planetary Sciences by dePater and Lissauer
• Atmospheres by Goody and Walker
• The Physics of Atmospheres by Houghton
• Energetic Charged-Particle Interactions with
  Atmospheres and Surfaces by R.E. Johnson
• The New Solar System by Kelly Beatty et al.
• Atmospheres in the Solar System by Mendillo et
  al.
• Planets and their Atmospheres by Lewis and Prinn
  
• Planetary Science by Cole and Woolfson
• Introduction to Space Physics by Kivelson
  Russell

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TYPES OF ATMOSPHERES     Type Name Mass Escape
p T (eV/u) (bar)
(K) H/He Gas Balls Jupiter 318 18 128
Saturn 95 6.5 98 Uranus 14.5 2.3
56 Neptune 17.0 2.8 57   Terrestrial Venus
0.81 0.56 90 750 Earth 1 0.65 1
280 Mars 0.11 0.13 8mb
240 Titan 0.022 0.051 1.5
94 Triton 0.022 0.051 17?b
38 Escaping Io 0.015 0.034 10nb
130 Europa 0.008 0.021 .02nb
120 Ganymede0.024 0.024 .01nb
140 Enceladus 0.000013 0.00024
150? Pluto 0.002 0.008 1?b
36 Comets small 0   Collisionless Mercury 0.05
3 0.093 Moon 0.012 0.029 Other moons   T
for Jovian they are Teq for the terrestrial
they are mean surface temperatures for icy
satellites they are the subsolar T   1eV
1.16x104 K 1 bar 105 Pa 105 N/m2.
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COMPOSITION Molecular
Sun H (H2) 0.86 He 0.14 O 0.0014 C 0.0008 Ne 0.0
002 N 0.0004 Jupiter Saturn Uranus Neptune H2 0
.898 0.963 0.825 0.80 He 0.102 0.0325 0.152 0.19
CH4 0.003 0.0045 0.023 0.015 NH3 0.0026 0.0001 -7 Mars Titan CO2 0.0031
0.965 0.953 N2 0.781
0.035 0.027 0.97 O2
0.209 0.00003 0.0013 CH4
0.00015 0.03 H2O 0.01 0.0003 9Ar 0.009 0.0001
0.016 0.01? Variable       
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Pressure and Size Pressure is the weight of a
column of gas force per unit area     p mg N
(column density N) Thickness if frozen
Hs   p(bar) Hs(m) Ma/Mp (10-5) Mars
0.008 2 0.049 Earth 1 10
0.087 Titan 1.5 100 6.8 Venus 90
1000 9.7 How big might Mars atmosphere have
been (in bars) based on its size? How big might
the earths have been?
 
 
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Structure of an Atmosphere?   p, T, n
(density) Equation of State   Conservation
of Species Continuity Equation Diffusion
and Flow Sources / Sinks Volcanoes
Escape (top)
Condensation/ Reaction
(surface) Chemical Rate Equations  
Conservation of Energy Heat Equation
Conduction, Convection, Radiation
Sources Sun and Internal Sinks
Radiation to Space, Cooling to Surface
Radiation transport   Conservation of
Momentum Pressure Balance
Flow Rotating Coriolis   Atomic
and Molecular Physics Solar Radiation
Absorption and Emission
Heating Cooling Chemistry Solar Wind
Aurora
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First simple rule Ener. Eq. Radiation
Equilibrium Temperature   Heat In Heat
Out or Source (Sun) Sink (IR Radiation
to Space)
Planetary body with radius a it absorbs
energy over an area pa2     Cooling IR
radiation out If the planetary body is
rapidly rotating or has winds rapidly
transporting energy, it radiates energy from
all of its area 4pa2
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Solar Flux In and IR Ou vs. wavelenght
Fraction of radiation absorbed in
atmosphere vs. wavelength Principal absorbing
species indicated
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SourceAbsorb Area heat flux amount
absorbed pa2 x F / Rsp2 x
1-A   A Bond Albedo total amount
reflected (Complicated)
Solar Flux 1AU F 1370W/m2
Rsp distance from sun to planet in
AU   LossEmitted (ideal radiator) Area
radiated flux 4pa2 x sT4 s
Stefan-Boltzman Constant 5.67x10-8 J/(m2 K4 s)
  . Fig. Radiation/ Albedo
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Absorption and Reflections of Solar
Radiation
Bond Albedo, A, is fraction of sunlight
reflected to space Surface, clouds, scattered
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Set Equal   Heat In Heat Out   Te
(F / Rsp2) (1-A) / 4? 1/4     Rsp
A Te Ts   Mercury 0.39 0.11
435 440 Venus 0.72 0.77 227
750 Earth 1. 0.3 256 280 Mars
1.52 0.15 216 240 Jupiter 5.2
0.58 98 134       If the
radiation was slow but evaporation was fast, like
in a comet, describe the loss term that would the
IR loss Fig. Sub T
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Temperature limited by Sublimation
Right hand axis
melting point
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Second simple rule Force Eq. Force Balance
Pressure vs. Altitude   Hydrostatic
Law   Force Up Force Down     p-
Aarea
---------------------------------------------  Dra
w forces ?z    -------------------------------
-------------- p   mg (?A ?z) g  Result
Net Force 0 - (?p A) - (?A ?z)
g   where ?p p-- - p dp/dz - ?g
  Now Use Ideal Gas Law p nkT (k1.38 x
10-23 J/K) ?kT/m or p (R/Mr)?T Gas
constant RNak 8.3143 J/(K mole) with Mr
the mass in grams of a mole substitute for
? dp/dz - p(mg/kT) -p/H H is an effect
height Gravitational Force/ Thermal
Energy Same result for a ballistic atmosphere
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Pressure vs. Altitude p po exp( - ? dz /
H) (assuming T constant)   p po
exp( - z / H) or Density vs.
Altitude   r r0 exp( - z / H)    
Scale Height H   H kT/mg (or
H RT / Mr g)  
Mr g(m/s2) Ts(K) H(km) Venus CO2
44 8.88 750 16 Earth N2 ,O2 29
9.81 288 8.4 Mars CO2 44
3.73 240 12 Titan N2 , CH4 28 1.36
95 20 Jupiter H2 2 26.2
128 20   Note did not use Te , used Ts for
V,E,M
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Pressure p   p weight of a column of gas
(force per unit area)    1bar 106 dyne/cm2105
Pascal0.987atmospheres PascalN/m2
Torratmosphere/760 1.33mbars   Venus 90
bars Titan 1.5 bars Earth 1 bar Mars
0.008 bar
 
Column Density N p mg N     Surface of
earth N ? 2.5 x 1025 molecules/cm2. What would N
be at the surface of Venus?   If the atmosphere
froze (like on Triton), how deep would it
be? n(solid N2) ? 2.5 x 1022 /cm3 N/n 10m
 
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PARTIAL PRESSURES   Lower Atmosphere   Mixing
dominates use ?m or ?Mr       Upper
atmosphere   Diffusive separation
Partial Pressure (const T)  
p ? pi(z) ? poi exp - z/Hi     Hi
kT/ mig   Fig. Density vs. z
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Pressure and Density vs. z Showing Region where
gases diffusively separate
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Pressure and Density vs. z Of individual
species Showing Region where gases diffusively
separate
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Hydrostatic Again
r is radial distance from center of planet Mp
mass of planet
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Temperature vs. Altitude   Convection
Dominates ? Adiabatic Lapse Rate In the
troposphere   Radiation Dominates ? Greenhouse
Effect In the troposphere and
stratosphere Conduction Dominates ? Thermal
Conductivity In the thermosphere   Fig. T
vs. z
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Temperature vs. Altitude Earths
Atmosphere Shows layered atmosphere Radiation
Absorption Indicated
See Atmospheric Structure of Other Atmospheres in
dePater and Lissauer
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First Law Energy Conservation   Imagine gas
moving up or down adiabatically no heat in or
out of the volume Energy Internal energy
Work dq cvdT p dV   (energy per mass
of a volume of gas V 1 / ?) Adiabatic no
heat in or out dq 0 cv dT - p dV   Ideal
gas law p nkT ?(R/Mr)T pV
(R/Mr)T   Differentiate   p dV dp V
(R/Mr) dT   or cv dT - (R/Mr) dT
V dp   (cv R/Mr) dT dp / ? cp (dT/dz)
(dp/dz) / ?   Apply Hydrostatic Law
(dp/dz) - ?g  
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Adiabatic Lapse Rate
(dT/dz) -g / cp - ?d   Heating
at surface Slow vertical motion.   T Ts
- ?d z  T falls off linearly with altitude
cp (erg/gm/K) ?d
(deg/km) Venus 8.3 x 106 11 Earth 1.0
x 107 10 Mars 8.3 x 106 4.5
Jupiter 1.3 x 108 20
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Evaluate cp   cp Cp / m cv
(R/Mr) Cv k
m   CvT
heat energy of a molecule   Atom Cv (3/2)k
kinetic energy only   3-degrees of
freedom each with k/2 N2 One would think
that there are 6-degrees
of freedom 3 3 or 3
(CM) 2 (ROT) 1 (VIB)
Cv 3k   But potential energy of internal
vibrations needed Cv ? 3.5 k 4.8 x 10-16
ergs/K 1 mass unit 1.66x 10-24
gm cv ? 1.0 x 107 (ergs/gm/K)
fortuitous as Cp ? 3.5 Define ? Cp/Cv
Using the above ? - 1 k/Cv or
(? - 1) / ? k/ Cp k/(mcp)
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ADIABATIC HYDROSTATIC Now have
p(z) with T dependence.   Use (dT/dz) -g / cp
and dp/dz - ? g and p nkT dp/p
- mgdz/kT m cp/k dT/T x dT/T x
?/(?-1) ?cp/cv
1/x 0.2 for N2 0.17 for CO2 0 for
large molecule (?5/3, 7/3, 4/3 for
mono, dia and ployatomic gases) Solve and
rearrange (p/po) (T/To)x
using T Ts - ?d z  p(z) po1 -
z/(xH)x -- po exp(-z/H) for x
small   POTENTIAL TEMPERATURE   ? T
(po/p)1/x Adiabatic ? Entropy
Constant  Gas can move freely along constant
? lines Using dq T dS where S is
entropy Can show S cp ln? const

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1 Summary   Things you should know   Te and how
is it obtained The average albedo The hydrostatic
law for an atmosphere The atmospheric scale
height The adiabatic lapse rate Potential
Temperature