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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 earth’s atmosphere. Of course, in trying to understand the workings of our solar system or even the evolution of the earth as a body, the earth’s 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 ofmatter that we live, and therefore, it is interesting to us. It is also clear now that the earth’s gaseous envelopeis 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 differentstages 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 earth’s atmosphere is evolving, Interpreting the data on other atmospheres, given to us bySpacecraft and telescope data, is crucial and is one goal ofthis course..
OutlineOverview of Solar SystemBasic Properties of Atmospheres Composition Size Equilibrium T Scale Height Adiabatic Lapse Role Mixing in TroposphereRadiation Absorption Absorption Cross Section Heating by Absorption Chapman Layer Ozone Production: Stratosphere Thermospheric Structure Ionospheres Green House EffectAtmospheric Evolution Water: Venus, Earth, Mars Loss by Escape Isotope Ratios CO2 cycle: Earth, Venus, MarsAtmospheric Circulation Coriolis Effect Local Circulation Boundary Layer Global Circulation Zonal Belts Cloud FormationTopical Problems in Planetary Atmospheres
Space Science I:Atmospheres
Books on Reserve
Theory of Planetary Atmospheres Chamberlain & Hunten
Planetary Sciences by dePater and LissauerAtmospheres by Goody and WalkerThe Physics of Atmospheres by Houghton Energetic Charged-Particle Interactions with
Atmospheres and Surfaces by R.E. JohnsonThe 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
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 98Uranus 14.5 2.3 56Neptune 17.0 2.8 57
Terrestrial Venus 0.81 0.56 90 750
Earth 1 0.65 1 280Mars 0.11 0.13 8mb 240Titan 0.022 0.051 1.5 94Triton 0.022 0.051 17b 38
Escaping Io 0.015 0.034 10nb 130Europa 0.008 0.021 .02nb 120Ganymede0.024 0.024 .01nb 140Enceladus 0.000013 0.00024 150?Pluto 0.002 0.008 1b 36Comets small ~0
Collisionless Mercury 0.053 0.093
Moon 0.012 0.029Other 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 K1 bar = 105 Pa = 105 N/m2.
COMPOSITIONMolecular
SunH (H2) 0.86
He 0.14O 0.0014C 0.0008Ne 0.0002N 0.0004
Jupiter Saturn Uranus NeptuneH2 0.898 0.963 0.825 0.80
He 0.102 0.0325 0.152 0.19CH4 0.003 0.0045 0.023 0.015
NH3 0.0026 0.0001 <10-7 <6x10-7
Earth Venus Mars TitanCO2 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 <0.0002 0.0003
9Ar 0.009 ~0.0001 0.016 0.01?*Variable
Pressure and SizePressure 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 0.049Earth 1 10 0.087Titan 1.5 100 6.8Venus 90 1000 9.7
How big might Mars atmosphere have been (in bars) based on its size? How big might the earth’s have been?
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
Equilibrium Temperature
Heat In = Heat Outor
Source (Sun) = Sink (IR Radiation to Space)
Planetary body with radius a it absorbs energy over an area a2
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 4a2
First simple rule: Ener. Eq. Radiation
Solar Flux In and IR Ou vs. wavelenght
Fraction of radiation absorbed in atmosphere vs. wavelength
Principal absorbing species indicated
Source=Absorb Area heat flux amount absorbeda2 x [F / Rsp
2] x [1-A]
A = Bond Albedo: total amount reflected
(Complicated)
Solar Flux 1AU: F =1370W/m2
Rsp= distance from sun to planet in AU
Loss=Emitted (ideal radiator) Area radiated flux 4a2 x T4
= Stefan-Boltzman Constant= 5.67x10-8 J/(m2 K4 s)
.Fig. Radiation/ Albedo
Bond Albedo, A, is fraction of sunlight reflected to space: Surface, clouds, scattered
Absorption and Reflections of Solar Radiation
Set Equal
Heat In = Heat Out
Te = [ (F / Rsp2) (1-A) / 4 ]1/4
Rsp A Te Ts
Mercury 0.39 0.11 435 440Venus 0.72 0.77 227 750Earth 1. 0.3 256 280Mars 1.52 0.15 216 240Jupiter 5.2 0.58 98 134*
If the radiation was slow but evaporation wasfast, like in a comet, describe the loss term that would the IR lossFig. Sub T
Pressure vs. Altitude
Hydrostatic Law
Force Up = Force Down
p- A=area ---------------------------------------------
Draw forces Δz ---------------------------------------------
p+ mg = (ρA Δz) g Result:
Net Force= 0 = - (Δp A) - (ρA Δz) g where p = p-- - p+
dp/dz = - g
Now Use Ideal Gas Law p = nkT (k=1.38 x 10-23 J/K) =kT/m orp = (R/Mr)T [Gas constant: R=Nak =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 EnergySame result for a ballistic atmosphere
Second simple rule: Force Eq. Force Balance
Pressure vs. Altitudep = po exp( - ∫ dz / H)
(assuming T constant)
p = po exp( - z / H)
or Density vs. Altitude =0 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
Pressure: p p = weight of a column of gas (force per unit area) 1bar = 106 dyne/cm2=105 Pascal=0.987atmospheresPascal=N/m2 ; Torr=atmosphere/760= 1.33mbars Venus 90 barsTitan 1.5 barsEarth 1 barMars 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
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
Hydrostatic Again
r is radial distance from center of planetMp = mass of planet
€
Radial Case
dp
dr= −g(r)ρ
g(r) = G M p
r2
Assume Isothermal
Problem
(a) Show
p(r) = p(r0) exp −G M p
r02
m
KT(r − r0)
r0
r
⎡
⎣ ⎢
⎤
⎦ ⎥
(b) Show how this reduces to the flat atmosphere case
discussed when
r - r0 = z with z << r0
Temperature vs. Altitude Convection Dominates Adiabatic Lapse Rate
In the troposphere
Radiation Dominates Greenhouse Effect In the troposphere and stratosphere
Conduction Dominates Thermal ConductivityIn the thermosphere
Fig. T vs. z
Temperature vs. Altitude Earth’s Atmosphere
Shows layered atmosphereRadiation Absorption Indicated
See Atmospheric Structure of Other Atmospheres in dePater and Lissauer
First Law: Energy Conservation
Imagine gas moving up or down adiabatically: no
heat in or out of the volume
Energy = Internal energy + Workdq = 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
orcv dT = - (R/Mr) dT + V dp
(cv +R/Mr) dT = dp / cp (dT/dz) = (dp/dz) / Apply Hydrostatic Law (dp/dz) = - g
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
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 gmcv 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)
ADIABATIC + HYDROSTATIC Now have p(z) with T dependence. Use (dT/dz) = -g / cp and dp/dz = - ρ 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) = po[1 - 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