RENEE CONDORI APAZA, JULIO

VALDIVIA SILVA, Christopher P. McKay

A principal reason for studying planetary atmospheres isto try to understand the origin and evolution of theearth’s atmosphere. Of course, in trying to understandthe workings of our solar system or even the evolutionof the earth as a body, the earth’s atmosphere isessentially irrelevant since its mass is negligible. Forthat matter, the mass of the earth is only a smallfraction of the mass of the sun. So we are consideringa thin skin of gravitationally bound gas attached to aspeck of matter in a dynamic and, in thepast, violent, system. Therefore, it is a formidableproblem.

However, it is in that thin skin of gas and on that speckof matter that we live, and therefore, it is interesting tous.

It is also clear now that the earth’s gaseous envelope ischanging and has changed. In fact it is abundantlyclear that the present atmosphere barely resembles theoriginal residual gas left when the earth formed.

Because of this it is also important to study the otheratmospheres in the solar system, since they are eitherdifferent end states or in different stages of atmosphericevolution. They may all have had roughly similarmaterials as sources, but either these atmospheres areon objects of a very different size or at a very differentdistance from the sun. Since, we can not carry outmany experiments to see how the earth’s atmosphere isevolving, Interpreting the data on otheratmospheres, given to us by Spacecraft and telescopedata, is crucial and is one goal of this theme.

Basic Properties of AtmospheresCompositionSizeEquilibrium TScale HeightAdiabatic Lapse RoleMixing in Troposphere

Radiation AbsorptionAbsorption Cross SectionHeating by AbsorptionChapman LayerOzone Production:

StratosphereThermospheric StructureIonospheresGreen 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

Overview of Solar System

Type Name Mass Escape p T*(eV/u) (bar) (K)

H/He Jupiter 318 18 128 Gas Balls Saturn 95 6.5 98

Uranus 14.5 2.3 56Neptune 17.0 2.8 57

Terrestrial Venus 0.81 0.56 90 750Earth 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 120Ganymede 0.024 0.024 .01nb 140Enceladus 0.000013 0.00024 150?Pluto 0.002 0.008 1b 36Comets small ~0

Type Name Mass Escape p T*(eV/u) (bar) (K)

Collisionless Mercury 0.053 0.093Moon 0.012 0.029Other moons

T*: for Jovian they are Teq ; for the terrestrialthey are mean surface temperatures; for icysatellites they are the subsolar T

1eV = 1.16x104 K1 bar = 105 Pa = 105 N/m2.

Molecular

SunH (H2) 0.86He 0.14O 0.0014C 0.0008Ne 0.0002N 0.0004

Jupiter Saturn Uranus NeptuneH2 0.898 0.963 0.825 0.80He 0.102 0.0325 0.152 0.19CH4 0.003 0.0045 0.023 0.015NH3 0.0026 0.0001 <10-7 <6x10-7

Molecular

Earth Venus Mars TitanCO2 0.0031 0.965 0.953N2 0.781 0.035 0.027 0.97O2 0.209 0.00003 0.0013CH4 0.00015 0.03H2O* 0.01 <0.0002 0.00039Ar 0.009 ~0.0001 0.016 0.01?*Variable

Pressure is the weight of a column of gas: forceper 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?

p, T, n (density) Equation of State

Conservation of SpeciesContinuity Equation: Diffusion and FlowSources / Sinks: Volcanoes

Escape (top)Condensation/ Reaction (surface)

Chemical Rate EquationsConservation of Energy

Heat Equation: Conduction, Convection, Radiation Sources: Sun and InternalSinks: Radiation to Space, Cooling to SurfaceRadiation transport

Conservation of MomentumPressure Balance FlowRotating: Coriolis

Atomic and Molecular Physics Solar Radiation: Absorption and Emission

Heating; Cooling; ChemistrySolar 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 pa2

Cooling: IR radiation outIf the planetary body is rapidly rotating or haswindsrapidly transporting energy, it radiates energy

from all of its area 4pa2

Fraction of radiation absorbed in atmosphere vs. wavelength

Principal absorbing species indicated

Source=Absorb

Area heat flux amount absorbedpa2 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 flux4pa2 x T4

= Stefan-Boltzman Constant= 5.67x10-8 J/(m2 K4 s)

Fig. Radiation/ Albedo

Bond Albedo, A, isfraction of sunlightreflected to space:Surface, clouds, scattered

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 theIR loss.Fig. Sub T

Right hand axis melting point

Pressure vs. Altitude

Hydrostatic Law

Force Up = Force Down

p- A=area---------------------------------------------

Draw forces Δz---------------------------------------------

p+ mg = (ρ A Δz) gResult:

Net Force= 0 = - (Δp A) - (ρ A Δz) g

where p = p-- - p+

dp/dz = - g

Now Use Ideal Gas Lawp = nkT (k=1.38 x 10-23 J/K) =kT/m

or

p = (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 Energy

Same result for a ballistic atmosphere

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=0.987atmospheres

Pascal=N/m2 ; Torr=atmosphere/760= 1.33mbars

Venus 90 barsTitan 1.5 barsEarth 1 barMars 0.008 bar

Column Density: N

p = m g 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

ShowingRegion wheregasesdiffusivelyseparate

Convection Dominates Adiabatic Lapse RateIn the troposphere

Radiation Dominates Greenhouse Effect In the troposphere and stratosphere

Conduction Dominates Thermal ConductivityIn the thermosphere

Fig. T vs. z

Shows layered atmosphereRadiation Absorption Indicated

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 = 0cv dT = - p dV

Ideal gas law [p = nkT = (R/Mr)T ]

pV = (R/Mr)T

Differentiatep 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

(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

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 + 3or 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)

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

= 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

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