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

Temperature limited by Sublimation

Right hand axis melting

point

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

Pressure and Density vs. zShowing Region where gases diffusively separate

Pressure and Density vs. zOf individual species

Showing Region where gases diffusively separate

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

#1 Summary Things you should know Te and how is it obtained

The average albedoThe hydrostatic law for an atmosphereThe atmospheric scale heightThe adiabatic lapse ratePotential Temperature