The document discusses planetary atmospheres and their evolution. It aims to understand the origin and evolution of Earth's atmosphere by studying other atmospheres in the solar system. These atmospheres can be in different evolutionary stages or on objects of different sizes and distances from the sun. The document provides overviews of the basic properties and composition of different planetary atmospheres. It discusses concepts like scale height, adiabatic lapse rate, and potential temperature which are important for understanding the structure and dynamics of atmospheres. The goal is to interpret data from spacecraft and telescopes on other atmospheres to learn about how Earth's atmosphere has changed over time.

1. RENEE CONDORI APAZA, JULIO
VALDIVIA SILVA, Christopher P. McKay

2. 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
of matter that we live, and therefore, it is interesting to
us.

3. It is also clear now that the earth’s 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 earth’s 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 theme.

4. 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
Overview of Solar System

5. 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 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
Ganymede 0.024 0.024 .01nb 140
Enceladus 0.000013 0.00024 150?
Pluto 0.002 0.008 1b 36
Comets small ~0

6. Type Name Mass Escape p T*
(eV/u) (bar) (K)
Collisionless Mercury 0.053 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.

7. Molecular
Sun
H (H2) 0.86
He 0.14
O 0.0014
C 0.0008
Ne 0.0002
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 <10-7 <6x10-7

8. Molecular
Earth Venus 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 <0.0002 0.0003
9Ar 0.009 ~0.0001 0.016 0.01?
*Variable

9. 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 earth’s have been?

10. 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

11. 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

12. Fraction of radiation absorbed in atmosphere vs. wavelength
Principal absorbing species indicated

13. Source=Absorb
Area heat flux amount absorbed
pa2 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
4pa2 x T4
 = Stefan-Boltzman Constant= 5.67x10-8 J/(m2 K4 s)
Fig. Radiation/ Albedo

14. Bond Albedo, A, is
fraction of sunlight
reflected to space:
Surface, clouds, sc
attered

15. Set Equal
Heat In = Heat Out
Te = [ (F / Rsp
2) (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

16. Right hand
axis melting
point

17. Pressure vs. Altitude
Hydrostatic Law
Force Up = Force Down
p- A=area
---------------------------------------------
Draw forces Δz
---------------------------------------------
p+ mg = (ρ A Δz) g
Result:
Net Force= 0 = - (Δp A) - (ρ A Δz) g
where p = p-- - p+

18. dp/dz = - g
Now Use Ideal Gas Law
p = 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

19. Pressure vs. Altitude
p = 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

20. 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 bars
Titan 1.5 bars
Earth 1 bar
Mars 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

21. 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

23. Showing
Region where
gases
diffusively
separate

25. 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

26. Shows layered
atmosphere
Radiation
Absorption
Indicated

27. 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

28. 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

29. (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

30. 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

31. 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)

32. 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

33.  = 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

34. 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