Reading in Planetary Sciences

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Reading in Planetary Sciences
for Wednesday, February 11 Planetary Atmospheres
--- Chapter 4, sections 4.1-4.4 for Monday,
February 16 Planetary Atmospheres --- Chapter 4,
sections 4.5-4.9
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Homework I
due Wednesday, February 11 outline of your
paper or research project (worth 10 points)
print out and hand in (Latex format
preferred) 10 pieces required 1. Abstract
(bullets) 2. Introduction (why do we
care?) 3. Motivation (why do YOU care?) 4.
Sections listed (observations done/planned) 5.
Discussion (bullets) 6. Tables listed 7.
Figures listed 8/9/10. three REFEREED
references
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Homework II
due Monday, February 23 second step of your
paper or research project (worth 10 points)
1. 1 title 2/3/4. 3 sentences of the
Abstract 5/6/7. 3 sentences of the
Introduction (include two references)
8/9/10. 3 sentences about YOUR Motivation
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Non-Blackbody Features Emission
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Non-Blackbody Features Reflection
remember, blackbodies are big fat
lies monchromatic albedo --- A? ratio of
emitted/incident energy at a specific wavelength
(note that emitted reflected
scattered) geometric albedo --- A ratio of
emitted/incident energy if you are looking at
the object head-on (zero phase angle for the
Sun) Bond albedo --- Ab ratio of total
emitted/total incident energy, integrated over
all wavelengths Bond 0.1 Me/Ma/Moon Bond
0.3 E/J/S/U/N Bond 0.8 V reflectivity leads
to implications for planet observability
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Star vs. Planet
1081
1041
reflected
emitted
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Astrometry Instead?
Sun as seen from 10 parsecs over 65 years
1 mas
Jupiter 11.9 yrs 0.52 milliarcsec Saturn
29.4 yrs 0.95 milliarcsec Uranus 83.8
yrs 1.91 milliarcsec
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Temp, Temp, Temp
brightness temperature (Tb) --- temperature
measured if you fit a small bit of spectrum with
a flux for a blackbody curve that matches that
bit of spectrum effective temperature (Teff) ---
temperature measured if you get the total flux
from an object and you match that flux under the
non-blackbody spectrum to a blackbody that has
the same total flux under its curve equilibrium
temperature (Teq) --- for planets, temperature
measured if the emitted radiation depends only on
the energy received from the Sun, assuming energy
in energy out
any discrepancies between the effective
temperature and the equilibrium
temperature contain valuable information about
the object
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Equlibrium Temp Derivation
equilibrium temperature (Teq) --- for planets,
temperature measured if the emitted radiation
depends only on the energy received from the Sun,
assuming energy in energy out
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Tweaks to Planet Temps
The Planet solar irradiation is not uniform
across planetary surface albedo is not
constant due to surface features albedo is
not constant due to clouds reradiation will
certainly be at different wavelengths than
incident The Dynamics planets rotation is
assumed to be fast planets obliquity will
change energy deposition/emission planets
orbital eccentricity will affect radiation
input The Sun solar constant is not
constant
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Planet Temperatures
Tequil Tsurf or Teff causes of
differences
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Energy Transport in Planets
CONDUCTION (solids) --- transport of energy by
particle collisions
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Energy Transport in Planets
CONVECTION (fluids/gases) --- motion in a fluid
caused by density gradients that are
the result of temperature differences
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Energy Transport in Planets
RADIATION (gases) --- transport of energy by
photons
Jupiter at radio wavelengths with surrounding
cloud of electrons trapped in magnetosphere
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Conduction
operates below planetary surfaces
temperature variations of the surface vary daily,
depending on the thermal skin depth
LT (2 KT / ?rot ?
cp)1/2 where KT is the thermal
conductivity in erg s-1 cm-2 K-1 ?rot is the
rotation rate of the planet ? is the density
of the planet at the surface
cp is the specific heat energy
required to raise temp of 1 g by 1 K temp
variations are largest right at surface,
variations have exponential dropoff with
depth, with scale depth equal to
LT conduction takes time, so heating/cooling not
immediate surface is insulator at night because
conduction is temp dependent seasonal effects can
also be significant observations are made at
radio wavelengths

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Thermal Conductivity, KT
it really is a useful, measurable thing (units
are J s-2 m-2 C-1)
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Convection
operates in planetary atmospheres (near
surfaces), liquid and molten environments occurs
when the temp decreases with height so rapidly
that pressure equilibrium
not reached rising blobs of gas/liquid
continue to rise if adiabatic lapse rate (dT/dz)
followed, then no convection if superadiabatic
conditions, convection occurs (temp gradient
steeper than adiabatic) derivation of adiabatic
lapse rate begins with assumption of hydrostatic
equilibrium, the condition when pressure and
gravity forces are balanced
dP/dz g(z) ?(z) variables can be
swapped around easily if the equation of state
(relates pressure, temp, and density in any
material) follows the ideal gas law
P
? R T / µ assume first law of thermodynamics
(energy conserved) and that no heat is
exchanged with surroundings (i.e. the air blob
moves adiabatically)
dT/dz g /
cP where cp is the specific heat capacity (erg
g-1 K -1) at constant pressure

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Radiation
heat transport by radiation in atmospheres where
optical depth not large or small
typically upper troposphere and stratosphere
(where we fly) need radiative transfer
equations PHOTONS interact with ATOMS and
MOLECULES observe interaction using
spectroscopy
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Atomic and Molecular Spectra
H2 H
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Radiation
B? blackbody radiation I? specific intensity
(blackbody is one example) J? mean intensity
(integral of I? over solid angle / solid
angle) Einstein A coeff probability/time
emission occurs Aul Einstein B coeff
probability/time event occurs Blu J? (normal
absorption)
Bul J? (stimulated
emission) Classic Case When in thermodynamic
equilibrium the following are true 1.
isotropic blackbody radiation field I? J?
B? 2. absorption rates emission rates Nl
Blu J? Nu Aul Nu Bul J? 3.
temperature of gas determines number
density of atoms in given energy state Ni e
Ei/kT
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Radiative Transfer I

• What does radiative transfer actually mean?
• ? used when the primary way that energy is
  transported is via photons!
• ? so, the pressure-temperature profile is
  determined by the following radiative
• transfer equation, where dI? is the
  change in intensity inside a gas cloud
• 
  dI? / dt? I? S?
• where I? is the incident intensity to the gas
  parcel, and S? is the source function
• (effectively, these are absorption and emission
  factors)
• t is the optical depth, given by
• 
  t? ? a(z) ?(z) dz
• in which a(z) is the extinction (absorption
  scattering) and ?(z) is the density
• Integrating the first equation (assuming S? does
  not vary with t) yields
• I? (t?)
  S? e-t? ( I?,o S? )

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Radiative Transfer II
I?
(t?) S? e-t? ( I?,o S? ) Real world
considerationswhat intensity, I? , do you
see? If t? gtgt 1, then the second term goes
away and I? S? so, the emission you
receive is determined entirely by the source
function, or by the ratio of the
emission/absorption in the thick atmosphere If
t? ltlt 1, then e-t? 1, the source function
becomes irrelevant, and I? I?,o so, the
incident radiation completely defines the
radiation you measure from a very thin
atmosphere If t? 1, then the source function
of the atmosphere and the incident
intensity battle it out to see which has the
most effect on what you see If the gas is
non-emitting, S? 0 and any incident radiation
is attenuated by the optical depth in a (nearly)
directly observable way If the gas is in LTE,
the source function is a blackbody function, S?
B?
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Reality Check
Greenhouse effectdoes it make sense? Assuming
an atmosphere that is in radiative equilibrium
and LTE (g ground)
Tg 4 Teff 4 ( 1 0.75 tg
) Implies that Venus has optical depth to
ground 119 Earth has optical depth to
ground 0.6 Mars has optical depth to
ground 0.2
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Whats it all good for?
conduction measurements probe surfaces to
various depths in radio for temp variations
whats it made of? convection
measurements atmospheric structure and
temperature variations where are the
molecules? photochemical rates of reaction at
various levels where is the chemistry?
radiation
measurements colors are seen at various
wavelengths whats in the atmosphere/on
surface? temperature profiles with height
where is it raining, and what is it?
if Teff ? Tequil then you know something is
fishy
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Planets at Radio Wavelengths
Jupiter
Venus
Mercury
Mars
Moon
Saturn