THE EARTH AS A PLANET, part 1
PROOFS it is (nearly) a sphere and rotates (other than Greek):
Masts of ships visible before their decks.
Cicumnavigation in 1522!
Distances corresponding to degree of latitude change;
it bulges near the equator.
Newton realized that a rotating object has extra support
perpendicular to its axis:
R_{e} = 6.378136 x 10^6 m
R_{p} = 6.356753 x 10^6 m
ELLIPTICITY = (R_{e}-R_p)/R_e = 1/298.257 = 0.0033528.
If the earth were `mushier', the same rotation speed would
yield a
higher ellipticity.
FOUCAULT PENDULUM --- fixed plane of oscillation,
with the
Earth rotating underneath it.
Satellites in POLAR ORBIT see different sections every 90
minutes as the
Earth rotates under the satellite's FIXED path.
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TIDES
are due to the DIFFERENTIAL force of GRAVITY.
A VERY USEFUL FIGURE, 7.21 in the text,
was shown in class.
F_tidal = G M M_other R / d^3
TWO HIGH TIDES a day because of Earth rotating through
BOTH the
FRONT
and BACK bulges.
SPRING (strong) TIDES: new moon and full moon;
the Sun's weaker tide and the Moon's stronger one
add up -- See Fig. 7.22
NEAP (weak) TIDES: first and third quarter moon
the Sun's weaker tide partially cancels the Moon's stronger one
Energy is dissipated by oceans rubbing
against crust: the Earth's spin slows down
(but only 1.5 ms/century!)
Another way of looking at this is as an example of
CONSERVATION OF
ANGULAR MOMENTUM:
as the Earth's rotation slows, decreasing its angular momentum (AM), the
Moon's orbital AM increases--the Moom moves slightly further away!
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SIDEBAR ON ANGULAR MOMENTUM
Angular momentum is the product of mass, velocity and size.
IT IS CONSERVED IF NO TORQUES ARE ACTING.
Spin angular momentum (ballerina, diver, earth on its axis) is
AM_spin ~= mass x size x spin speed
Orbital angular momentum (earth around sun, moon around earth) is
AM_orb = mass x distance x orbital speed.
Since the earth's orbital speed is 30 km/s and it's spin
speed
is about 0.46 (estimated as 0.5) km/s AND
the earth's distance from Sun (1AU = 1.5 x 10^8 km) is >> its radius (6.378 x 10^3 km)
we conclude the earth's orbital angular momentum is
>>> than its spin angular momentum.
To be more precise,
AM_orb/AM_spin = (30.0/0.46)x(1.5 x 10^8/6.4 x 10^3) = 1.5x10^6
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THE EARTH'S ATMOSPHERE
PRESSURE DECREASES WITH HEIGHT:
drops by a factor
of 10 roughly every 14.5 km, so 50% w/in 5 km.
P propto rho T
Since T doesn't change too much, density (rho)
declines
at a similar rate.
4 LAYERS WITH REVERSING TEMPERATURE GRADIENTS
TROPOSPHERE: weather zone, up to ~ 12 km -- clouds only here!
Temperature drops
with altitude (from 290 K to 235 K).
STRATOSPHERE: up to ~ 45 km --- T rises back up to 270 K,
gas is heated by propinquity to radiation.
MESOSPHERE: up to ~ 90 km --- OZONE LAYER near boundary
betw.
Stratosphere and Mesosphere --- T drops back to below 200 K.
IONOSPHERE (or THERMOSPHERE): when density is
low enough,
solar radiation
strips electrons from atoms, above ~ 90 km and T rises very slowly
again.
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ATMOSPHERIC COMPOSITION
By mass: 78% N_2 , 21% O_2 , 1% Ar (H_2 O up to 4%).
BUT IT EVOLVED TO THAT: First there was a
PRIMARY ATM: H_2, He, CH_4 , NH_3
--- too light for
earth's gravity to hold. This was ollowed by a
SECONDARY ATM: Outgassed from volcanos:
H_2 O, CH_4 ,
CO_2 , SO_2 , N_2 , NO.
UV radiation decomposed many compounds and H escaped;
less atm -> cooling
H_2 O into oceans, much CO_2 dissolved into them.
O_2 only important after ALGAE and other PLANT
LIFE produced
it in huge quantities, starting about 3.5 Gyr ago.
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GREENHOUSE EFFECT
Molecules with high opacity to IR radiation trap much reradiated
heat
from the surface. Most important is CO_2 , but CH_4
and rarer gases play big roles.
This current greenhouse effect makes the earth about 40 C
(or about 70 F) warmer than it otherwise would be.
The injection of CO_2 via fossil fuel burning is causing
additional global warming.
We'll talk more about this when we discuss Venus, where there
is a
RUNAWAY GREENHOUSE EFFECT!
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OZONE HOLE
The O_3 molecules at the stratospheric/mesospheric boundary
project us from solar UV.
But a decent fraction of them, particularly over the
polar regions, have been destroyed
by the catalytic
action of CCFs (chloroflurocarbons -- refrigerants like Freon
and spray can propellants).
The manufacture of these have been banned by a global treaty,
and the amount of CCFs
in the atm has been dropping, so
this problem is likely to go away -- in another 50 years or
so --
since the CCFs survive a long time up there.
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