Earth 202 The Earth's Interior Winter 2020 Remote version - Seth Stein Leah Salditch James Neely
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Earth 202
The Earth’s Interior
Winter 2020
Remote version
Seth Stein
Leah Salditch
Click for James Neely
audio
Topic 1a 1
Earth & Planetary Sciences 202 - Earth's Interior: On-line version syllabus
https://sites.northwestern.edu/sethstein/courses-and-field-trips/earth-202-earths-interior-remote/
Instructors:
Seth Stein seth@earth.northwestern.edu
Leah Salditch (TA) LeahSalditch2021@u.northwestern.edu
James Neely (TA) JamesNeely2022@u.northwestern.edu
This online version is being used because of the COVID-19 pandemic. It’s an experiment, so things won’t be perfect
and will evolve. We’ll all have to be flexible in this tough time. Still, we can have a good time and learn a lot. If you
encounter difficulties, let us know and we’ll work on them with you.
Topics: Earth’s size, mass, & density, seismic waves; earth structure from seismology; minerals and rocks;
composition of mantle and core;, radiometric age dating; origin of the elements; formation of the solar system;
meteorites, formation of the planets; heat and temperature in the earth; plate tectonics.
Grade: 40% Homework problems, 20% Lecture Questions, 20% Lab problems, 20% Class questions
Lectures are prerecorded, so you can download the powerpoints and watch them at your own convenience and
pace. These include audio and video. You can also download a pdf to print. Contact us if you have difficulties.
We’ll have Zoom meetings at the scheduled time (12:00 - 1:20 central time) Tuesday and Thursdays for discussion of
lecture questions and homework due that day, aspects of the material, and homework help.
You may work (presumably remotely) with other students on the homework problems and class questions, as long as
at the beginning of each assignment you list whom you worked with and on which parts. Computer problems can be
done by writing programs or using Excel, Matlab, or equivalent. Please turn in problems and questions on Canvas.
Topic 1a 2
Topic 1a 3
Planet Earth is a dynamic evolving system - from 4.6 billion years
ago to now – its structure & composition reflect ongoing evolution
COURSE Evolution depends on how heat- "the geological lifeblood of planets" -
THEMES transferred out of cooling earth by thermal convection (hot stuff rises)
Thermal convection causes plate tectonics:
“Elevator Plates of Earth's surface move relative to each other
pitch” at a few mm/yr (about speed fingernails grow)
Plate motions cause earthquakes, volcanos, mountain building
Science at plate boundaries
and
Plate tectonics makes Earth what it is –
society different from neighbor planets, Mars & Venus
Plate motions are crucial for the origin of life, its survival, and our
climate
Plate motions provide resources as well as hazards to society
"Civilization exists by geological consent"
Topic 1a 4
How does Earth work and why does it differ from neighbor planets?
Topic 1a 5
How does Earth work and why does it differ from neighbor planets?
http://www.8planets.co.uk/the-planets
6
Topic 1a 6
Back to the moon? Artemis is the Greek goddess of of the hunt,
wilderness, moon and archery. She is the twin sister of
Apollo and one of the gods who live on Mount
Olympus. She spends much of her time in the forest
12/9/2020
surrounded by animals such as hunting dogs, bears,
and deer. Her powers included perfect aim with the
bow and arrow, the ability to turn herself and others
into animals, healing, disease, and control of nature.
https://www.ducksters.com/history/ancient_greece/artemis.php
NASA’s plan to return astronauts to
the Moon has challenges. Project
Artemis has ambitious goals
including placing “the first woman
and next man” on the Moon by
2024. Aside from the technical
challenges, there’s the question of
budgets. As Apollo taught us,
reaching the moon doesn’t come
cheap! According to NASA, it will
cost taxpayers $28 billion between
2021 and 2025.
https://www.universetoday.com/1480
01/nasas-new-budget-for-artemis-
28-billion/
Click for video
7
Topic 1a 7
Even if the sale proceeds, the politically
Explore & drill for oil in ANWR? charged nature of development in ANWR
makes it hard to imagine many large oil
companies wanting to bid. Bidders are likely
to be small speculators and exploration
firms hoping to acquire leases on the cheap
NY Times and sell them later at a higher price, when
12/7/2020 the political environment changes and
modern seismic data on the potential
resource become available.
More broadly, opposition among
environmentalists means participation
would have serious implications for any
bidders' green credentials because
environmental criteria have become
important for investors, in the US and
worldwide. And successful bidders face the
prospect of being tied up in court for years
by lawsuits brought by environmental
groups. "Any company foolish enough to bid
in this illegal lease sale is bidding on
enormous legal and financial uncertainty,
not to mention a massive public backlash,"
Sierra Club executive director Michael
Brune says.
Click for video
https://www.argusmedia.com/en/news/2166573-
trumps-alaska-gamble-holds-little-appeal-for-
big-oil?backToResults=true
Topic 1a 8
Prepare for tsunami?
https://www.ktvb.com/article/news/local/scientists-say-new-tsunami-zone-building-law-puts-
oregonians-in-danger/283-f8a52a1d-e429-46f7-bc65-157a9d14c48c
Topic 1a 9
Lecture Question LQ 1.1: If you’re given a present
that you’re not allowed to open, what can you do to
try to figure out what’s in box?
Give as many methods as you can
10
Topic 1a 10Probing the interiors of Earth
and other planets
We live on the surface and can
only penetrate by drilling a little
ways. So our studies are indirect.
Seismology uses the travel times and amplitudes of seismic waves to study
variations in seismic wave velocity and density
Geodesy studies the planet’s size and shape
Gravity studies measure variations in density
Magnetic studies give insight into the core's magnetic field
Heat flow measurements at surface gives insight into thermal structure
Together with results from studies of rock properties and other data, develop
models of planet's composition, temperature, and internal processes
Topic 1a 11https://blogs.agu.org/onthejob
/2019/07/22/project-apollo/
Topic 1a 12Landed
November 26, 2018
Click for video
Topic 1a 13Mars 2020 Perseverance Rover Landing February 18, 2021
Studying Mars' habitability, seeking signs of past microbial life, collecting and
caching samples, and preparing for future human missions
Click
for
video
14
Topic 1a 14Mars 2020
Perseverance
Rover
Landing
February 18,
2021
EDL - entry,
descent, and
landing
Seven minutes
of terror
Topic 1a 15Mars 2020 Perseverance Rover Landing February 18, 2021
Landing on Mars is challenging. Only about 40% of missions sent to Mars –
by any space agency - have been successful.
Click
for
video
16
Topic 1a 16Mars 2020 Perseverance Rover Landing February 18, 2021
Searching for life
Click
for
video
Topic 1a 17Loss of Mars Climate Observer Units
Hopefully, better luck this time Matter
https://www.youtube.com/watch?v=urcQAKKAAl0
18
Topic 1a 18Topic 1 – Earth’s shape, size & mass
GPS
Geodesy
studies the
size and
shape of
Earth
TOPEX/POSEIDON
19
Topic 1b 19Lecture Question LQ 1.2: How do we know the earth is
approximately a sphere?
Give as many lines of evidence as you can
20
Topic 1b 20How large is Earth?
How can we measure it?
In a famous
4) During aerror, Columbus
lunar eclipse used
– all shadows castaon moon by the earth
are arcs of circles
too-small value for the number of km in a
degree, which convinced him the earth was
much smaller than it really was, making it
only a few weeks sail from Europe to Asia
https://spectrum.ieee.org/tech-talk/at-work/test-and-measurement/columbuss-geographical-miscalculations
21
Topic 1b 21However, long before (200 BC) Eratosthenes
measured the earth’s radius using the sun’s
elevation on the same day in two places
The sun cast its shadow into a well in Syene (now Aswan), but made an
angle of 7 degrees and 12 minutes with the vertical at Alexandria (Egypt),
5000 stadia (the unit that became our “stadium”) away
5000 statida /circumference
= 7 degrees 12 minutes/360 degrees
circumference = 250,000 stadia =
46,250 km = 2p radius
This gives radius = 7361 km,
close to the modern value = 6371 km
http://mathandmul
timedia.com/2010
This, together with the length of the day (24 hrs) and year (365 /11/22/eratosthen
es-and-the-
days) are the first important earth parameters to be determined. earth’s-
Note that these must be derived from observations! circumference/
22
Topic 1b 22Earth’s mass, density, and moment of inertia
To learn what the earth is made of, our first constraint is its
density = mass / volume ρ = M/V
The universal law of gravity says that the force F between
objects M and m a distance r apart is given by the inverse square law
F = GMm / r 2
From experiments, the gravitational constant
G = 6.67 x 10-8 dyne-cm 2 / gm 2 = 6.67 x 10-11 N-m2 / kg 2
23
Topic 1b 23m
Consider a small object with mass m
at the earth’s surface (radius r)
Using Newton’s second law that force F = m a = mass times acceleration
Using Newton’s second law that force
F = ma = mass times acceleration
The acceleration of gravity at
the surface, g , is
g = F / m = GM / r 2
We measure g = 980 cm/sec2 = 9.8 m/sec2
Solving for Earth’s mass gives M = 5.95 x 1024 kg
24
Topic 1b 24Do objects with different
masses fall at the same
speed? Or is that "fake
news”? Apollo 14 tried it
Click for video
Lecture Question LQ 1.3:
a) Show, using the results from the previous slide, that objects
with different masses should fall at the same speed
b) How would the results of the moon experiment differ on Earth?
25
Topic 1a 25Another method of finding Earth’s mass
To check the result, use rotation period of a satellite about earth. For
an object in circular orbit with radius r, the centripetal acceleration
that accelerates inward
and keeps the satellite in orbit is v 2 / r
The force causing this is gravity, so from F = ma
F = GmM / r 2 = mv 2 / r
So Earth’s mass is M = r v 2 / G
Find the speed v of the satellite,
from the period that it takes for one orbit, T = 2 pr / v
M = r (2pr / T )2/ G = r3 (2p / T ) 2/ G
How did people use this method even before
artificial satellites (1957)?
26
Topic 1b 26Assume the moon is in circular orbit. First, we need the radius of
the moon’s orbit about the earth. This has been known since
Ptolemy (140 AD) used his knowledge of earth’s radius
Measure the angle from vertical ϴ to the moon, at a site an angular distance ɸ from
another site at where the moon is overhead
Given the earth’s radius R, we have two angles of a triangle and one side, so the
distance can be found. Ptolemy estimated the distance to the moon as 59 times
earth’s radius 59 x 6371 = 375,889 km. This was a good estimate, because the
modern value = 384,405 km.
Hence the radius of the orbit r = 3.84 x 105 km = 3.84 x 108 m
and the period T = 27.3 days = 2.36 x 106 sec give the mass
M = 6.1 x 1024 kg , which agrees with our earlier result.
This analysis involves being careful with the units!
27
Topic 1b 27Now, let’s find Earth’s average (mean) density
ρ = M / V = M / [ (4/ 3) p R 3 ] = 5.5 gm/cm3
Surface rocks have density 2.8 to 3.5 gm/cm3
So the interior is on the average denser
due, as we will see, to a dense core.
This analysis only gets us so far.
Since we don’t know if all the
mass is near the surface or at depth,
any distribution with the same total
mass will work.
Could Earth be hollow?
28
Topic 1b 28Moment of inertia
Another constraint comes from the earth’s moment of inertia.
Remember that for linear motion
momentum = (mass) (velocity) = mv
Similarly, rotating bodies have
angular momentum = (moment of inertia) (angular velocity) L=I ⍵
Just as linear velocity gives the change in position per unit time dx/dt
angular velocity or rotation rate is the change in angle per unit time
⍵ = dϴ/dt
Similarly, just as mass measures
an object’s resistance to acceleration,
its moment of inertia I shows how
hard it is to get it rotating https://xaktly.com/Angu
larVelocity.html
29
Topic 1b 29To find the moment of inertia, I
We consider a body to be made up of volumes dVi with masses mi
and sum (or integrate) them weighted by their
perpendicular distance li from the rotation axis
I = Σ m i (li ) 2 = ∫ ρ(r ) l(r)2 dv
Stein & Wysession
Angular momentum = (moment of inertia) (angular velocity) L=I⍵
Is conserved
A skater pulls in their arms, giving a smaller moment of inertia, so ⍵ increases
30
Topic 1b 30The moment of inertia ratio I /Mr2,
where r is the planet’s radius and M is its mass,
depends on the density distribution
If a planet is homogenous (uniform density), I /Mr 2 = 0.4
If all the mass is on the outside, I /Mr2 = 0.667
The moment of inertia is higher, for the same mass,
because material is further from the rotation axis.
Smaller I /Mr 2 shows more mass concentrated in center
For a two layer planet with a mantle of ρ = 5 gm/cm3
and a denser core with ρ = 10 gm/cm3 whose
radius is 0.55 that of the entire planet, I/ Mr2 = 0.36
Earth I /Mr 2 = 0. 33 due to the dense core.
Moon I /Mr2 = 0. 395, so it’s close to homogenous
Saturn I /Mr2 = 0.22, much denser at center
Sun I /Mr2 = 0.06, very much denser at center.
We’ll see why these occur later.
31
Topic 1b 31You can also read
