Earth: Shaken and Stirred Our Dynamic Planet

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Weighing Earth
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Announcements Reminders
1. ES 123 Essay Due Friday November 24, 300
p.m. (BGS 10) 2. Lab final Tuesday December 5,
1030 - 1120 a.m. room NS-145 3. Course final
Saturday December 9, 200 - 400 p.m. NS-1
FORMAT Multiple choice (45 questions)
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Proposed Change to Course Marking Scheme

• Either the original marking scheme, or
• ES 023 final exam 75
• ES 123 final exam 65 ... whichever is
  higher.

4
Essay Marking Scheme
Style, Format, Grammar, Research, Clarity
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A brief history of gravity

• Too Much Thinking, Too Few Facts
• Four basic elements - earth, water, air, and
  fire.
• Objects move toward their own elemental sphere -
  e.g., rocks fall to earth.
• Proof, he claimed, that heavier objects fall
  faster than lighter ones.

Aristotle (384 BC-322 BC).
http//library.thinkquest.org/27585/history/
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A brief history of gravity

• New Ideas, Old Observations
• Nicolaus Copernicus proposed that Earth orbits
  the Sun (with the rest of the planets).
• Legend says that Galileo disproved Aristotle by
  dropping two weights from the leaning tower of
  Pisa.
• Johannes Kepler (1571 AD-1630 AD) discovered
  three laws of planetary motion.

Nicolaus Copernicus (1473 AD-1543 AD).
Galileo Galilei (1561 AD-1642 AD)
http//library.thinkquest.org/27585/history/
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A brief history of gravity

• A Man, an Apple, and a New Theory
• Legend says that Newton was struck on the head
  by a falling apple, prompting his ideas on
  gravity.
• Based on Keplers laws, Newton formulated the
  Universal Law of Gravitation
• Published in 1687 in Philosophiae Naturalis
  Principia Mathematica, or simply Principia.

Sir Isaac Newton (1643 AD-1727 AD)
http//library.thinkquest.org/27585/history/
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Newtons Universal Law of Gravitation
F GMm
r2
F Force of gravity (in Newtons, of course) G
Universal Gravitational Constant 6.67x10-11
N-m2/kg2 M,m masses of two objects (kg) r
distance between the two objects (m)
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Gravitational Acceleration
g GM
r2
Using this formula, we can weigh Earth! (g
9.80 m/s2, r 6.38x106 m) M r2g/G
5.98x1024 kg
OK, but not so easy for other planets ...
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A brief history of gravity

• Gravity Version 2
• Einsteins General Theory of Relativity (GTR)
  again changed our view about gravity.
• GTR predicts black holes, slowing down of time
  bending of light by a gravitational field.
• The predicted bending of light by the sun was
  observed in 1919.

Albert Einstein (1879 AD-1955 AD)
http//library.thinkquest.org/27585/history/
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Keplers Third Law
T orbital period, in seconds r average radius
of orbit A 5.92x1011 s2-kg/m3
Sample calculation 1 Mass of the Sun T
365x24x3600 3.15x107 s r 1.50x1011 m M
Ar3/T2 2.01x1030 kg
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Keplers Third Law
T orbital period, in seconds r average radius
of orbit A 5.92x1011 s2-kg/m3
Sample calculation 2 Geostationary orbit T
24x3600 86400 s ME 5.98x1024 kg r
MET2/A1/3 4.22x107 m 42,400 km Height of
orbit 42400 - RE 35700 km
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Measuring g Exploration Geophysics

• Absolute g can be measured accurately in the
  laboratory using pendulums
• In the field, relative g can be measured using a
  gravimeter
• Spatial variations in g can be used to map
  subsurface geology

Worden gravimeter
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Measuring g Exploration Geophysics

• Gravity data reduction removes the effects of
• Earth rotation and ellipsoidal shape, using the
  International Gravity Formula
• Instrument drift
• Elevation, using the Bouguer and Free Air
  corrections
• Local topography, using the Terrain correction

Worden gravimeter
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Measuring g Exploration Geophysics

• Units of gravitational acceleration
• 1 Gal 1 cm/s2
• Typical unit for gravity maps
• mGal 10-5 m/s2

NA Mid-continent rift Gravity anomaly