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Weighing Earth

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Announcements & Reminders 1. ES 123 Essay: Due Friday November 24, 3:00 p.m. (B&GS 10) 2. Lab final: Tuesday December 5, 10:30 - 11:20 a.m. room NS-145 3. Course final: Saturday December 9, 2:00 - 4:00 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.

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Essay Marking Scheme Style, Format, Grammar, Research, Clarity

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

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

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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 Kepler’s 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/ A brief history of gravity

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Newton’s Universal Law of Gravitation F = GMm r2r2 F = Force of gravity (in Newtons, of course) G = Universal Gravitational Constant = 6.67x10 -11 N-m 2 /kg 2 M,m = masses of two objects (kg) r = distance between the two objects (m)

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Gravitational Acceleration g = GM r2r2 Using this formula, we can weigh Earth! (g = 9.80 m/s 2, r = 6.38x10 6 m) M = r 2 g/G = 5.98x10 24 kg … OK, but not so easy for other planets...

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Gravity: Version 2 ! Einstein’s 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) A brief history of gravity http://library.thinkquest.org/27585/history/

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T 2 = A r 3 M T = orbital period, in seconds r = average radius of orbit A = 5.92x10 11 s 2 -kg/m 3 Kepler’s Third Law Sample calculation 1: Mass of the Sun T = 365x24x3600 = 3.15x10 7 s r = 1.50x10 11 m M = Ar 3 /T 2 = 2.01x10 30 kg

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T 2 = A r 3 M T = orbital period, in seconds r = average radius of orbit A = 5.92x10 11 s 2 -kg/m 3 Kepler’s Third Law Sample calculation 2: Geostationary orbit T = 24x3600 = 86400 s M E = 5.98x10 24 kg r = [M E T 2 /A] 1/3 = 4.22x10 7 m = 42,400 km Height of orbit = 42400 - R E = 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 NA Mid-continent rift: Gravity anomaly ! Units of gravitational acceleration: 1 Gal = 1 cm/s 2 ! Typical unit for gravity maps: mGal = 10 -5 m/s 2

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