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Weighing Earth

Weighing Earth. 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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Weighing Earth

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  1. Weighing Earth

  2. 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)

  3. 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

  5. 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/

  6. 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/

  7. 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 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/

  8. Newton’s 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)

  9. 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 ...

  10. A brief history of gravity • 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) http://library.thinkquest.org/27585/history/

  11. Kepler’s Third Law T2 = A r3 M 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

  12. Kepler’s Third Law T2 = A r3 M 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/A]1/3 = 4.22x107 m = 42,400 km Height of orbit = 42400 - RE = 35700 km

  13. 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

  14. 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

  15. 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

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