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Look Up? (Astronomy) Three Worlds to Explore Look at Surface? (Geology) Look Down? (Geophysics) Deep wells and boreholes (4 to 12 km) The Earth’s Interior Astronomical Observations The Earth: What’s it made of? Gravity Seismology N S Magnetism Heat Flow Density of Water 1 gm/cm3 Mantle 3.3-5.7 gm/cm3 Outer Core 10-12 gm/cm3 Crust 2.6-3.1 gm/cm3 Inner Core 13-14 gm/cm3 P and S Wave Paths Relatively simple experiment to estimate some basic properties of the Earth’s interior: Mass = M Radius = R Average Density = D Rough Estimate of Variation of Density in Interior Newton’s Law of Gravitation r F M F m Force of attraction (F) is proportional to the masses, and is inversely proportional to the square of the distances between the masses. Newton’s Law of Gravitation r F F M Mm F = G r2 m Henry Cavendish (1731-1810) determined the universal constant of gravitation G in 1798. torsion fiber massive lead spheres F m R Mm F = G 2 R M F R2 M = Gm F m ? R Measure the force M 2 FR M = Gm Can measure in lab If we could measure R, we could determine M. Use a known mass How can we measure R? Greek Scientist: Eratosthenes (276-194 BCE) Eratosthenes (276-194 BCE) Observed the angles of the noonday Sun in two Egyptian cities that were roughly north and south of each other. Syene (presently Aswan) and Alexandria Eratosthenes (276-194 BCE) The angles differed by 7 degrees (or 1/50 of a complete circle). Circumference of the Earth must be 50 times the distance between the cities. Eratosthenes (276-194 BCE) The cities are 788 km apart. Circumference of the Earth must be 50 x 788 km = 39,400 km R = 39,400/2p = 6,271 km (modern value = 6,371 km) Astronomical Observations The Earth: What’s it made of? Gravity Seismology N S Magnetism Heat Flow F m R M Eratosthenes Measure the force 2 FR M = Gm Can measure in lab Use a known mass M = 6x1027 gm = 6,000,000,000,000,000,000,000,000,000 gm 4 3 Volume = pR 3 R M Mass Density = Volume Average Density = 5.5 gm/cm3 Average density of the Earth = 5.5 gm/cm3 Dense Material? Average density of crustal rocks = 2.7 gm/cm3 Density must increase with depth. Density must increase with depth. But, how can we obtain a more detailed picture of the variation of density with depth? Dense Material? Astronomical Observations Earth’s axis of rotation points towards different stars at different times. Gravitational forces from the Sun and the Moon cause the Earth to twist and turn in its orbit around the Sun. “Precession” of the Earth causes the North Pole to point to different parts of the sky during a 26,000 year cycle. “Precession” of the Earth is similar to the motion of a spinning top. From precession of the Earth it is possible to measure the moment of inertia of the Earth. Moment of inertia is a measure of how hard it is to twist an object. Moment of inertia is a measure of how hard it is to twist an object. The more that the mass is concentrated towards the center of an object, the easier it is to twist the object. Higher moment of inertia Lower moment of inertia Density of Water 1 gm/cm3 Mantle 3.5-5.7 gm/cm3 Outer Core 10-12 gm/cm3 Crust 2.6-3.1 gm/cm3 Inner Core 13-14 gm/cm3 Astronomical Observations The Earth: What’s it made of? Gravity Seismology N S Magnetism Heat Flow Earthquake in Japan Magnitude 8.0 September 25, 2003 19:50 UTC Izmit Turkey Seismogram P and S Wave Paths