Condensed Lecture Notes 18-26

# Condensed Lecture - LECTURE 18 GRAVITY AND MOUNTAINS The force of gravity causes every particle that has mass to attract every other particle As

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LECTURE 18: GRAVITY AND MOUNTAINS The force of gravity causes every particle that has mass to attract every other particle. As the amount of mass increases, the gravitational attraction in creases. As the distance between the particles increases, the gravitational attraction de creases. To describe the attractive force between bodies composed of many particles (for example, gravitative force between your body and the earth), it is convenient to think of all of the mass to be located at a single point – the object’s “center of gravity.” For example, the earth’s center of gravity lies at its physical center. The mathematical expression is: Force of gravity is proportional to m 1 m 2 / r 2 , where m 1 and m 2 are two masses, and r is the distance between their centers of gravity. We may describe the shape of the earth by a series of approximations. To a first approximation the earth is a sphere . Even if it had not started out with a spherical shape, it would have become a sphere as every particle tries to get as close as possible to the center of the earth (its center of gravity). This implies that the shape of the earth can change; the earth can deform, which implies further that rocks in the deep interior, although solid and under very high pressure, do not have much strength. On a short time scale, a rock acts as a brittle material ; it shatters when hit by a hammer or it ruptures by fault action. On a long time scale of thousands of years or longer, rock acts as a ductile material ; it flows just as a ball of silly putty flattens under its own weight. (On a short time scale, silly putty also acts as a brittle material. If you throw a ball of silly putty at a hard surface, it bounces; if you abruptly stretch the silly putty it breaks apart.) Secondly, the spherical earth is rotating, which draws the equatorial region outward into a bulge while the polar regions are flattened. A sphere, and the modified shape of a rotating earth, the spheroid , are smooth surfaces described by simple mathematical expressions. If you were standing at sea level on the Equator, you would weigh less than if you were standing at the North Pole. This is because (i) the earth’s equatorial radius is larger than polar radius (at the Equator there is a greater distance between you and the earth’s center), and because (ii) the daily rotation tends slightly to “levitate” you away from the earth at the Equator, but not at the North Pole. Thirdly, the spheroid is the basis for a further approximation, an irregular shape with depressions and humps, the geoid . Sea level describes the shape of the geoid. Because each water molecule is able freely to seek the lowest possible elevation, the sea surface is level . (It is not flat ; it wraps around the globe!) Sea level in the interior of a continent could be determined in principle by digging a slot canal to that spot, and connected to the world ocean at the other end. The ups and downs of the geoid are not well understood, as they are the result of uneven distribution of mass (and associated gravity field) very

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## This note was uploaded on 11/03/2010 for the course GEO 26750 taught by Professor Kocurek during the Spring '10 term at University of Texas at Austin.

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Condensed Lecture - LECTURE 18 GRAVITY AND MOUNTAINS The force of gravity causes every particle that has mass to attract every other particle As

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