measuring gravity quiz

gravity methods

measures the strength of the gravitational field of the Earth

Lateral variations in density

give rise to the spatail variations in the field

Potential Field

strength and direction of field depends on position of observation within the field, for gravity field, lines of are directed toward the center of the earth

Newtons Law of Universal Gravitation

states that there isa. force of attraction F between two particles with masses mi and m2 seperated by distance r that is represented by

F= G x m1m2/r² or F= G x mMe/Re² if we assume spherical earth with uniform density distrubution

little g, Earth’s gravitational acceleration

F=ma when a is caused by the gravitational attraction of Earth F=mg = G x mME/Re² or g = GMe/Re²

Challenge #1

earth is not stationary, it rotates, result: earth not round but bulges at equator and is flattened at the poles

Equatorial Radius (6378 km) is 21 kilometers greater than at the poles (6357 km)

Earth’s mass is —

not symmetetrical about the equatarioal plane, therefore earth is pear shaped

the shape of the earth is. aconsequence because

of the balance beteen gravitational and centrifugal acelerations resulting in OBLATE SPHEROID

gravity varies as a function of latitude, therefore

gravity is greater at poles than at the equator (5186 mGal)

why is gravity greater at poles than at the equator

points at the poles are closer to the center of the earth than at the equator, centrifugal acceleration is greater at the equator than at poles, earth’s rotation

A- Effect if Centrifugal Force

during the rotation of the Earth (f acts in direction opposite to gravity), reduces the measured value of g at the equator, diminishes to zero at the poles

gpoles- gequator= 3.4 gals

B- Distance Factor

the earth’s rotation causes its shape to be an ellipsodial revolution, flattened at the poles and bulged at the equator, earth’s radius is greater at the equator than the poles, the surface is close to the center of the earth at the poles than at the equator

gpoles-gequator=6.6 gals

C- Mass Factor

because of the larger radius length at the equator than at the poles, more mass is positioned between the surface and center of the earth at the equator than at the poles

gequator-gpoles=4.8 gals

the combined effect of rotation, distance, and the mass factor

gpoles-gequator=5.2 gals

gpoles=983.2gals

gequator=987.0 gals

Reference Ellipsoid

an imaginary, regular surface that corresponds to the true gross shape of the earth and it coincides closely (not exactly) with sea level over open oceans

Geoid

the surface passing through the sea level surface around the world. this surface contains broad undulations that are minor compared to the over all dimensions. the regular surface which most nearly approximates the surface of the actual Earth

On land, the geoid is the surface that would be determined by

the level to which water would rise in narrow canals cut through the continents

the geoid is an equipotential surface which means

gravitational field has equal value

under continents, geoid heights are

larger than ellipsodial heights

under oceans, geoid heights are

less than ellipsodial heights

absolute gravity

actual gravitational acceleration at a specific location

relative gravity

the difference in gravity between two observation stations

Period

the amount of time it takes to complete one swing cycle, T for an ideal oendelium with a constant I. T=2pi square root over I/g

the difference in. gat two observations stations A and B is

deltag= gobsA-gobsB

Zero length spring

a spring is zero length only if a plots force versus length extrapolates back to zero force at zero length

The Falling Body Method

measures the amount of time it takes an object to fall a distance z, z=o.5xgxt²

density

important physical property investigated in gravity surveying

Factors influencing rock density

• unconsolidated sediments: composition, porosity saturation

• sedimentary rocks: composition, age and depth of burial (compaction), cementation, porosity pore fluid

• Igenous Rocks: composition(silica content), fracturaing (porosity)

porosity and pore fluid content are

probably the most important factors affecting density in the shallow subsurface

sedimentary rocks

have the lowest densities

igneous rocks densities

vary according to composition - silica content, decreasing with increasing silica content

metamorphic rock densities

vary with grade of metamorphism incresding with grade of metamorphism

most accurately determined by direct measurements of densities of

unweathered rocks