Published on November 13, 2007
LECTURE – 2 : LECTURE – 2 SHAPE and ROTATION of the EARTH Shape of the Earth Rotation of the Earth Major Features of the Continents Major Features of the Oceanic Basins Shape of the Earth: Shape of the Earth SPHEROID is an oblate ellipsoid of revolution used to approximate the Earth’s shape assuming that the Earth is in hydrostatic equilibrium. It gives the best fit to the sea-level surface. The shape of the spheroid is defined by its flattening. Equatorial radius (a)=6378.140 km Polar radius (b)=6356.755 km Average radius (r) 6371 km Flattening (a-b/a)=1/298.257 Presently, the Earth’s shape can be determined by the radar ranging from satellites. GEOID is the sea-level equipotential surface to which the direction of gravity is everywhere perpendicular. a) The Earth’s equatorial bulge makes the orbit of an eastward moving artifical satellite regress towards the west. b) Height of the geoid (solid line) relative to a spheroid of flatening 1/298.25 (broken line) assuming the Earth to be axially symmetrical about the polar axis (Bott, 1982, p 3).: a) The Earth’s equatorial bulge makes the orbit of an eastward moving artifical satellite regress towards the west. b) Height of the geoid (solid line) relative to a spheroid of flatening 1/298.25 (broken line) assuming the Earth to be axially symmetrical about the polar axis (Bott, 1982, p 3). Slide4: Flatening (f): 1643-1727 Isaac Newton f=1/230 (based on homogeneous density assumptions and calculations) 1959 Jeffreys f=1/297.3 (from gravity measurements) 1976 Moritz f=1/298.257 (from satellite orbital variations) GEOID is at the sea level on ocean and above the sea level on continent. SPHEROID is above the geoid on ocean and below the geoid on continent. Forces acting on a planet: Forces acting on a planet Forces operating between the material bodies are (Smith,1981 and Bott, 1982): Electromagnetic Gravitational Nuclear The total attraction experienced by any one planet is the vector sum of the individual attractions. A schematic representation of the forces acting on the Earth that will perturbthe rotation and motion (Smith, 1981, p 96): A schematic representation of the forces acting on the Earth that will perturb the rotation and motion (Smith, 1981, p 96) Slide7: Periods Forces Annual Seasonal air mass and ice water shifts 14 months Chandler wobble: random impulses of unknown origin that are damped by the Earth’s elasticity Decade Electromagnetic coupling of the core-mantle boundary Century Variations in the sea level Thousand years Tidal friction Million years Continental drift Amplitudes vary between 1/1000 of a second arc and tens of degrees. Orbital and Spin Motions: Orbital and Spin Motions Forces operating between the material bodies are: Electromagnetic Gravitational Nuclear The total attraction experienced by any one planet is the vector sum of the individual attractions. Orbital Motion: Orbital Motion The Earth moves around the Sun in an elliptical orbit (the ecliptic). Most solar system bodies do not move far out of this plane. The Earth’s instantaneous rotation or spin is about an axis that is inclined to the ecliptic by about 66.5o an angle that remains more or less constant. Therefore, the Earth’s equator is inclined at an equal angle to the ecliptic and this inclination is responsible for the annual seasonal motion of the Sun’s path in the sky as seen from the Earth. The length of year and the eccentricity of the Earth’s orbit are related to the conditions at the time of formation of the planet. The length of the Earth’s day is the consequences of the subsequent dynamic evolution of the Solar System. (Hesser and Leach, 1989): (Hesser and Leach, 1989) Spin Motion: Spin Motion The polar diameter of the Earth is about 43 km shorter than the equatorial diameter. This departure from the radial symmetry causes the Sun and Moon to exert the additional forces (torques) on the Earth, inducing shifts in the position of the rotational axis in space. These shifts are called as the precession and nutation. Rotation of the Earth It is affected by long term and short term periodic and irregular variations: a) changes in the direction of the spin-axis in space (precession and nutation), b) movement of the instantaneous pole of rotation (polar motion), c) changes in the length day resulting from the variation of the rate of rotation. Orbital geometry of the Earth-Moon system (Smith, 1981, p 98): Orbital geometry of the Earth-Moon system (Smith, 1981, p 98) Slide13: Precession An observer on the Earth’s north (or south) pole can view that stars appear to trace out concentric circles whose center defines the celestial north (or south) pole, the extension of the Earth’s rotational axis. The celestial north pole currently lies close to the star Polaris. The position of this celestial pole changes relatively to the stars. The rotation axis is observed slowly to trace out a cone with a half-angle 23.5o about the pole ecliptic. The period of the precession is 25 700 years. This period is used to determine the Earth’s moments of inertia. Slide14: Nutation The Earth’s rotational axis is inclined to the ecliptic.Therefore, the net gravitational force on the Earth due to the Sun does not pass through the center of mass of the Earth. This results in a torque being exerted about the centre. The torque attempts to draw the equator into the plane of the ecliptic but the spinning Earth resists this. As a result, the torque achieves a motion of the spin axis about the pole of the ecliptic. The Moon acts on the Earth in a similar way. These solar torques varies periodically as a result of the irregularities in the orbital motions of the Earth and Moon. The net result is that the secular precessional motion of the rotational axis is perturbed by small oscillations or nodding motions called forced nutations. The principal nutation term has a period of 19 years. The size of the nodding motion is nine seconds of arc. Slide15: The amplitudes of the precessional and nutational motions depend on the oblateness of the Earth and provide information on the internal structure of the Earth. Polar motion A motion of the rotational axis relative to an Earth-fixed reference frame is referred to as polar motion. The motion is made up of 2 periodic oscillations; fourteen-month period, twelve-month period oscillations with amplitudes of the order of 0.1 arc second. They help us to understand the Earth’ s internal structure. The apparent migration of the pole relative to the surface is known as polar wandering. The pole path from 1968 to 1970. The pole positions are given at intervals of 0.05 year. The x axis is directed towards the Greenwich meridian. The origin corresponds to the mean position of the pole for years 1900-5 and the pole now appears to rotate about a mean position that has shifted a total about 0.25 arc second in a direction about 90o west of the Greenwich meridian (Smith, 1981, p 95): The pole path from 1968 to 1970. The pole positions are given at intervals of 0.05 year. The x axis is directed towards the Greenwich meridian. The origin corresponds to the mean position of the pole for years 1900-5 and the pole now appears to rotate about a mean position that has shifted a total about 0.25 arc second in a direction about 90o west of the Greenwich meridian (Smith, 1981, p 95) Slide17: Causes of the oscillations (wobbles) are : large earthquakes or the catastrophic seismic shock the mass distribution (within the Earth and between the Earth and atmosphere, oceans, surface and ground water) resulting in the annual changes in polar motion the exchange of water mass between the polar ice sheets and the oceans and the Earth’s response to the changing load on its surface. Slide18: Changes in the length of day The variations in the rate of rotation of the Earth’s surface cause the changes in the length of day. Astronomers observe the times of transit of a star across their meridian using precise atomic clocks to establish the time scale and this provides a measure of the length of the day. Several of the observed periodic changes in length day are attributable to known meteorological, tidal and other hydrological phenomena. Slide19: Any force that exerts a torque on the Earth’s crust or that results in a redistribution of mass within the Earth, is candidate for perturbing the Earth’s rotation. There is a wide range of phenomena that do this including the secular tidal torques, mantle convection, fluctuations in the magnetic field, relative motions in the core, oceans and atmosphere, the direct attraction of the Sun and Moon and the tidal deformations. Major Features of the Continents(Hamblin and Christiansen, 1998): Major Features of the Continents (Hamblin and Christiansen, 1998) Continents (600 milion years ↑↑ years old): Shield Stable plaform Folded mountain belts Shield (a basement complex) Extensive flat region of a continent (complexely deformed old crystalline rocks are exposed) Low relief (a few hundreds meters of sea level) Resistant rocks (50-100 m above the surroundings) Complex internal structure an complex arrangements of rocks Rocks of the shields were formed several kilometers below the surface Example: Canadian shield of the North American Continent. Slide21: Stable platforms The basement complex covered by the sedimentary rocks Stable for 500-600 million years Nearly horizontal layered sedimentary rocks Example: Western Canada Shield +stable platforms=Craton Folded Mountains Young folded mountains => along the margin of continents Mountain belts => long, linear zone in the Earth’s crust Intensely deformed rocks Example: Appalachian mountains (Plummer and McGeary, 1991): (Plummer and McGeary, 1991) (Hamblin and Christiansen, 1998 ): (Hamblin and Christiansen, 1998 ) Major Features of the Ocean Basins (Hamblin and Christiansen, 1998) : Major Features of the Ocean Basins (Hamblin and Christiansen, 1998) Oceanic area (~ 150 million years old) The oceanic ridge The abyssal floor Seamounts Trenches Continental margins Oceanic ridge Broad fractured rise: 1400 km wide, 300 m higher peaks Rift valley ~ 70 000 km Fracture systems which are perpendicular to the ridge Examples: Atlantic, Pasific, Indian Ocean (Plummer and McGeary, 1991): (Plummer and McGeary, 1991) (Plummer and McGeary, 1991): (Plummer and McGeary, 1991) Slide27: The Abyssal Floor Smooth deep ocean basins 4000 m depth Abyssal Floor=Abyssal Hill + Abyssal Plains Abyssal Hill => 900 m above the surrounding ocean floor (80-85% of sea floor) Trenches The lowest area on the Earth’s surface Deepest part of the ocean => 11 000 m below the sea level Trenches => 8000 m deep Trenches are close to the volcanic chains (island arcs) Most intense volcanic activity and earthquakes Slide28: Seamounts Isolated peaks o submarine volcanoes Island and seamounts ~ extensive volcanic activity ongoing through out the ocean basins Continental margins The transition region between a continent and an oceanic basin The submerged part of a continent ~ continental shelf (11 % of the continental surface) The continental slope marks the edge of the continental rock mass. Examples: North America, South America and Africa Slide29: (Plummer and McGeary, 1991) REFERENCES: REFERENCES Watts, A.B., 2001, Isostasy and Flexure of the lithosphere, Cambridge Univ. Press, p 9-13 (İTU Mustafa İnan Library, QE 511 W38 2001) Plummer, C.C. And McGeary, D., 1991, Phsical Geology, Wm. C. Brown Pub. p 396-407 (İTU Mustafa İnan Library, QE 28.2 .P58) Bott, M. H. P., 1982, The Interior of the Earth: its structure, constitution and evolution, Elsevier, p 1-5, 30-31, 87-88 (İTU Mustafa İnan Library, QE 28.2 .B68) Smith, D.G. , 1981, The Cambridge Encycopedia of Earth Sciences, Cambridge Univ. Press, p 93-102. Hamblin W.K. and Christiansen, E.H., 1998, Earth’s Dynamic System, Brigham Young Univ. Utah, p 1-708 (İTU, Mustafa İnan Library, QE 28.2 H36 1998).