Chapter 7. Earth’s Field
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1. Overview
2. Earth’s Gravitational Field
a. Calculation of Latitude and Longitude of High Point Stimulation
1. Overview
⑴ Earth’s field : Flow of Earth’s forces
⑵ Fields are divided into gravitational and magnetic fields
2. Earth’s Gravitational Field
⑴ Gravity
① Definition of gravity : Sum of the universal force towards the center of the Earth and the centrifugal force due to Earth’s rotation that objects on Earth receive
② Universal force F is inversely proportional to the square of the distance between two objects and directly proportional to the product of their masses
○ Gravity is maximum at the poles and minimum at the equator
③ Centrifugal force : f = mrω2 (r : distance from the axis of rotation, ω : angular velocity of Earth’s rotation)
○ Centrifugal force is zero at the poles and maximum at the equator
④ Direction of gravity : Toward the center of the Earth at the equator and poles, not toward the center at other places
⑵ Measurement of gravity
① Using gravimeter : Using a sensitive plumb line balance
② Use of pendulum method : The period of a pendulum with length ℓ is as follows
③ Measurement of universal gravitational constant : Measured for the first time by the Cavendish experiment
Figure. 1. Cavendish Experiment
⑶ Gravitational acceleration
① Surface gravitational acceleration
○ Small-scale movements on the Earth’s surface have constant gravity due to nearly constant distance between objects and the Earth
○ Gravitational acceleration varies locally due to differences in underground density and equatorial centrifugal force
② Gravitational acceleration in the atmosphere
③ Gravitational acceleration within the Earth
○ When calculating gravitational acceleration within the Earth, the outer shell beyond a specific point doesn’t have an effect (∵ principle of similarity)
Figure. 2. Gravitational Acceleration Inside Earth and Shell
○ Assuming constant Earth density, gravitational acceleration is proportional to the distance from the Earth’s center
④ Actual profile of Earth’s gravitational acceleration
Figure. 3. Actual Profile of Earth’s Gravitational Acceleration
⑤ Gravity on the Earth’s surface is 6 times that on the Moon’s surface
⑷ Anomalies in gravity
① Standard gravity : Theoretical value calculated for a uniform ellipsoid closest to the geoid with the same mass as the actual Earth, as a function of latitude (Φ)
② Gravity anomaly = Measured gravity - Standard gravity
○ Positive gravity anomaly : Presence of high-density materials (e.g., iron ore, basalt)
○ Negative gravity anomaly : Presence of low-density materials (e.g., petroleum, halite)
③ Correctional gravity : Gravity on a flat terrain on the geoid
④ Bouguer anomaly = Correctional gravity - Standard gravity
○ Bouguer anomaly appears due to differences in underground material density
○ (+) value in regions with high underground density (mainly ocean), (-) value in regions with low underground density (mainly land)
⑤ Distribution of gravity anomalies : Also called “Potato Model” of gravity anomalies
Figure. 4. Potato Model of Gravity Anomalies
⑸ Role of Gravity
① Forms in the contraction of cold interstellar material → Energy source in Earth’s early formation
⑹ Isostasy
① Theory that low-density lithospheres float on high-density mantle while maintaining equilibrium
② In this equilibrium process, compensatory movement occurs
③ Theory 1. Pratt’s hypothesis : Different lithospheric densities with the same Moho depth. (Note) Remember as “flat”
④ Theory 2. Airy’s hypothesis : Same lithospheric density with different Moho depths
Figure. 5. Comparison of Pratt’s and Airy’s Hypotheses
⑤ Actual lithosphere fits with Airy’s hypothesis since it’s divided into continental and oceanic lithospheres, and Pratt’s hypothesis applies to each lithosphere
Figure. 6. Isostasy in Actual Lithosphere
⑺ Motion of Artificial Satellites
① First cosmic velocity : Velocity required for circular motion just above Earth’s surface. About 7.9 km/s
② Second cosmic velocity : Escape velocity required to leave Earth’s gravitational field from its surface. About 11.2 km/s
③ Third cosmic velocity : Escape velocity required to leave the solar system from Earth’s surface. About 16.7 km/s
④ Geostationary satellites
○ Geostationary satellites : Those with an orbital period matching Earth’s rotation period. Otherwise called non-geostationary satellites
○ Geostationary satellites remain fixed over the same point on Earth’s surface
3. Earth’s Magnetic Field
⑴ Overview : Earth can be considered as a magnetic dipole with its South Pole at the geographic North
⑵ Three Elements of Earth’s Magnetism
Figure. 7. Three Elements of Earth’s Magnetism
① Declination (Magnetic Azimuth) : Represented by α
○ The angle formed by the direction of magnetic north (needle’s north) with respect to true north (geographic north)
○ Positive when the needle’s north points east, negative when it points west
② Inclination : Represented by β
○ Angle formed by the inclination of the magnetic needle to the horizontal plane. Also known as the angle between the horizontal magnetic force and the vertical magnetic force
○ Magnetic dip : 0°, North Pole : +90°
○ Increases with latitude
Figure. 8. Inclination Based on Latitude
Arrows point to the geographic North, which is the South Pole of the magnetic dipole
③ Horizontal magnetic force : Represented as A or H
○ Horizontal component of Earth’s magnetic force
○ Maximum at the magnetic equator
○ Horizontal magnetic force H = F cos I, I : Inclination
○ Vertical magnetic force V = F sin I, I : Inclination
⑶ Variations in Earth’s Magnetic Field
① Present Earth’s magnetic field : 2.0 × 10-5 T
② Secular variation : Gradual change in Earth’s magnetic field due to changes in Earth’s interior
○ No periodicity
○ Normal and reversed polarity
Figure. 9. Magnetic Field Lines Profile during Reversed Polarity
Note: Consider that geographic North is the magnetic South
○ Magnetic anomalies measured near the Wrangel Island region
Figure. 10. Magnetic Anomalies Measured near Wrangel Island Region
③ Diurnal variation : Variations in Earth’s magnetic field due to changes in the Sun’s altitude
○ More prominent during daylight than nighttime
④ Magnetic storms : Sudden and rapid changes in Earth’s magnetic field that occur irregularly over several hours to 2-3 days due to solar flares
○ Accompanied by the phenomenon of auroras and the Van Allen belts
⑤ Aurora Phenomenon (aurora)
○ Fluorescent phenomenon caused when electrons and ions previously present in solar winds excite atmospheric particles, which emit light afterward
○ Electrons or ions experience a perpendicular Lorentz force to their velocity and magnetic field, resulting in their spiraling path
Figure. 11. Trajectory of Electrons or Ions Generating Aurora
⑷ Causes of Earth’s Magnetism and Van Allen Belts
① Dynamo Theory : Theory that currents generated by the motion of the outer core produce the Earth’s magnetic field
○ (Note) Circular loop of current : Iron ions (Fe2+) do not rotate due to Earth’s rotation, so a North Pole bar magnet is not formed
○ Coriolis force and convection lead to the creation of a South Pole bar magnet (considering geographic North as magnetic South)
Figure. 12. Actual Movement of Fe2+[Note:7]
② Causes of Earth’s magnetic field variations
○ Internal cause : Causes secular variation due to changes in Earth’s interior
○ External cause : Causes diurnal variation, magnetic storms, auroras, etc., due to changes in solar activity
③ Van Allen belts
○ Belt-shaped regions that block solar winds and cosmic rays
○ Inner radiation belt (Internal cause) : Composed mainly of protons, located at around 3,000 km above the Earth’s surface
○ Outer radiation belt (External cause) : Composed mainly of electrons, located at around 15,000 km above the Earth’s surface
Input : 2019.08.16 22:36