Chapter 5. Structure of the Earth
Recommended Article : 【Earth Science】 Table of Contents
3. Mass and Density of the Earth
1. Shape of the Earth
⑴ Ancient People’s Perceptions of the Earth’s Shape
① Ancient people thought the Earth was flat, believing there were cliffs at the edge of the world.
② Sumerians believed in a round celestial dome on a flat, disk-shaped Earth.
③ Indians thought that a turtle and an elephant supported the Earth.
④ Ancient Egyptians believed it was constructed by gods.
⑵ Ellipsoid
① The actual shape of the Earth : an oblate spheroid with bulging at the equator.
② Evidence of Earth’s roundness
○ Sunrise times get earlier as one travels east.
○ “During a lunar eclipse, the shadow cast on the Moon is round.” - Aristotle
○ Magellan’s successful circumnavigation proved the possibility of returning to the original position by continuous sailing.
○ Ships approaching from the sea to a port become visible from the mast first, while ships moving away from the coast disappear from the bottom.
○ Constellations visible vary with latitude.
○ Polaris (North Star) appears higher above the horizon as latitude increases.
③ Evidence of Earth’s oblateness
○ Distance between two points at latitude 1° increases as latitude goes higher.
○ Clocks with pendulums run faster at higher latitudes, indicating an increase in gravitational force.
④ Reason for Earth’s oblateness : Due to the centrifugal force (inertia) caused by Earth’s rotation.
⑤ Flattening
○ Flattening parameter e: e = 0 for a sphere, 0 < e < 1 for an ellipsoid, e = 1 for a flat plane.
○ Flattening of the Earth: In terms of equatorial radius a and polar radius b.
⑥ Utilization of Geoid : Used for establishing the reference surface for trigonometric measurements, determining Earth’s radius, surface area, volume, flattening, and standard gravity.
⑶ Geoid
① Imaginary mean sea level.
② Surface perpendicular to the direction of gravity.
③ Surface where the potential energy is constant at zero.
④ Reference surface for altitude, i.e., altitude of 0 meters above sea level.
⑤ Varies based on the density distribution underground.
○ Areas with higher density like metallic ores radiate from that region.
○ Areas with lower density like salt formations and petroleum converge towards those regions.
⑥ Utilization of Geoid : Used for establishing the reference surface for leveling measurements and measuring altitudes.
⑷ Comparison between Geoid and Ellipsoid
① Ellipsoid : Reference for trigonometric measurements, geometric surface, no curvature.
② Geoid : Reference for leveling measurements, physical surface, curvature present.
2. Size of the Earth
⑴ Initial Attempt : Eratosthenes
① Assumption 1: Earth is a perfect sphere.
② Assumption 2: Sun’s rays are parallel to Earth’s surface.
③ Premise 1: At noon on the solstice, sunlight shines directly into a well in Syene.
④ Premise 2: At noon on the solstice, the shadow cast by a vertical stick in Alexandria, almost due north, is inclined about 7.2º to the north.
⑤ Premise 3: Distance between Syene and Alexandria: 925 km.
⑥ Measurement of Earth’s circumference.
Figure 1. Measurement of Earth’s circumference
⑦ Sources of error
○ About 15% error.
○ Cause 1: Inaccuracies in latitude, longitude, and distance.
○ Cause 2: Earth is an oblate spheroid.
⑵ Measurement Using Latitude Difference
① Extension of Eratosthenes’ method.
② Proportional relationship
○ 2πR : Distance between two points = 360 : Difference in latitude between two points.
③ Condition : Longitudes should be the same.
⑶ Measurement Using Polar Altitude Difference
① Polar altitude is equal to the latitude of the observation point.
Figure 2. Relationship between polar altitude and latitude
② Measurement using polar altitude difference is similar to measurement using latitude difference.
3. Mass and Density of the Earth
⑴ Mass of the Earth
① Method using a balance scale by Cavendish
○ The scale is in equilibrium, so the gravitational force acting on each side of the balance is equal.
○ For Earth’s radius R⊕, Earth’s mass M⊕, and gravitational constant G:
② Method using gravitational acceleration : Utilizes the equivalence of universal gravitation and gravity.
③ Method using artificial satellites : Utilizes the equivalence of centrifugal force and universal gravitation.
⑵ Density of the Earth
① Average density of the Earth
② Approximate average density of the crust ≒ 2.7 g/cm³
③ Density of materials within the Earth is greater.
Input : 2016.06.22 20:54