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Earth's gravity is the net acceleration resulting from the combined effects of gravitation and the centrifugal force from its rotation.
Answer: True
Explanation: Earth's gravitational acceleration is indeed the resultant vector sum of the gravitational attraction due to its mass distribution and the centrifugal force arising from its rotation.
An object's weight is calculated as mass multiplied by gravitational acceleration, but is also affected by centrifugal force.
Answer: True
Explanation: Weight is indeed the product of mass and gravitational acceleration (W=mg). The apparent weight can be influenced by other forces, such as the centrifugal force resulting from Earth's rotation.
The gravitational pull of the Moon and Sun are considered primary factors affecting an object's weight on Earth's surface, alongside Earth's rotation.
Answer: False
Explanation: While the gravitational pull of the Moon and Sun cause tidal effects, they are typically considered secondary influences on an object's weight compared to Earth's own gravity and rotation. The primary factors affecting weight on Earth's surface are Earth's gravity and the centrifugal force from its rotation.
The gravitational pull of the Moon and Sun are considered primary factors affecting an object's weight on Earth's surface, alongside Earth's rotation.
Answer: False
Explanation: While the gravitational pull of the Moon and Sun cause tidal effects, they are typically considered secondary influences on an object's weight compared to Earth's own gravity and rotation. The primary factors affecting weight on Earth's surface are Earth's gravity and the centrifugal force from its rotation.
The formula g = G * M_earth / r² estimates Earth's gravity but does not account for the Earth's rotation or non-uniform density.
Answer: True
Explanation: The fundamental formula g = G * M_earth / r² provides a foundational estimate of gravitational acceleration based on universal gravitation. However, it inherently assumes a point mass or uniform sphere and does not account for the complexities of Earth's rotation (centrifugal force) or its non-uniform internal density distribution.
What are the two primary forces that contribute to Earth's gravity?
Answer: Gravitation and the centrifugal force from Earth's rotation
Explanation: Earth's gravitational acceleration is the resultant vector sum of the gravitational attraction due to its mass distribution and the centrifugal force arising from its rotation.
Besides gravitational acceleration and mass, what other factor influences an object's weight on Earth?
Answer: Centrifugal force from Earth's rotation
Explanation: Weight is the product of mass and gravitational acceleration (W=mg). The apparent weight can be influenced by other forces, such as the centrifugal force resulting from Earth's rotation.
What does the formula g = G * M_earth / r² estimate, and what factors does it initially ignore?
Answer: Earth's gravity; rotation and non-uniform density.
Explanation: The fundamental formula g = G * M_earth / r² provides a foundational estimate of gravitational acceleration based on universal gravitation. However, it inherently assumes a point mass or uniform sphere and does not account for the complexities of Earth's rotation (centrifugal force) or its non-uniform internal density distribution.
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Earth's gravity is measured in units of kilograms per second squared (kg/s²).
Answer: False
Explanation: The standard units for measuring gravitational acceleration are meters per second squared (m/s²) or, equivalently, newtons per kilogram (N/kg), not kilograms per second squared.
The conventional value for standard gravity, 9.80665 m/s², is the precise gravitational acceleration measured at Earth's equator.
Answer: False
Explanation: The value of 9.80665 m/s² represents a conventional standard for gravity, established for consistency in measurements and definitions, rather than the precise gravitational acceleration found at Earth's equator, which is slightly lower.
The formula g_h = g_0 * (R_e / (R_e + h))² approximates the variation of Earth's gravity with depth inside the Earth.
Answer: False
Explanation: This formula, g_h = g_0 * (R_e / (R_e + h))², is specifically used to approximate the variation of Earth's gravity with *altitude* (h) above the surface, not with depth inside the Earth.
Gravimeters are instruments used to measure gravitational fluctuations.
Answer: True
Explanation: Gravimeters are indeed highly sensitive instruments employed in gravimetry to measure minute variations in the Earth's gravitational field.
The International Gravity Formula 1967 (Helmert's equation) estimates sea-level gravity based on latitude.
Answer: True
Explanation: The International Gravity Formula 1967, also known as Helmert's equation, provides a standard mathematical model used to estimate the acceleration due to gravity at sea level as a function of latitude.
The WGS 84 gravity formula utilizes Earth's equatorial semi-axis but does not require the polar semi-axis for its calculations.
Answer: False
Explanation: The WGS 84 gravity formula, like other geodetic gravity models, requires both the Earth's equatorial semi-axis (a) and its polar semi-axis (b) to accurately calculate gravity as a function of latitude.
Gravimetry is the scientific term for measuring the Earth's magnetic field.
Answer: False
Explanation: Gravimetry is the scientific discipline concerned with the measurement of the Earth's *gravity* field, not its magnetic field. Magnetometry is the term used for measuring magnetic fields.
Standard gravity (9.80665 m/s²) is a conventional value used to define units like the kilogram force.
Answer: True
Explanation: The conventionally defined value for standard gravity (9.80665 m/s²) serves as a reference point for various scientific and engineering applications, including the definition of units such as the kilogram force.
Satellite laser ranging is effective for determining lower-degree parameters of Earth's gravity field, such as oblateness.
Answer: True
Explanation: Satellite laser ranging (SLR) provides precise measurements that are particularly effective for determining lower-degree parameters of Earth's gravity field, including its oblateness and the motion of its geocenter.
The approximate formula for gravity variation with altitude is g_h = g_0 * (R_e / (R_e + h))².
Answer: True
Explanation: The formula g_h = g_0 * (R_e / (R_e + h))² is a standard approximation used to calculate the variation of Earth's gravitational acceleration (g_h) at a specific altitude (h) above the surface, relative to the standard gravity (g_0) and Earth's mean radius (R_e).
A plumb bob is used to determine the local vertical direction, aligning with the local gravitational pull.
Answer: True
Explanation: A plumb bob, consisting of a weight suspended from a string, naturally aligns itself with the direction of the local gravitational force, thereby indicating the local vertical direction.
The International Gravity Formula 1967 provides several equivalent formulas that use trigonometric functions of latitude to calculate gravity.
Answer: True
Explanation: The International Gravity Formula 1967 (Helmert's equation) is designed to estimate sea-level gravity based on latitude and offers multiple equivalent formulations employing trigonometric functions of latitude for this purpose.
Modern satellite missions provide detailed gravity models, often presented as maps of geoid undulations or gravity anomalies.
Answer: True
Explanation: Contemporary satellite missions are instrumental in generating comprehensive gravity models of Earth, frequently visualized as maps depicting geoid undulations or gravity anomalies, thereby enhancing our understanding of the planet's gravitational field.
The WGS 84 formula uses the Earth's equatorial semi-axis (a) of 6,378,137.0 meters and a polar semi-axis (b) of 6,356,752.314245 meters.
Answer: True
Explanation: The WGS 84 (World Geodetic System 1984) gravity formula relies on precise values for Earth's equatorial semi-axis (a = 6,378,137.0 m) and polar semi-axis (b = 6,356,752.314245 m) to calculate gravity as a function of latitude.
Gravimetry is the scientific discipline concerned with the measurement of the Earth's gravity field.
Answer: True
Explanation: Gravimetry is the scientific discipline dedicated to the precise measurement and study of the Earth's gravity field and its variations.
In what units is Earth's gravity typically measured?
Answer: Meters per second squared (m/s²)
Explanation: The standard units for measuring gravitational acceleration are meters per second squared (m/s²) or, equivalently, newtons per kilogram (N/kg).
What is the approximate value of Earth's gravitational acceleration near the surface, assuming negligible air resistance?
Answer: 9.8 m/s²
Explanation: Near Earth's surface, the acceleration due to gravity is approximately 9.8 m/s², meaning a freely falling object's speed increases by about 9.8 meters per second every second, assuming air resistance is negligible.
What is the purpose of the defined value for standard gravity (9.80665 m/s²)?
Answer: To define units like the kilogram force and serve as a conventional value
Explanation: The conventionally defined value for standard gravity (9.80665 m/s²) serves as a reference point for various scientific and engineering applications, including the definition of units such as the kilogram force.
Which formula approximates the variation of Earth's gravity with altitude?
Answer: g_h = g_0 * (R_e / (R_e + h))²
Explanation: The formula g_h = g_0 * (R_e / (R_e + h))² is a standard approximation used to calculate the variation of Earth's gravitational acceleration (g_h) at a specific altitude (h) above the surface, relative to the standard gravity (g_0) and Earth's mean radius (R_e).
What is the primary purpose of the International Gravity Formula 1967 (Helmert's equation)?
Answer: To estimate sea-level gravity based on latitude.
Explanation: The International Gravity Formula 1967, also known as Helmert's equation, provides a standard mathematical model used to estimate the acceleration due to gravity at sea level as a function of latitude.
What is gravimetry?
Answer: The measurement of Earth's gravity field.
Explanation: Gravimetry is the scientific discipline dedicated to the precise measurement and study of the Earth's gravity field and its variations.
What does the formula g' = g * (1 - d/R) approximate?
Answer: Gravity at a depth 'd' inside the Earth (simplified model).
Explanation: This formula, g' = g * (1 - d/R), provides a simplified approximation for the gravitational acceleration (g') at a depth 'd' within the Earth, assuming a constant density and a spherically symmetric mass distribution. 'g' represents the surface gravity and 'R' the Earth's radius.
What information can be obtained from satellite laser ranging regarding Earth's gravity field?
Answer: Lower-degree parameters like Earth's oblateness.
Explanation: Satellite laser ranging (SLR) provides precise measurements that are particularly effective for determining lower-degree parameters of Earth's gravity field, including its oblateness and the motion of its geocenter.
Gravity anomalies are local variations caused by uniformities in Earth's mass distribution.
Answer: False
Explanation: Gravity anomalies are, by definition, local and regional variations in the gravitational field that deviate from the expected value. These deviations are caused by *non-uniformities* in the distribution of mass within the Earth, not by uniformities.
The study of gravity anomalies is practically utilized to locate resources like oil and mineral deposits.
Answer: True
Explanation: The analysis of gravity anomalies is a valuable tool in geophysical exploration, enabling the identification of subsurface geological structures with different densities, which often correlate with the presence of oil, gas, and mineral deposits.
NASA's GRACE mission data correlates stronger gravity with regions of recent volcanic activity and ridge spreading.
Answer: True
Explanation: NASA's GRACE mission data has revealed a strong correlation between regions exhibiting stronger-than-theoretical gravity and the locations of recent volcanic activity and mid-ocean ridge spreading, indicative of underlying mass concentrations.
A vertical deflection is a measure of the change in gravitational acceleration with altitude.
Answer: False
Explanation: A vertical deflection is not a measure of the change in gravitational acceleration with altitude. Instead, it refers to a deviation in the direction of the local gravitational force from the direction pointing towards the Earth's center, typically caused by nearby mass anomalies.
Blue areas on NASA's GRACE gravity anomaly map indicate regions with weaker gravity than the standard value.
Answer: True
Explanation: On NASA's GRACE gravity anomaly maps, blue areas typically signify regions where the measured gravitational acceleration is weaker than the reference or standard value, indicating areas of lower mass density or different geological structures compared to the surrounding regions.
Gravity anomalies are caused by variations in topography, rock density, and deeper tectonic structures.
Answer: True
Explanation: Gravity anomalies arise from local and regional deviations in the Earth's gravitational field, which are directly attributable to non-uniformities in mass distribution, including variations in surface topography, subsurface rock densities, and deeper geological structures.
What causes gravity anomalies?
Answer: Non-uniformities in the distribution of mass within the Earth.
Explanation: Gravity anomalies arise from local and regional deviations in the Earth's gravitational field, which are directly attributable to non-uniformities in mass distribution, including variations in surface topography, subsurface rock densities, and deeper geological structures.
How are gravity anomalies practically utilized in resource exploration?
Answer: To locate mineral deposits and oil fields based on density variations.
Explanation: The analysis of gravity anomalies is a valuable tool in geophysical exploration, enabling the identification of subsurface geological structures with different densities, which often correlate with the presence of oil, gas, and mineral deposits.
What correlation did NASA's GRACE mission data reveal regarding gravity and geological features?
Answer: Stronger gravity correlated with regions of recent volcanic activity and ridge spreading.
Explanation: NASA's GRACE mission data has revealed a strong correlation between regions exhibiting stronger-than-theoretical gravity and the locations of recent volcanic activity and mid-ocean ridge spreading, indicative of underlying mass concentrations.
What does a 'vertical deflection' in gravity refer to?
Answer: A deviation in the direction of local gravity from the Earth's center.
Explanation: A vertical deflection is not a measure of the change in gravitational acceleration with altitude. Instead, it refers to a deviation in the direction of the local gravitational force from the direction pointing towards the Earth's center, typically caused by nearby mass anomalies.
What do blue areas on NASA's GRACE gravity anomaly map illustrate?
Answer: Regions with weaker gravity than the standard value.
Explanation: On NASA's GRACE gravity anomaly maps, blue areas typically signify regions where the measured gravitational acceleration is weaker than the reference or standard value, indicating areas of lower mass density or different geological structures compared to the surrounding regions.
Astronauts in orbit feel weightless because Earth's gravity is negligible at that altitude.
Answer: False
Explanation: Astronauts in orbit experience weightlessness not because Earth's gravity is negligible, but because they are in a state of continuous free-fall around the planet. Gravity at orbital altitudes is still substantial, often around 90% of surface gravity.
The Shell theorem, which took Newton 20 years to prove, simplifies calculations for gravity inside a spherical body.
Answer: False
Explanation: The Shell theorem, a complex proof that occupied Isaac Newton for approximately 20 years, states that the gravitational force exerted by a uniform spherical body on a particle *outside* the body is equivalent to the force exerted if all the body's mass were concentrated at its center. The question incorrectly specifies 'inside'.
Henry Cavendish used gravity measurements (g) and Earth's radius (r) along with the gravitational constant (G) to estimate the mass of the Earth.
Answer: True
Explanation: Henry Cavendish's seminal work involved determining the gravitational constant (G) through torsion balance experiments, which, when combined with known values for Earth's radius (r) and gravitational acceleration (g), allowed for the estimation of Earth's mass.
Modern satellite missions like GOCE and CHAMP are vital for determining parameters of Earth's gravity field.
Answer: True
Explanation: Satellite missions such as GOCE (Gravity Field and Steady-State Ocean Circulation Circulation) and CHAMP (CHAllenging Minisatellite Payload) have been crucial in providing highly detailed measurements and models of Earth's static and time-variable gravity field.
The GRACE mission consisted of a single satellite that mapped gravitational changes across Earth.
Answer: False
Explanation: The GRACE (Gravity Recovery and Climate Experiment) mission comprised two identical satellites flying in tandem, which allowed for precise measurements of gravitational changes by detecting minute variations in the distance between them.
The Shell theorem states that the gravitational force exerted by a uniform spherical body on an external particle is equivalent to the force if all mass were at its center.
Answer: True
Explanation: The Shell theorem, a fundamental concept in Newtonian gravity, posits that the gravitational force exerted by a uniform spherical shell on a particle outside the shell is identical to that exerted if all the shell's mass were concentrated at its center.
Henry Cavendish's work primarily focused on measuring the precise gravitational acceleration at different locations on Earth.
Answer: False
Explanation: Henry Cavendish's seminal work involved determining the gravitational constant (G) through torsion balance experiments, which, when combined with known values for Earth's radius (r) and gravitational acceleration (g), allowed for the estimation of Earth's mass.
What is the primary reason astronauts in orbit experience weightlessness?
Answer: They are in a state of continuous free-fall around the Earth.
Explanation: Astronauts in orbit experience weightlessness not because Earth's gravity is negligible, but because they are in a state of continuous free-fall around the planet. Gravity at orbital altitudes is still substantial, often around 90% of surface gravity.
What is the Shell theorem primarily concerned with?
Answer: The gravitational force exerted by a uniform spherical body on an external particle.
Explanation: The Shell theorem, a fundamental concept in Newtonian gravity, posits that the gravitational force exerted by a uniform spherical shell on a particle outside the shell is identical to that exerted if all the shell's mass were concentrated at its center.
How did Henry Cavendish contribute to understanding Earth's mass?
Answer: By using gravity measurements (g) and Earth's radius (r) to estimate Earth's mass.
Explanation: Henry Cavendish's seminal work involved determining the gravitational constant (G) through torsion balance experiments, which, when combined with known values for Earth's radius (r) and gravitational acceleration (g), allowed for the estimation of Earth's mass.
What do modern satellite missions like GOCE and CHAMP primarily help determine?
Answer: Parameters of Earth's gravity field.
Explanation: Satellite missions such as GOCE (Gravity Field and Steady-State Ocean Circulation Circulation) and CHAMP (CHAllenging Minisatellite Payload) have been crucial in providing highly detailed measurements and models of Earth's static and time-variable gravity field.