What is the gravity of Earth, and what two primary forces contribute to it?

The gravity of Earth, denoted by the symbol g, is the net acceleration imparted to objects. It is the result of the combined effects of gravitation, caused by the distribution of mass within Earth, and the centrifugal force generated by Earth's rotation.

What is the defined value for standard gravity, and what is its purpose?

The defined value for standard gravity is 9.80665 m/s². This is a conventional value established by the General Conference on Weights and Measures, used when a precise local value is not known or not important. It also serves to define units like the kilogram force and pound force.

How does the weight of an object relate to Earth's gravity, and what factors influence it?

The weight of an object on Earth's surface is the downward force acting on it, calculated using Newton's second law (Force = mass × acceleration). While gravitational acceleration is the primary contributor, factors like the centrifugal force from Earth's rotation also affect the apparent weight. The gravitational pull of the Moon and Sun are typically considered separately as tidal effects.

Why does Earth's gravity vary across its surface, unlike a perfect, non-rotating sphere?

Earth's gravity varies because it is not a perfect sphere; it bulges at the equator and is flatter at the poles, forming an oblate spheroid. Furthermore, Earth's rotation generates a centrifugal force that counteracts gravity, causing variations in the net acceleration.

What is the approximate range of gravitational acceleration on Earth's surface, considering the highest and lowest points mentioned?

The gravitational acceleration on Earth's surface varies by about 0.7%. The text mentions values ranging from approximately 9.7639 m/s² at Nevado Huascarán in Peru to 9.8337 m/s² at the surface of the Arctic Ocean.

How does latitude influence the strength of Earth's gravity?

Gravity is generally weaker at the equator and stronger at the poles. This difference is primarily due to two factors: the centrifugal force from Earth's rotation is greater at the equator, and the Earth's equatorial bulge places points on the equator farther from the planet's center than points at the poles.

What is the approximate percentage difference in an object's weight between the poles and the equator due to latitude-related factors?

Due to the combined effects of the equatorial bulge and the centrifugal force from rotation, an object will weigh approximately 0.5% more at the poles than it does at the equator.

How does gravity change as altitude increases above Earth's surface?

Gravity decreases as altitude increases because the distance from Earth's center increases. For instance, an increase in altitude from sea level to 9,000 meters causes a weight decrease of about 0.29%, assuming other factors remain constant.

Besides the distance from Earth's center, what other factor related to altitude affects an object's apparent weight?

The decrease in air density at higher altitudes reduces the buoyant force acting on an object. This reduction in buoyancy slightly increases the object's apparent weight, counteracting some of the decrease caused by increased distance from Earth's center.

Is the sensation of weightlessness experienced by astronauts in orbit due to the absence of Earth's gravity?

No, this is a common misconception. Astronauts in orbit are not weightless because gravity is still significant at orbital altitudes, typically around 90% as strong as at the Earth's surface. The feeling of weightlessness occurs because orbiting objects are in a state of continuous free-fall around the Earth.

What formula approximates the variation of Earth's gravity with altitude?

The approximate formula for gravity variation with altitude is g_h = g_0 * (R_e / (R_e + h))², where g_h is the gravitational acceleration at height h, g_0 is the standard gravitational acceleration, R_e is Earth's mean radius, and h is the altitude above sea level.

How does gravity change as one moves deeper into the Earth, assuming a spherically symmetric density distribution?

Assuming a spherically symmetric density, the gravitational force at a radius 'r' from the center depends only on the mass enclosed within that radius (M(r)). The formula is g(r) = -G * M(r) / r². This implies that gravity generally decreases as one moves deeper into the Earth, particularly towards the center, because the enclosed mass M(r) decreases faster than r².

What is the Shell theorem, and how did it impact Newton's work?

The Shell theorem 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. Proving this theorem took Isaac Newton 20 years, which delayed his broader work on gravity.

If Earth had a constant density, how would gravity vary with the distance from its center?

If Earth had a constant density (ρ), gravity would increase linearly with the distance from the center (r), following the formula g(r) = (4/3)πGρr. This means gravity would be zero at the center and increase towards the surface.

How is the approximate gravity at a depth 'd' calculated using the surface gravity 'g' and Earth's radius 'R'?

In a simplified model, the gravity (g') at a depth 'd' is approximated by g' = g * (1 - d/R), where 'g' is the surface acceleration due to gravity and 'R' is the Earth's radius. This formula suggests that gravity decreases linearly with depth.

What are 'gravity anomalies,' and what causes them?

Gravity anomalies are local and regional variations in Earth's gravitational field that differ from the expected value. They are caused by non-uniformities in the distribution of mass within the Earth, such as variations in topography, rock density, and deeper tectonic structures.

How are gravity anomalies studied, and what instruments are used?

Gravity anomalies are studied through the field of gravitational geophysics. Scientists use highly sensitive instruments called gravimeters to measure gravitational fluctuations. By analyzing these measurements and accounting for known factors like topography, they can infer information about subsurface geology.

In what practical ways are gravity anomalies utilized in resource exploration?

The study of gravity anomalies is used by prospectors to locate resources like oil and mineral deposits. Denser geological formations, often associated with mineral ores, create higher local gravitational fields, while less dense sedimentary rocks result in lower fields, both of which can be detected.

What correlation has been observed between NASA GRACE gravity data and geological features like volcanic activity?

NASA's GRACE mission data has shown a strong correlation between regions exhibiting stronger-than-theoretical gravity and the locations of recent volcanic activity and ridge spreading. These areas tend to have higher gravitational pull.

Besides Earth's mass and rotation, what other factors can influence the measured strength of gravity?

Other factors include buoyancy forces from the surrounding medium (like air or water), which reduce the apparent weight of an object. Additionally, the gravitational pull of the Moon and Sun, responsible for tides, causes small variations in apparent gravity, typically around 2 μm/s².

Is the direction of Earth's gravity always precisely towards the planet's center?

No, the direction of gravity is not always perfectly towards the center. Due to Earth's oblate shape, there are deviations related to the difference between geodetic and geocentric latitudes. Local mass anomalies, such as mountains, also cause smaller deviations known as vertical deflection.

What is a 'vertical deflection' in the context of Earth's gravity?

A vertical deflection refers to a slight deviation in the direction of the local gravitational force from the direction pointing towards the Earth's center. These deflections are caused by nearby mass anomalies, like mountains or variations in subsurface density.

How do latitude and altitude generally affect gravity readings in different cities around the world?

Cities located at higher latitudes typically experience stronger gravity than those closer to the equator. Similarly, cities at higher altitudes tend to have slightly weaker gravity compared to sea-level locations at similar latitudes, due to increased distance from Earth's center and reduced air buoyancy.

Can you provide examples of cities with high and low gravity values mentioned in the text?

Yes, cities with higher gravity values mentioned include Anchorage (9.826 m/s²) and Helsinki (9.825 m/s²), which are at higher latitudes. Examples of cities with lower gravity values include Kuala Lumpur (9.776 m/s²) and Mexico City (9.776 m/s²), located near the equator or at higher altitudes.

What is the International Gravity Formula 1967, also known as Helmert's equation?

The International Gravity Formula 1967, or Helmert's equation, is a mathematical model used to estimate the acceleration due to gravity at sea level based on latitude. It provides several equivalent formulas that use trigonometric functions of latitude to calculate the gravity value.

What is the WGS 84 Ellipsoidal Gravity Formula, and what key parameters does it utilize?

The WGS 84 formula is another model for calculating gravity as a function of latitude. It uses the Earth's equatorial and polar semi-axes (a and b), the square of its eccentricity (e²), and specific constants related to the defined gravity at the equator (G_e) and poles (G_p).

What are the standard values for Earth's semi-axes used in the WGS 84 gravity formula?

The WGS 84 formula uses an equatorial semi-axis (a) of 6,378,137.0 meters and a polar semi-axis (b) of 6,356,752.314245 meters.

How can Earth's gravity (g) be estimated using the law of universal gravitation?

Earth's gravity can be estimated by applying the law of universal gravitation (F = G * m1 * m2 / r²) and Newton's second law (F = m * a). By equating these and considering the force on a mass 'm' due to Earth's mass 'M_earth' at radius 'r', we derive g = G * M_earth / r².

What are the primary reasons why a calculated value of 'g' using the universal gravitation formula might differ from measured values?

The calculated value can differ from measured values because Earth is not homogeneous in density, it's not a perfect sphere (requiring an average radius), and the basic calculation doesn't account for the reduction in apparent gravity caused by Earth's rotation and the resulting centrifugal force.

How did Henry Cavendish contribute to understanding Earth's mass through gravity measurements?

Henry Cavendish utilized known values for the gravitational constant (G), Earth's radius (r), and measured acceleration due to gravity (g) to perform a reverse calculation. This method allowed him to estimate the mass of the Earth.

What is the scientific term for the measurement of Earth's gravity?

The scientific term for the measurement of Earth's gravity is gravimetry.

What role do modern satellite missions play in measuring Earth's gravity field?

Modern satellite missions like GOCE, CHAMP, Swarm, and GRACE/GRACE-FO are crucial for determining both static and time-variable parameters of Earth's gravity field. They provide detailed gravity models, often presented as maps of geoid undulations or gravity anomalies.

What specific information about Earth's gravity can be obtained from satellite laser ranging?

Satellite laser ranging is particularly effective for determining lower-degree parameters of Earth's gravity field, such as the Earth's oblateness and the motion of its geocenter.

What did the GRACE mission contribute to the study of Earth's gravity?

The GRACE (Gravity Recovery and Climate Experiment) mission consisted of two satellites that detected gravitational changes across Earth. These changes could be presented as temporal variations in gravity anomalies, providing insights into mass redistribution over time.

What does the image depicting Earth's gravity anomalies, measured by NASA's GRACE mission, illustrate?

The image illustrates deviations in Earth's gravity from a theoretical, smooth Earth model. Red areas signify stronger gravity than the standard value, while blue areas indicate weaker gravity, as detected by NASA's GRACE mission.

What does the image comparing Earth's gravity with altitude demonstrate?

The image demonstrates the inverse relationship between Earth's gravity and the distance from the planet's center. It shows how gravity decreases as altitude increases, extending from the surface up to 30,000 km.

What information is conveyed by the image showing gravity at different internal layers of Earth?

This image visually represents how gravitational force changes within Earth's internal structure, from the crust and mantle down to the core, indicating varying gravitational strengths at different depths.

What do the graphs related to the Preliminary Reference Earth Model (PREM) show about Earth's gravity?

The graphs associated with the PREM illustrate Earth's radial density distribution and its corresponding gravity. They also include comparative models assuming constant or linearly decreasing density, highlighting how density variations influence gravity.

What correlation exists between NASA GRACE gravity measurements and geological features like volcanic activity?

A strong correlation has been observed between regions where NASA's GRACE mission measured gravity to be stronger than theoretical predictions and the locations of recent volcanic activity and ridge spreading.

What does the image of a plumb bob demonstrate in relation to Earth's gravity?

The image of a plumb bob demonstrates its function in determining the local vertical direction, which aligns with the direction of the local gravitational pull exerted by the Earth.

What does the map of gravity anomalies around the Antarctic continent illustrate?

The map illustrates the variations in Earth's gravity field specifically around the Antarctic continent, highlighting regional differences in gravitational strength due to local geological factors.

What is the definition of Earth's gravity (g)?

Earth's gravity (g) is defined as the net acceleration imparted to objects due to the combined effects of gravitation from Earth's mass distribution and the centrifugal force resulting from Earth's rotation.

What is the approximate value of standard gravity (g_n)?

The conventionally agreed-upon value for standard gravity (g_n) is 9.80665 m/s².

What causes the difference between geodetic latitude and geocentric latitude, and how does it affect gravity direction?

The difference arises because Earth is an oblate spheroid, not a perfect sphere. Geocentric latitude is measured from the Earth's center, while geodetic latitude is measured perpendicular to the reference ellipsoid surface. This difference causes slight deviations in the direction of gravity, known as vertical deflection.

What is the approximate difference in gravity between the equator and the poles at sea level?

At sea level, gravity increases from about 9.780 m/s² at the equator to about 9.832 m/s² at the poles, representing a difference of roughly 0.5% in the force experienced.

How does the Earth's mass distribution affect the direction of gravity?

Variations in Earth's mass distribution, such as the presence of mountains or differences in subsurface density, cause local anomalies in the gravitational field. These anomalies lead to deviations in the direction of gravity, known as vertical deflection.

What is the purpose of the International Gravity Formula 1967?

The International Gravity Formula 1967 provides a standard mathematical model to estimate the acceleration due to gravity at sea level based on latitude, serving as a reference value when precise local measurements are unavailable or unnecessary.

How does the formula g = G * M_earth / r² relate to estimating Earth's gravity?

This formula estimates Earth's gravity by using the universal gravitational constant (G), the Earth's mass (M_earth), and the Earth's radius (r). It's derived by equating the gravitational force formula with Newton's second law (F=mg).

Gravimetry is the scientific discipline concerned with the measurement of the Earth's gravity field.

Gravity Of Earth Wiki: Gravitational Dynamics of Earth: An Analytical Exploration

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Definition

The Net Acceleration

The gravity of Earth, denoted by $g$ , represents the net acceleration imparted to objects. This is a resultant force derived from two primary components: the gravitational attraction due to Earth's mass distribution and the centrifugal force arising from Earth's rotation.

Vectorial Quantity

Gravity is fundamentally a vector quantity. Its direction aligns with that of a plumb bob, indicating the local vertical. The magnitude, represented by g, is measured in meters per second squared (m/s²) or Newtons per kilogram (N/kg).

Conventional Value

A standardized value, known as standard gravity, is defined as 9.80665 m/s². This value serves as a reference point, particularly when precise local measurements are unavailable or not critical for the context. It is also instrumental in defining units like the kilogram-force.

Magnitude

Approximate Value

Near Earth's surface, the acceleration due to gravity is approximately 9.8 m/s². This signifies that, in the absence of air resistance, the velocity of a freely falling object increases by about 9.8 meters per second every second.

Global Range

The precise magnitude of gravity varies across Earth's surface. Measurements range from approximately 9.7639 m/s² at Nevado Huascarán in Peru to 9.8337 m/s² in the Arctic Ocean. This variation is influenced by factors such as latitude, altitude, and local geological density.

Weight vs. Mass

An object's weight on Earth's surface is the downward force experienced, calculated as Force = mass × acceleration (F=ma). While gravitational acceleration contributes significantly, factors like Earth's rotation also influence apparent weight, reducing it slightly at the equator compared to the poles.

Variations

Latitude Effects

Earth's oblateness (bulging at the equator) and rotation cause gravity to vary with latitude. The centrifugal force counteracts gravity more strongly at the equator (up to 0.3%), and the increased distance from Earth's center at the equator also reduces gravitational attraction. Consequently, gravity increases from the equator to the poles.

Altitude Effects

As altitude increases, the distance from Earth's center increases, leading to a decrease in gravitational force. For instance, rising 9,000 meters reduces weight by about 0.29%. While increased altitude also slightly lessens air buoyancy (increasing apparent weight by ~0.08%), the dominant effect is the reduction in gravitational pull.

Local Geology

Variations in topography and the density of underlying geological structures create local and regional gravity anomalies. Denser rocks, often associated with mineral deposits or volcanic activity, result in higher local gravity readings. Conversely, less dense sedimentary rocks lead to lower readings. These anomalies are crucial in geophysical exploration.

Models

Spherical Approximation

Assuming a spherically symmetric Earth, the gravitational acceleration g(r) at a distance r from the center is determined by the mass enclosed within that radius, M(r), and the gravitational constant G, following the Shell Theorem: $g (r) = - G M (r)/ r 2$ . This simplified model is useful for understanding fundamental principles.

Latitude Formulas

More precise models account for Earth's shape and rotation. The International Gravity Formula (1967) and the WGS 84 Ellipsoidal Gravity Formula provide mathematical expressions to calculate gravity based on latitude ( $φ$ ), incorporating parameters like Earth's semi-axes and constants derived from empirical data.

The International Gravity Formula (Helmert's equation) approximates gravity at sea level based on latitude $φ$ :

g\{\phi \}

The WGS 84 formula is another widely used model:

g\{\phi \}

These models are essential for precise geodetic calculations and global positioning systems.

Altitude and Depth

Gravity decreases with altitude according to the inverse square law, approximated by $g h = g 0 (R e / (R e + h)) 2$ . Inside Earth, gravity increases towards the center if density is uniform, but decreases in reality due to non-uniform density distribution, as described by models like PREM.

Measurement

Satellite Gravimetry

Modern gravity field models are derived from satellite missions like GRACE, GOCE, and Swarm. These missions measure subtle variations in Earth's gravitational field by tracking minute changes in satellite orbits, providing detailed global gravity maps and insights into mass transport within the Earth system.

Gravimeters

Gravimetry, the science of measuring gravity, employs highly sensitive instruments called gravimeters. These devices detect minute local variations in gravitational acceleration, crucial for geophysical surveys, resource exploration (oil, minerals), and understanding geological structures.

Data Interpretation

Measured gravity data is processed to remove known effects (like latitude and altitude corrections) to reveal gravity anomalies. These anomalies provide valuable information about subsurface density variations, aiding in geological mapping and resource prospecting.

Related Concepts

Geophysics & Geodesy

The study of Earth's gravity is intrinsically linked to geophysics and geodesy. Geophysics investigates Earth's physical processes, while geodesy focuses on measuring and understanding Earth's geometric shape, orientation in space, and gravitational field.

Celestial Mechanics

Concepts like escape velocity and orbital mechanics are directly influenced by gravitational forces. Understanding Earth's gravity is fundamental to calculating trajectories for satellites, spacecraft, and predicting phenomena like tides caused by lunar and solar gravity.

Mathematical Physics

The precise modeling of Earth's gravity involves advanced mathematical techniques, including spherical harmonics and calculus. These tools are essential for accurately representing the complex gravitational field and its variations across the planet.

Gravity Values in Major Cities

The following table illustrates the variation in gravitational acceleration (m/s²) across various global cities, highlighting the influence of latitude, altitude, and local factors.

Acceleration due to gravity in various cities
Location	m/s²	ft/s²	Location	m/s²	ft/s²	Location	m/s²	ft/s²	Location	m/s²	ft/s²
Anchorage	9.826	32.24	Helsinki	9.825	32.23	Oslo	9.825	32.23	Copenhagen	9.821	32.22
Stockholm	9.818	32.21	Manchester	9.818	32.21	Amsterdam	9.817	32.21	Kotagiri	9.817	32.21
Birmingham	9.817	32.21	London	9.816	32.20	Brussels	9.815	32.20	Frankfurt	9.814	32.20
Seattle	9.811	32.19	Paris	9.809	32.18	Montréal	9.809	32.18	Vancouver	9.809	32.18
Istanbul	9.808	32.18	Toronto	9.807	32.18	Zurich	9.807	32.18	Ottawa	9.806	32.17
Skopje	9.804	32.17	Chicago	9.804	32.17	Rome	9.803	32.16	Wellington	9.803	32.16
New York City	9.802	32.16	Lisbon	9.801	32.16	Washington, D.C.	9.801	32.16	Athens	9.800	32.15
Madrid	9.800	32.15	Melbourne	9.800	32.15	Auckland	9.799	32.15	Denver	9.798	32.15
Tokyo	9.798	32.15	Buenos Aires	9.797	32.14	Sydney	9.797	32.14	Nicosia	9.797	32.14
Los Angeles	9.796	32.14	Cape Town	9.796	32.14	Perth	9.794	32.13	Kuwait City	9.792	32.13
Taipei	9.790	32.12	Rio de Janeiro	9.788	32.11	Havana	9.786	32.11	Kolkata	9.785	32.10
Hong Kong	9.785	32.10	Bangkok	9.780	32.09	Manila	9.780	32.09	Jakarta	9.777	32.08
Kuala Lumpur	9.776	32.07	Singapore	9.776	32.07	Mexico City	9.776	32.07	Kandy	9.775	32.07

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References

"Wolfram|Alpha Gravity in Kuala Lumpur", Wolfram Alpha, accessed November 2020

Resolution of the 3rd CGPM (1901), page 70 (in cm/s2). BIPM â Resolution of the 3rd CGPM

"I feel 'lighter' when up a mountain but am I?", National Physical Laboratory FAQ

T.M. Yarwood and F. Castle, Physical and Mathematical Tables, revised edition, Macmillan and Co LTD, London and Basingstoke, Printed in Great Britain by The University Press, Glasgow, 1970, pp. 22 & 23.

A full list of references for this article are available at the Gravity of Earth Wikipedia page

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This page was generated by an Artificial Intelligence and is intended for informational and educational purposes only. The content is based on a snapshot of publicly available data from Wikipedia and may not be entirely accurate, complete, or up-to-date.

This is not professional scientific advice. The information provided on this website is not a substitute for professional consultation in physics, geophysics, or geodesy. Always refer to official documentation and consult with qualified professionals for specific applications or research needs.

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Gravitational Dynamics of Earth

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Definition 🌍

⚖️ The Net Acceleration

📏 Vectorial Quantity

⏱️ Conventional Value

Magnitude 📈

🔢 Approximate Value

🌐 Global Range

⚖️ Weight vs. Mass

Variations 📍

🌍 Latitude Effects

⛰️ Altitude Effects

🪨 Local Geology

Models 🧮

🌌 Spherical Approximation

📈 Latitude Formulas

🧮 Altitude and Depth

Measurement 🛰️

🛰️ Satellite Gravimetry

📏 Gravimeters

📊 Data Interpretation

Related Concepts 📚

🔭 Geophysics & Geodesy

🌌 Celestial Mechanics

🧮 Mathematical Physics

Gravity Values in Major Cities 🏙️

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Dive in with Flashcard Learning!

Definition

The Net Acceleration

Vectorial Quantity

Conventional Value

Magnitude

Approximate Value

Global Range

Weight vs. Mass

Variations

Latitude Effects

Altitude Effects

Local Geology

Models

Spherical Approximation

Latitude Formulas

Altitude and Depth

Measurement

Satellite Gravimetry

Gravimeters

Data Interpretation

Related Concepts

Geophysics & Geodesy

Celestial Mechanics

Mathematical Physics

Gravity Values in Major Cities

Teacher's Corner

True or False?

Test Your Knowledge!

Gamer's Corner

Discover other topics to study!

References

Feedback & Support

Disclaimer

Important Notice