Why Do Gravitational Force Values Vary and How Are They Measured?

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Discussion Overview

The discussion centers on the variations in gravitational force values, specifically the acceleration due to gravity (g), and how these values are measured. Participants explore the differences in reported values, the factors affecting these variations, and the methods of measurement.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that the commonly cited value of g is 9.8 m/s², while others argue for 9.81 m/s² or 9.80665 m/s² as more accurate, depending on the context.
  • It is mentioned that g varies based on location, with specific values given for different latitudes and altitudes, such as 9.780 m/s² at the equator and 9.832 m/s² at the poles.
  • Participants discuss the experimental determination of g, suggesting that it involves measuring the acceleration of falling objects, but details on the methodology are not provided.
  • There is a correction regarding the terminology used, clarifying that the discussion is about acceleration due to gravity rather than gravitational force itself.
  • Concerns are raised about the accuracy of values for the gravitational constant (G) and Earth's mass as provided by online calculators, with references to more precise values from authoritative sources.
  • Some participants emphasize the importance of using defined values for g and related constants to ensure consistency in calculations.

Areas of Agreement / Disagreement

Participants express differing views on the most accurate value for g and the implications of using various approximations. There is no consensus on a single value, and multiple competing perspectives remain throughout the discussion.

Contextual Notes

Variations in gravitational acceleration are noted to depend on factors such as latitude, altitude, and local geological conditions. The discussion highlights the complexity of measuring gravitational forces and the potential discrepancies in commonly used values.

Who May Find This Useful

This discussion may be of interest to those studying physics, particularly in the areas of gravitational theory, measurement techniques, and the implications of varying gravitational values in practical applications.

alyafey22
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Sometimes we hear 9.8 m/s^2 and sometimes 10 m\s^2 ?? what is the most correct and how did they manage to find it?
 
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I believe that 9.80 m/s2 is the more accurate value (it's certainly more precise), but this must be some sort of average or typical value, because g actually changes from place to place on the surface of the Earth. 10 m/s2 is just used as a rough approximation (i.e. to 1 significant figure) in order to simplify calculations. Note: you often hear it stated that g = 9.81 m/s2. I guess it depends on how you decide what should be the typical value.

It was determined experimentally. I don't know the details of how, but I'm sure that there have been many many measurements over the years. (EDIT: I guess one way would be to just measure the accelerations of falling objects as precisely as possible). But g is also theoretically equal to GM/R2 where G is the universal gravitational constant, M is the mass of the Earth, and R is the radius of the Earth (I guess this assumes a perfectly spherical Earth).

Check out http://www.google.ca/search?hl=en&c...arth)/(radius+of+earth)^2&aq=f&aqi=&aql=&oq=" (click on the link)
 
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cepheid said:
Note: you often hear it stated that g = 9.81 m/s2. I guess it depends on how you decide what should be the typical value.
The correct value for g0 is 9.80665 m/s2, exactly.
http://www.bipm.org/en/CGPM/db/3/2/.


It was determined experimentally.
9.80665 m/s2 is a defined value.

Earth gravity (which conventionally includes centrifugal acceleration due to the Earth's rotation) varies with latitude, altitude, and location. Local acceleration due to gravity is about 9.780 m/s2 at the sea level at the equator, 9.832 m/s2 at sea level at the poles, and 9.779 m/s2 in Mexico City.

Gravitational acceleration, including centrifugal acceleration, can be measured extremely precisely with gravimeters, which are essentially a kind of accelerometer.

Check out http://www.google.ca/search?hl=en&c...arth)/(radius+of+earth)^2&aq=f&aqi=&aql=&oq=" (click on the link)
Watch out for that.
Google calculator has a lousy value for G and for the Earth's mass.

G, per google's calculator, is 6.67300×10-11 m3/kg/s2. The correct value is 6.67428(67)×10-11 m3/kg/s2 (see http://www.physics.nist.gov/cgi-bin/cuu/Value?bg).

Earth's mass, per google's calculator, is 5.9742×1024 kilograms. The agreed-upon value is 5.97219x1024 kg (see http://solarsystem.nasa.gov/planets/profile.cfm?Object=Earth&Display=Facts).

Rather than using those lousy values for G and Mearth, it is much better to use μearth = G*Mearth = 3.986004418(8)x1014 m3/s2 (see http://www.iers.org/nn_11216/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote32/tn32__009,templateId=raw,property=publicationFile.pdf/tn32_009.pdf , table 1.1). While G and Mearth have an error of about 1 part in 7,000, the product of the two has an error of about 1 part in 500 million.

The google calculator value for this product is 3.98658366×1014 m3/s2. If they are going to use bad values, they should at least be consistent.
 
Last edited by a moderator:
Notice that this is NOT the "gravitational force" as you titled this thread but the acceleration due to that force. The gravitational force on a body depends upon its mass. The acceleration due to gravitational force does not.
 
D H said:
The correct value for g0 is 9.80665 m/s2, exactly.
http://www.bipm.org/en/CGPM/db/3/2/.



9.80665 m/s2 is a defined value.

Earth gravity (which conventionally includes centrifugal acceleration due to the Earth's rotation) varies with latitude, altitude, and location. Local acceleration due to gravity is about 9.780 m/s2 at the sea level at the equator, 9.832 m/s2 at sea level at the poles, and 9.779 m/s2 in Mexico City.

Gravitational acceleration, including centrifugal acceleration, can be measured extremely precisely with gravimeters, which are essentially a kind of accelerometer.


Watch out for that.
Google calculator has a lousy value for G and for the Earth's mass.

G, per google's calculator, is 6.67300×10-11 m3/kg/s2. The correct value is 6.67428(67)×10-11 m3/kg/s2 (see http://www.physics.nist.gov/cgi-bin/cuu/Value?bg).

Earth's mass, per google's calculator, is 5.9742×1024 kilograms. The agreed-upon value is 5.97219x1024 kg (see http://solarsystem.nasa.gov/planets/profile.cfm?Object=Earth&Display=Facts).

Rather than using those lousy values for G and Mearth, it is much better to use μearth = G*Mearth = 3.986004418(8)x1014 m3/s2 (see http://www.iers.org/nn_11216/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote32/tn32__009,templateId=raw,property=publicationFile.pdf/tn32_009.pdf , table 1.1). While G and Mearth have an error of about 1 part in 7,000, the product of the two has an error of about 1 part in 500 million.

The google calculator value for this product is 3.98658366×1014 m3/s2. If they are going to use bad values, they should at least be consistent.

I stand corrected. Thanks for all the info D H
 
Last edited by a moderator:

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