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

[alyafey22]

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?

 

[cepheid]

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)

 

[D H]

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 M_earth, it is much better to use μ_earth = G*M_earth = 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 M_earth 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.

 

[HallsofIvy]

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.

 

[cepheid]

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 M_earth, it is much better to use μ_earth = G*M_earth = 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 M_earth 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