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

In summary, the value of 9.80665 m/s2 is considered the most accurate for the acceleration due to gravity on Earth. However, this value can vary slightly depending on location and other factors. It was determined experimentally through precise measurements and also theoretically through calculations involving the Earth's mass and radius. It is important to note that the values for the universal gravitational constant and Earth's mass used in these calculations can vary, leading to slight variations in the final value for g.
  • #1
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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  • #2
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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  • #3
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.
 
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  • #4
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.
 
  • #5
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
 
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1. What is gravitational force?

Gravitational force is a natural phenomenon by which all objects with mass are brought towards each other. It is the force responsible for the attraction between objects, such as the Earth and the Moon.

2. How is gravitational force measured?

Gravitational force is measured in units of newtons (N). It can be calculated using the equation F = G(m1m2)/r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

3. What is the value of the gravitational force on Earth?

The value of the gravitational force on Earth is approximately 9.8 m/s^2. This is often rounded to 10 m/s^2 for simplicity.

4. Does gravitational force vary on different planets?

Yes, gravitational force varies on different planets based on their mass and size. For example, the gravitational force on the surface of Mars is only about 38% of that on Earth.

5. Can gravitational force be manipulated or controlled?

Gravitational force cannot be manipulated or controlled by humans. However, the effects of gravity can be counteracted through the use of technology, such as rockets and spacecraft, to escape the pull of a planet's gravity.

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