High School The value of the standard acceleration due to Earth's gravity

[Sphere]

Hello, I noticed while trying to calculate the stardart gravity acceleration of the Earth that I never arrived at the defined value of 9.80665 m/s2 no matter that I calculate it with the equatorial radius, the polar radius, mean radius or the average of the equatorial and polar radius. With what terrestrial radius did they arrive to calculate this value of 9.80665 m/s2 and why?
Thank you !

 

[berkeman]

Hello, I noticed while trying to calculate the stardart gravity acceleration of the Earth that I never arrived at the defined value of 9.80665 m/s2 no matter that I calculate it with the equatorial radius, the polar radius, mean radius or the average of the equatorial and polar radius. With what terrestrial radius did they arrive to calculate this value of 9.80665 m/s2 and why?
Thank you !

Please show your calculations and the numbers you used for the Earth's mass, etc. Without seeing your calculations and numbers, I don't think we can be of much help. Thanks.

 

[Filip Larsen]

https://en.wikipedia.org/wiki/Standard_gravity

 

[FactChecker]

https://en.wikipedia.org/wiki/Standard_gravity

That says it is at a latitude of 45 deg. It accounts for the centrifugal acceleration at that latitude. The radius of the Earth (distance to the center of the Earth) is not what you want to use [EDIT] for the calculation of the centrifugal force. You want to find the perpendicular distance to the axis of rotation of the Earth. The shape of the Earth is complicated (see WGS 84 ellipsoid).

You can find a lot of detail on the calculation here: https://en.wikipedia.org/wiki/Theoretical_gravity. It's very complicated and it is no wonder that you are not matching their calculation.

You should be aware that there is some local variation of gravity due to varying densities (and surface altitudes?) that can not be accounted for by simple math models and must be measured locally. There are maps of measured gravity.

 

[Ibix]

(and altitudes?)

Yes. A careful experimentalist can measure the difference in $g$ over a few meters altitude using only a pendulum. I made a measurement in undergrad labs that was theoretically precise enough to care about my altitude above sea level.

In practice, either there is a serious mass anomaly underneath one end of my university's physics department or undergrads aren't all careful experimentalists.

 

[FactChecker]

Yes. A careful experimentalist can measure the difference in $g$ over a few meters altitude using only a pendulum. I made a measurement in undergrad labs that was theoretically precise enough to care about my altitude above sea level.

I know that there are maps of the gravity at locations on the Earth. I have never used them. I assume that they are accurate for the ground altitude at each location, but I do not know that for sure.

 

[PeroK]

With what terrestrial radius did they arrive to calculate this value of 9.80665 m/s2 and why?
Thank you !

Perhaps that's a measured value. That obviates the need for calculation.

 

[Filip Larsen]

Perhaps that's a measured value.

As far as I am aware, it is (now) a defined value with an exact value: https://physics.nist.gov/cgi-bin/cuu/Value?gn

 

[Klystron]

In my final undergraduate physics series at university, we measured and compared the acceleration of gravity at sea level using

1. pendulums,
2. dropping ferromagnetic material through electromagnetic fields, and
3. laser interferometer.

 

[Bystander]

I know that there are maps of the gravity at locations on the Earth. I have never used them. I assume that they are accurate for the ground altitude at each location, but I do not know that for sure.

"Station" at NBS/NIST, Boulder, Bldg. 2(?), NW corner in the "back" hallway; may still be there and certified current, or not. This was pre-Sumatra, https://www.jpl.nasa.gov/news/nasa-details-earthquake-effects-on-the-earth .

 

[Sphere]

Thanks to everyone !