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

• B
• Sphere
In summary, they arrived at the value of 9.80665 m/s2 by measuring the gravity at different altitudes on Earth.
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 !

Sphere said:
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.

FactChecker

vanhees71, PeroK and FactChecker
Filip Larsen said:
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.

Last edited:
FactChecker said:
(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.

vanhees71, Astronuc, ohwilleke and 1 other person
Ibix said:
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.

Sphere said:
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.

PeroK
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.

FactChecker said:
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 .

FactChecker, Astronuc and ohwilleke
Thanks to everyone !

berkeman

## 1. What is the standard acceleration due to Earth's gravity?

The standard acceleration due to Earth's gravity, commonly denoted as g, is the acceleration experienced by a freely falling object near the Earth's surface. It is approximately equal to 9.8 meters per second squared (m/s²).

## 2. How is the value of g determined?

The value of g is determined by measuring the acceleration of a freely falling object near the Earth's surface. This can be done using various methods, such as dropping a ball from a known height and measuring the time it takes to reach the ground, or using specialized equipment such as accelerometers.

## 3. Does the value of g vary on different parts of Earth?

Yes, the value of g can vary slightly on different parts of Earth due to factors such as altitude, latitude, and local geology. However, these variations are very small and the standard value of 9.8 m/s² is used for most calculations.

## 4. How does the value of g affect objects on Earth?

The value of g affects objects on Earth by determining their weight and the force of gravity acting on them. This is why objects feel lighter on the Moon, where the value of g is only 1/6 of that on Earth.

## 5. Can the value of g change over time?

The value of g can change over time due to various factors, such as changes in the Earth's mass or rotation, or external forces like tides or atmospheric pressure. However, these changes are very small and do not significantly affect the standard value of 9.8 m/s².

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