Calculating g Value with Longitude and Altitude: Formula and Reference

In summary, the conversation revolved around finding the formula for determining the accurate value of g given the longitude and height above sea level. The formula is derived from Newton's law of universal gravitation and second law of motion, while taking into account the Earth's rotation. A link to a helpful website was also provided.
  • #1
Tawcan
Hi, new to here...

I'm looking for the formula to determine accureate value of g when value of longitude and height above sea level are given.

If you know if would be helpful if you could post a site that has the formula. (Want to have it as a reference).

Thanx!
 
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  • #2
I assume you mean latitude, not longitude. g varies with latitude because of the Earth's rotation.

Here's one page that may help:

http://www.npl.co.uk/pressure/faqs/altgrav.html

In general, you know Newton's law of universal gravitation:

F = G M m / r^2

and you know Newton's second law of motion:

F = m a

so you can substitute and solve for a:

a (g) = G M / r^2

Plug in the Earth's mass for M and your distance from its center as r. Voila. This calculation, of course, does not include the small effect of the rotation.

- Warren
 
  • #3
Originally posted by Tawcan
I'm looking for the formula to determine accureate value of g when value of longitude and height above sea level are given.

Do you want a theoretical prediction, assuming the Earth is a uniform rotating sphere, or do you want some kind of empirically-fit formula from measured data, taking into account all the irregularities in the Earth?

(By the way, do you mean latitude, not longitude?)
 
  • #4
Oops you guys are right.

Yep that's exactly the formula I'm looking for! Thanx for your help! :)
 

1. What is the formula for calculating the g value with longitude and altitude?

The formula for calculating the g value with longitude and altitude is g = 9.80616 - 0.002637cos(2Φ) - 0.0000059cos(2Φ)^2 + (3.086 * 10^-6)h, where Φ is the latitude and h is the altitude in meters.

2. Why is calculating the g value important?

Calculating the g value is important because it helps us understand the force of gravity at a particular location, which can have implications for a variety of scientific fields, such as geology, geophysics, and aerospace engineering.

3. How does longitude and altitude affect the g value?

The g value is affected by both longitude and altitude because they both contribute to the distance from the center of the Earth. The further away from the center, the weaker the force of gravity, resulting in a lower g value.

4. Can the g value change over time?

Yes, the g value can change over time due to factors such as changes in altitude or variations in the Earth's rotation and shape. It can also be affected by nearby geological features or changes in the Earth's mass distribution.

5. Are there any limitations to this formula for calculating the g value?

Yes, this formula is only an approximation and may not be accurate for locations near the poles or at very high altitudes. It also does not take into account local variations in the Earth's gravity field, which can be caused by factors such as mountains or underground structures.

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