Source: https://www.youtube.com/watch?v=XkG1iFanoNo

Cody Don Reeder, a science educator, did a nice experiment to show that gravity (and hence weight) changes based on your location. The two main things that affect gravity are latitude and elevation, and you should be able to detect these with a sensitive enough scale and a large enough change in altitude and/or location.

Cody uses a 295g cube of non-magnetic tungsten, and a jewelry scale that weighs up to 500g with an accuracy of 0.030g (30mg). He weighs this in Logan UT, and Manchester NH.

The weight varies as expected. At higher altitudes you are further from the center of the Earth, so the gravity and weight decrease. At higher latitudes (more North) the effects of the spin of earth are less, and so apparent gravity is greater (plus you are closer to the center of the earth, due to the equatorial bulge).

Going from Logan, UT to Manchester,NH is both a lower elevation and a higher latitude, so weight is expected to increase, which it does by about 0.22g, or 0.074%. With just an increase in altitude from 4,500 to 7,600 ft the weight decreases by about 0.06g, or 0.020%.

We can calculate the expected weight, assuming the Earth is of even density, with this calculator, which also gives the equations used:

https://www.sensorsone.com/local-gravity-calculator/

The

Actual local g varies based on the composition of the Earth, this can be local variations based on the type of rock nearby (see: Bouguer anomaly), but also deeper variations inside the Earth. However the direction and magnitude of the changes demonstrate both that gravity decreases as you get higher, and increases as you move away from the equator.

Cody Don Reeder, a science educator, did a nice experiment to show that gravity (and hence weight) changes based on your location. The two main things that affect gravity are latitude and elevation, and you should be able to detect these with a sensitive enough scale and a large enough change in altitude and/or location.

Cody uses a 295g cube of non-magnetic tungsten, and a jewelry scale that weighs up to 500g with an accuracy of 0.030g (30mg). He weighs this in Logan UT, and Manchester NH.

The weight varies as expected. At higher altitudes you are further from the center of the Earth, so the gravity and weight decrease. At higher latitudes (more North) the effects of the spin of earth are less, and so apparent gravity is greater (plus you are closer to the center of the earth, due to the equatorial bulge).

Going from Logan, UT to Manchester,NH is both a lower elevation and a higher latitude, so weight is expected to increase, which it does by about 0.22g, or 0.074%. With just an increase in altitude from 4,500 to 7,600 ft the weight decreases by about 0.06g, or 0.020%.

We can calculate the expected weight, assuming the Earth is of even density, with this calculator, which also gives the equations used:

https://www.sensorsone.com/local-gravity-calculator/

(Note, the FAC value is approximating a section of the inverse square curve with a straight line. This is accurate for altitudes within the atmosphere)

The formulas used by this calculator are based on the International Gravity Formula 1980 (IGF) which determines the gravity from the position of latitude, and the Free Air Correction (FAC) which corrects for height above sea level.

IGF = 9.780327 (1 + 0.0053024 x sin2(Φ) – 0.0000058 x sin2(2 x Φ))

FAC = -3.086 x 10^-6 x h

g = IGF + FAC

Symbols

- g = Theoretical local gravity
- IGF = International Gravity Formula
- FAC = Free Air Correction
- Φ = Lattitude
- h = Height relative to sea level

The

*theoretical*local g values are given in the diagram above. The Manchester value increases by .052% (vs. .074% observed). The Higher altitude Logan value varies by about (.028%). The differences here are due to this being a

*theoretical*local g.

Actual local g varies based on the composition of the Earth, this can be local variations based on the type of rock nearby (see: Bouguer anomaly), but also deeper variations inside the Earth. However the direction and magnitude of the changes demonstrate both that gravity decreases as you get higher, and increases as you move away from the equator.

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