Cody's Lab: How Weight Changes With Location and Velocity

Mick West

Staff member
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 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
Content from External Source
(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 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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Mick West

Staff member
The fact that weight decreases as you get higher is a bit a problem for the rather odd "density" theory of gravity. Air gets measurably less dense as you go higher. So if relative density is what makes things fall down then they would weigh more as they moved into less dense air. However they weigh less. They weight less because "density" has nothing to do with.

Mick West

Staff member
The scale used by Cody is a generic Chinese scale, costing about \$10: http://amzn.to/2qRMNvh

The accuracy listed is 0.01g. Reviews on amazon are generally positive, but say the scale might not be calibrated perfectly. However for the purposes of this experiment the only important figures are the relative weights. So long as the measurements are carried out with the same scale then it does not matter if there's a small calibration error.

And if you want to repeat the experiment exactly, here's the tungsten cube for \$75: http://amzn.to/2sLMliL

Tungsten is great because:
• It's not magnetic
• It will not absorb water or change weight by chemical reactions
• It's easy to carry around, as it's so dense.

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Z.W. Wolf

Senior Member.
The first to measure a difference in the strength of the earth's gravitational field due to location was Jean Richer during an expedition to French Guiana in 1671-1673. He found that his seconds pendulum didn't keep proper time (as measured against the stars). It lost 2m 28s per 24 hours. He had to shorten the pendulum length by 2.8 mm in Guiana as opposed to its length in Paris.

From this data and from his theory of gravity (the force of gravity decreases with the inverse square of the distance between objects) and the assumption of a rotating earth, Newton created a theory that the earth is an oblate spheroid, and that this shape was produced by the centrifugal force of the rotation.

This led to the dispute between Newton and Cassini as to whether the earth is an oblate or prolate spheroid, which was only settled by a measurement of the meridian in Lapland and comparing it to the measurement of the meridian in France, showing that Newton was correct. A measurement of the meridian in Peru was further confirmation.

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Mick West

Staff member
The first to measure a difference in the strength of the earth's gravitational field due to location was Jean Richter during an expedition to French Guiana in 1671-1673. He found that his seconds pendulum didn't keep proper time (as measured against the stars). It lost 2m 28s per 24 hours. He had to shorten the pendulum length by 2.8 mm in Guiana as opposed to its length in Paris.

A related type of thing was used by George Airy, with a pit and a pendulum:
https://todayinsci.com/A/Airy_George/AiryGeorge-Pendulum.htm

Measuring the difference in period of a pendulum on the surface and down the pit. Essentially calculating the gravitational constant.

Z.W. Wolf

Senior Member.
The fact that weight decreases as you get higher is a bit a problem for the rather odd "density" theory of gravity. Air gets measurably less dense as you go higher. So if relative density is what makes things fall down then they would weigh more as they moved into less dense air. However they weigh less. They weight less because "density" has nothing to do with.

One also has to ask what the gravimeters used by mining engineers and so on are actually measuring.

https://en.wikipedia.org/wiki/Gravimeter
A gravimeter is a type of accelerometer, specialized for measuring the constant downward acceleration of gravity, which varies by about 0.5% over the surface of the Earth.
Content from External Source
Someone in the comments section of that YT video joked about buying gold somewhere where it's lighter and selling it somewhere where it's heavier. That's an old, old whimsical observation. But for that very reason, and others, precious metals are weighed on balance scales against reference masses.

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Mick West

Staff member
But for that very reason, and others, precious metals are weighed on balance beams

Or digital scales calibrated with a reference mass. Like the one I just ordered for the scale I also just ordered.
http://amzn.to/2sBdhCA

NobleOne

Member
I wonder if weight changes at the same location over night since the object gets further away from the Sun.

Mick West

Staff member
I wonder if weight changes at the same location over night since the object gets further away from the Sun.

Not easily measurably, and certainly not with this scale. Also the moon would have far more effect - still not measurable except with a super sensitive scale though. It's been done:

Source: https://physics.stackexchange.com/q...easurements-relate-to-gravitational-wave?rq=1
Source Article: http://iopscience.iop.org/article/10.1088/0026-1394/18/3/006/meta

1µm/s^2 (micrometers per second squared) is about 1 ten millionth of g, which is around 9.81 m/s^, or 9,810,000 µm/s^2

Astro

Senior Member
Such a setup should be capable of detecting the Eötvös effect in a commercial airliner (assuming you could average out vibrations during level flight), should it not? Was that accounted for in the theoretic difference, or might that help explain the deviation from the theoretical difference?

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Mick West

Staff member
Such a setup should be capable of detecting the Eotvos effect in a commercial airliner (assuming you could average out vibrations during level flight), should it not? Was that accounted for in the theoretic difference, or might that help explain the deviation from the theoretical difference?

See the video from 12:55 onwards. He measured on the plane, and average it out later. I left it out as it's a bit complex, but it's really another good piece of evidence for both the curvature and rotation of the Earth.

0x90

Closed Account
I wonder if weight changes at the same location over night since the object gets further away from the Sun.
Provided I haven't messed up some mundane detail, when earth is at perihelion, the gravitational force between the sun and a kilogram mass fluctuates by 1.063e-9 newtons (~108 nanograms in earth gravity) between noon and midnight, and 9.614e-10 newtons (~98 nanograms in earth gravity) at aphelion. Between perihelion and aphelion, it fluctuates a far greater 3.967e-4 newtons (~40 milligrams in earth gravity).

Mick West

Staff member
I've got one of those scales. Next time I drive up into the Sierra's I could check the altitude variation out.

That's a polished stone ball which should be a nice consistent weight. It seems like you can get 0.01 to 0.04g variations just from handling it with bare hands. Need to keep it clean and use gloves.

Ideally I'd have a 495g weight - the more mass, the more noticeable the difference in weight.

Astro

Senior Member
I'm thinking of trying that experiment on my next flight to try to capture the Eötvös effect. I see an identical looking scale for sale on ebay. Does it have an internal battery or do I have to supply external power for it?

Mick West

Staff member
I'm thinking of trying that experiment on my next flight to try to capture the Eötvös effect. I see an identical looking scale for sale on ebay. Does it have an internal battery or do I have to supply external power for it?
It uses two AAA batteries. I bough my scale from Amazon (\$10.10), the box is branded TBBSC TB011, but the scale itself is just the chinese generic. It does work well though. It powers off after a minute if the weight does not change, but I think the constant variation on the plane will keep it awake.

I also got a 500g calibration weight (\$11.58). That will be good for the ground based test, as I can calibrate the scale to 500g near sea level, and then that will give the maximum decrease in weight as I go higher. However you will probably want to use a lighter weight on the plane, as the scale stops with an error if you go over 501.00g momentarily.

You will also want some method (like a bullseye level, real or virtual) of verifying the scale is level (on average), as (experimentally) around 1° tilt gives an error of 1g for my 500g weight.

You want to be in straight and level flight, you should be able to verify this with a few minutes of video with the bubble not shifting significantly. Basically what Cody does.

NoParty

Senior Member.
I've got one of those scales. Next time I drive up into the Sierra's I could check the altitude variation out.

That's a polished stone ball which should be a nice consistent weight. It seems like you can get 0.01 to 0.04g variations just from handling it with bare hands. Need to keep it clean and use gloves.

Ideally I'd have a 495g weight - the more mass, the more noticeable the difference in weight.
Hmmm...a polished stone that shouldn't be touched by human hands.

Does this have something to do with debunking super powers?

Mick West

Staff member
I wonder if you could get a measurable Eötvös effect in a car? There's some flat straight roads round here. What if I went 50 mph?

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

Using SI units, not sure what Ω would be in? radians per second? 7.2921150*10^-5 according to Wikipedia

Assuming only east-west motion, so zero v, u = 50mph is 22.35 m/s, and I'm around 38.5°N latitude

R = Radius of Earth = 6371000m

ar = 2*(7.2921150*10^-5)*22.35*cos(38.5 degrees) +22.35^2/6371000 = 0.00262937596 m/s2 ??

given g=9.81, so for a 400g weight, that would be .00262937596/9.81*400 = +/- 0.1 gram variation, easily detectable.

Unless Ω is in rotations per second, which would make it 2pi smaller or about 0.016 grams, much harder.

Looking at this paper:
At latitude 43º where 2Ωsin(latitude) is approximately equal to 10^-4
Content from External Source
2*(7.2921150*10^-5)*sin(43 degrees) ~= 10^-4

So seems like a plausible experiment.

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Mick West

Staff member
I wonder if you could get a measurable Eötvös effect in a car? There's some flat straight roads round here. What if I went 50 mph?

Well, just did a little exploratory experiment at 30mph, and I think this one would need a bit more sophisticated equipment. I used a weight combination of 400g (screws in a plastic jar, on a high friction Bench Dog). However the weight varies by around +/- 8g just from variations in the road surface. That makes a 0.1g variation difficult to detect without continuous data logging.

angelote

New Member
Hi,

I would like to warn you will have different readings on the scale because the air density is not the same at sea level as inside the aircraft cabin.

At sea level the air density is r0 = 1,2 kg/m³ (20 ºC; 101325 Pa; 50 %HR).

Inside the plane the air pressure could be around 80 kPa, thus the air density would be r1 = 0,95 kg/m³.

If “your weight” (495 g) has a density around 2500 kg/m³, this mean the volume is around 200 cm³. The buoyancy (in mass units, actually it is a force) at sea level would be b0 = r0·V = 240 mg. The buoyancy inside the plane: b1 = r1·V = 190 mg. Thus, the difference between the two weighing readings, due to air density, would be Dm = b1 – b0 = 50 mg. That means the weighing reading inside the plane will be 0,05 g higher. This is just 5 intervals (the difference in mass between two consecutive indications) of your indicating device. This is too little, you can neglected

(For estimation of air density, see “Guidelines on the Calibration of Non-Automatic Weighing Instruments”, EURAMET Calibration Guide No. 18, Appendix A):
https://www.euramet.org/publications-media-centre/cgs-and-tgs/

Mick West

Staff member
If “your weight” (495 g) has a density around 2500 kg/m³ [...]That means the weighing reading inside the plane will be 0,05 g higher.

Steel has a density of 8000 kg/m3, so the error there will be around a third that. Tungsten has a density of 19,250 kg/m3, so the buoyancy error would be around 1/8 your calculation, or <0.01g

Assuming around 7,500 pressure altitude for the plane, the corresponding free air correction would be 0.38g

It's something to consider, but at worst it's just going to decrease the gravity/height effect slightly, it's going in the opposite direction, so you can't mistakenly ascribe gravity effects to density here.

Mick West

Staff member
A related experiment:
http://gnomeexperiment.com/
Gravity varies slightly, wherever you go. So can we measure this phenomenon with a set of Kern scales and our travelling assistant? Watch the film or explore the results so far:
Content from External Source
The site has a map showing how much an approximately 308g gnome weighs at different points on the globe.

drhex

New Member
Cool thread! I bring my digital scale and a reference weight whenever I'm traveling far. Steinberg systems SBS-LW-2000A, which weighs up to 2kg to a precision of 0.01g, so smallest detectable change is one part in 200000.
I thought at first that I could increase the precision further by using another unit than the default "gram". By dividing a measured weight with the smallest possible change in the last digit, one finds the total number of scale units up to that weight for any unit. Over the entire range of the scale, that was highest for "Jewelry taels", 270000 steps. But it turned out that it skips every fourth of the possible values so that there is still only 200000 (i.e. it internally produces a rounded value in grams and then scales and rounds that value again to display other units).
Leveling is essential when measuring small changes. The built-in spirit level was poorly calibrated, but I place a smartphone running a leveling app on the scale before any measurement to calibrate to 0.1 degrees.
I use a 2kg reference weight, so there is the risk that the displayed value will be too high and the display only shows 'error'. This could be fixed by going into to configuration settings and telling the scale that it in fact has 300000 scale units. Weights are the same anyway, but now i can make use of the calibration/tare margin and go up to about 2040 grams.
My greatest problem is that the weight does not remain constant if I just leave something on the scale, there is a slow "bounce" effect and the value creeps several values in the smallest digit as time passes. Thus I start a stopwatch when placing the weight and take the reading after exactly 15 seconds.

David Coulter

Senior Member.
Gravimetry is a common technique used in mineral exploration. You measure the variations in gravity very precisely and apply corrections to calculate the density of subsurface rocks. The LaCoste & Romberg G-meter was pretty much the standard instrument. The principle is that you adjust a mass so that it is level - this is optically observed using the eyepiece to view and align scribe marks on the mass and the frame. This has to be used on solid ground in the absence of any seismic activity as these accelerations will far exceed the range of the instrument. You also need precision location of measurement stations in lat, long, and elevation.

L&R G-Meter:

The G-Meter is an extremely sensitive and fragile instrument - a good bump with the mechanism unlocked requires recalibration. It is normally transported in a thermally stabilized (heated) container. There are much more sophisticated (i.e., VERY EXPENSIVE) gravimeters but the L&R is a workhorse that can be rented for reasonable prices (~\$150/day) and purchased for around \$50k.

For precision gravity you need to perform: Instrument (drift) correction; Latitude correction; Free-air correction; Bouguer correction (reduction to the Earth's geoid); and Terrain correction. Terrain correction is computationally intensive but very important - if you measure gravity in, for example Salt Lake City, the mountains above your measurement point are exerting a small but measurable gravitational force. This requires a digital elevation model of the nearby terrain whereas the other corrections only require knowing the location of the measurement.

Precision gravity can provide incredibly useful information about the near surface geology in terms of the density of materials (which can be approximated to rock type) as well as revealing crustal scale structures/faults.

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Mick West

Staff member
I’m repeating the on ground observation at Sacramento and Denver. Then on to Albuquerque.

Leifer

Senior Member.

But I have a few amateur questions.....

1) Can these scales compensate for altitude ? Are they spec'd for a range of altitude ?
In other words.....can their internal sensors and method of measurement fluctuate because of altitude during test ?

2) On an airliner... it seems there would be almost too many inperceivable "level" fluctuations, and if given inaccurately, the small weight differences/data might differ.

In fact, in a reverse way...if there were an accurate scale, plus an accurate 360* pressure sensor, the relative gravity could be deduced, and by the the motion of the aircraft.

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Staff member

Inti

Senior Member.
I wonder if weight changes at the same location over night since the object gets further away from the Sun.

To put 0x90's numbers in context, by my quick calculation we are 392.4 times closer to the sun in the northern winter than the daily increase in distance at night due to earth's rotation.

Mick West

Staff member
Back in Sacramento, 499.93. So it's back up, but not exactly back to 500.00.

Mick West

Staff member
I'm probably going to Las Vegas next month for the Flat Earth convention. I was thinking of doing this test at the Stratosphere Hotel which has an observation deck about 1000 feet up. Latitude is 36.14,
local g at 2000 feet = 9.79643
local g at 3000 feet = 9.79549

9.79549/9.79643*500 = 499.95

Hmm, this probably is not enough, as my scales seem to have a variance of around that (0.05). Still, a consistent weight of 500.00 at the bottom, then 499.95 less at the top, and 500.00 would at least illustrate the principle if I can get some Flat Earth folk to accompany me.

DavidB66

Active Member
This is a comment on 'flat earth and gravity'. Please excuse me if this is not the most appropriate place for it, but the thread came up when I searched for those terms.

I noticed a small nugget of information in today's (UK) Sunday Times magazine. In an article on the CERN Large Hadron Collider, it is stated that

The tunnel is so long it flexes with the phases of the moon [sic]…"the moon deforms the tunnel," explains Glyn Kirby, the Cern engineer in charge of magnets, "and so the LHC, like the sea, is moving. We correct for this with thousands of small magnets that push the beam back into position."

The author (not Kirby) is probably confusing the phases of the moon with the daily tides, which have no close connection with the phases, though the tides are indeed somewhat higher when the moon is full or new, when sun, earth and moon are in a straight line, than at half moons, when they are at right angles.

Regardless, it is an interesting example of a gravitational effect that can hardly be explained by 'buoyancy and density'. I have occasionally seen flat-earthers attempting to explain the tides of the sea by some obscure mechanism or other, but I don't recall anything that would begin to account for the influence of the moon on a tunnel deep underground. Of course, they can always deny the facts.

Amber Robot

Active Member
This is a comment on 'flat earth and gravity'. Please excuse me if this is not the most appropriate place for it, but the thread came up when I searched for those terms.

A lot of physics has to be wrong to even attempt to get a flat earth model to work so I’m guessing that flat earth proponents wouldn’t have a problem calling the LHC fake, just like they do for space travel.

Robert Fish

New Member
Is it possible that, because you zero your scales at different altitudes, air pressure is skewing the results? My first thought was an experiment using something like at the CN Tower or some sort of reasonably rapid elevation change with a stable platform at the apex. Seal a container with the scale and weight at the base, then run it to the top, should show change without possible air pressure bias, (if the scale would stay on for the entire trip time).

Another approach is to either evacuate or pressurize your containers which is an option that should allow for consistent results without any local air pressure bias.

Mick West

Staff member
Is it possible that, because you zero your scales at different altitudes, air pressure is skewing the results? My first thought was an experiment using something like at the CN Tower or some sort of reasonably rapid elevation change with a stable platform at the apex. Seal a container with the scale and weight at the base, then run it to the top, should show change without possible air pressure bias, (if the scale would stay on for the entire trip time).

Another approach is to either evacuate or pressurize your containers which is an option that should allow for consistent results without any local air pressure bias.
Not really, you can calculate the effect of buoyancy, and it's quite small.

JohnP

New Member
If we're considering tiny corrections in Cody's experiment, don't forget the speed of the aircraft. The centrifugal force due to the Earth's rotation changes gee by a few parts in a thousand (depending on latitude), and the speed of the aircraft isn't insignificant compared to that of the Earth's rotation.

Mick West

Staff member
If we're considering tiny corrections in Cody's experiment, don't forget the speed of the aircraft. The centrifugal force due to the Earth's rotation changes gee by a few parts in a thousand (depending on latitude), and the speed of the aircraft isn't insignificant compared to that of the Earth's rotation.
See the video from 12:55 onwards. He measured on the plane, and average it out later. I left it out as it's a bit complex, but it's really another good piece of evidence for both the curvature and rotation of the Earth.

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