The gravitational field strength of a planet depends on size and mass, and the Earth is not uniform in either respect. Because of its rotation Earth’s radius is 21km greater at the equator than at the poles and water (which covers 71.1% of Earth’s surface) is much less dense than the rock that covers the remaining 28.9%.
These two factors, combined with the centripetal force effect of Earth’s rotation itself mean that the strength of Earth’s gravitational field varies across its surface.
This gravity map from the GRACE satellite shows the variation of the gravitational field across Earth’s surface; red indicates higher gravitational field strength and blue lower.
The place with the lowest gravitational field strength is Mexico City (9.779 N/kg, 0.28% below average) helped by it’s elevation, more than two thousand metres above sea level. The highest gravitational field strength is found in Helsinki (9.819 N/kg, 0.13% above average) at a latitude of 60°N.
Because people confuse mass and weight and because Earth’s gravitational field changes the same bar of gold will be measured to have a different mass in different locations. One kilogram of gold will be measured to have a mass of 997.18 grams in Mexico City and 1001.3 grams in Helsinki.
This lends itself to a money-making scam: if I buy gold in Mexico City and sell it in Helsinki I can make a profit of £111 per kilogram (at the current price of £27230 per kilogram). In order to pay for my plane ticket (about £1500) I only need to carry thirteen and a half kilograms of gold (a cube with 9cm sides) with me, though this will cost me about £367000.
You can download the Excel spreadsheet I used to do the calculations for this post: gravity-gold-calculator (31kB, .xls).
See you guys in the airport
And to heck with the plane ticket! Have it measured by an accepted authority in Mexico and sell it on the Helsinki exchange. Hey… you had it weighed by an accepted authority in Mexico. If the weight is off when it reaches Helsinki, you blame it on those bastards working in luggage and customs!!
I would like to believe that this is why my scale at home is different than the scale at my doctor’s office. :-)
This reminds me of “Why don’t they put leap days in July when it’s warmer?” You are also confusing mass and weight. We have to ask how is the gold weighed. If it is weighed with reference to a standard weight (e.g. a mass balance) the reference will also be lighter or heavier in the same proportion. A spring scale shipped from Helsinki to Mexico City (and not re-calibrated on site)would result in the (amusing) scenario above.
I’m not confusing mass and weight, that’s the whole point of the post: the same mass of gold will have a different weight in different location. Good point about the difference reference points though.
Mr. Reid,
You really are confusing mass and weight. In the article, you say “because Earth’s gravitational field changes the same bar of gold will be measured to have a different mass in different locations. ” which is not true. Gravity affects weight, not mass.
Nope, I’m not.
All of the scales I own measure in kilograms, which is the unit of mass. Regardless of the fact that it is weight which is actually being measured, the scales “tell” you the mass. You’ve sort of missed the entire point of the article.
Yes, Mr Reid, I agree with you that the scales (IF they are spring scales, which is what many places like pawn shops and jewelers that buy scrap gold use) will measure the bar to have different masses in different locations. What it’s mass actually IS won’t vary but what’s it’s MEASURED to be will change.
Of course for that amount of profit, you’d have to invest a lot of money (as you noted), time and trouble (and anyone dealing in that volume of gold is probably NOT going to use spring scales simply cause of the inherent inaccuracies so they’d probably not be fooled here.)
Now if we could set up a small-scale place on the moon and convince people “spring scales really ARE accurate”, maybe we could make it profitable enough *laugh*
All scales are calibrated with a known reference mass, whether it’s in Helsinki or in Mexico…
Now what would differ is if the gold buyer in Mexico calibrated his balance in another place.
Anyway I would always put my gold on a balance I already calibrated because I don’t trust the gold buyer’s balance.