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Earth's gravity field anomalies Earth's gravity field anomalies

An entrepreneur reads about how gravity is different in different places around the world, as this animation shows, and gets a terrific idea of how to make money!

He sees that in Mexico City the gravitational acceleration is 9.776 m / s 2 , \SI[per-mode=symbol]{9.776}{\meter\per\second\squared}, while in Helsinki it's 9.825 m / s 2 \SI[per-mode=symbol]{9.825}{\meter\per\second\squared} . Why not buy gold in Mexico City, and then go to Helsinki and sell it there?

He estimates he can make about $200 profit per kg of gold, based on current gold prices. A single standard gold bar weighs about 12.4 kg \SI{12.4}{\kilo\gram} , meaning roughly $2500 profit per gold bar! He then flies out to Mexico City to put his money-making plan into action.

What's wrong with his plan, and why won't he make any money with it?

GIF animation is public domain, courtesy NASA

International laws require adjustment in gold prices be made to account for differences in gravity Gold dealers use different standard weights in the same way world uses different time zones Gold dealers use weighing devices that rely on standard masses, not weights, such as a balance scale Due to general relativity, the mass of the gold bar will decrease by the time he gets to Helsinki

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1 solution

Michael Mendrin
May 3, 2017

In Helsinki, the downward force of the gold bar may very well be greater than the force in Mexico City, but the dealer will be using using standard masses that will exert the same force as the gold bar. He pays according to the sum of the standard masses he has on his scale.

And this is the main reason why we have the International Prototype kilogram , whose mass (not weight) is defined as the definition of one kilogram.

P.S. How come the acceleration due to gravity you've used is nearly 1000 times of the actual values of g g ? :P

Tapas Mazumdar - 4 years, 1 month ago

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oh, that decimal point went AWOL! Thanks for the catch! The funny thing is, the guy still wouldn't be making any money!

Michael Mendrin - 4 years, 1 month ago

he'll be at a loss due to the money he would spend traveling :P

A Former Brilliant Member - 4 years, 1 month ago

Made me laugh, this one. Thanks for the comedy, regardless if it was intentional or not.

Ikoz Manzukovski - 2 years, 11 months ago

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