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Classical Mechanics Level 1

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 $\SI[per-mode=symbol]{9.776}{\meter\per\second\squared},$ while in Helsinki it's $\SI[per-mode=symbol]{9.825}{\meter\per\second\squared}$ . 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 $\SI{12.4}{\kilo\gram}$ , 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