# Making money from gravity

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).