# Will some precious metal say gold will weigh different when moved to a different location on earth?

The weight of an object is the force exerted on it due to earths gravity, which by second law of motion is given by:

$$W = mg$$ where $W$ is weight of the object, $m$ mass of the object and $g$ acceleration due to gravity.

Now acceleration due to gravity changes with location since earth is not perfectly spherical. The value being higher at poles than at equator. From Youngs, University Physics, the value varies between $9.78 m/s^2$ to $9.81 m/s^2$.

Thus, the ratio of two extreme weights a body can have is: $$\frac{W_h}{W_l} =\frac{g_h}{g_l} =\frac{9.81m/s^2}{9.78m/s^2} =1.003$$

Hence a body will weigh about 0.3 % more at poles than equator. Which is marginal but may not be ignored in case of some very precious element. If this is true how exports of gold/uranium etc. works?

• Since, as far as I know, no gold is actually sent to the poles, what's the maximum variation in the habitable portion of Earth (i.e. the region between 75 degrees S and 75 degrees N in latitude)? – probably_someone Dec 28 '16 at 12:22
• I'm not sure what the physics question here is - you already know that the weight varies from location to location. Asking how "exports work" in light of that seems to be not about physics, but about the real-world solution to this specific problem, which we generally consider off-topic as "engineering" here. – ACuriousMind Dec 28 '16 at 13:15
• @ACuriousMind I suspect the root of the question - a get rich quick scheme? Buy gold at one location (where gold is lighter) - sell at another (where it is heavier)? Don't forget to figure in the costs of moving the gold. – docscience Dec 28 '16 at 15:04

## 2 Answers

Obviously one is interested in the mass of the sample, not its weight. Balance scales measure mass, while common (digital) scales measure weight. Therefore the latter need to be calibrated for the particular location on Earth were they operate. Check this for more details

A key issue with this question is that the words "weigh" and "weight" and "weigh" in colloquial English refer to mass. An answer of 68 kilos is perfectly acceptable to the question "How much do you weigh?" This usage predates the scientific use of the term, where "weight" now refers to a force.

Gold is bought and sold in units of troy ounces, grams, or kilograms, all of which are units of mass. The canned goods, produce, meat, and bread one buys at a grocery are also sold in units of mass. A kilogram of gold weighs (colloquial meaning meaning of "weigh") the same at the North Pole, the peak of Mt. Chimborazo, the surface of Mars, and the surface of the Moon. The "weight" (scientific meaning of "weight") of a kilogram of gold varies considerably at those locations. But since gold is sold in units of mass, that it's weight varies depending on locale doesn't have much weight (yet another meaning of the word "weight") on how much one pays for gold.