Is Gravity Different In Your Neighborhood?

We bought a cheap digital scale recently for weighing Zed. Zed’s on a weight-reducing diet and we wanted a means to verify that it’s actually working. The scale came with a better-than-average instruction manual (better than the average instruction manual for a cheap Chinese-made product, that is) which contains one very strange paragraph, which I will reproduce here verbatim without sprinking it with the “[sic]”s that it merits:

CALIBRATION

When to calibrate – calibration is almost never required.

If the scale is inaccurate, calibration may be desired when the scale is first set up for use, or if the scale is moved to a different altitude or gravitation. This is necessary because the weight of a mass in one location is not necessarily the same in another location. Also, with time and use, mechanical deviations can occur.

It’s been many, many years since either my high-school or college Physics classes, but I’m pretty sure that I remember that there is no such thing as “a different gravitation”, at least not within our universe. In fact, had you asked me 25-odd years ago, I could have rattled off the Universal Gravitational Constant to at least three significant figures.

Now, technically speaking, it is accurate that “the weight of a mass in one one location is not necessarily the same in another location” if you interpret “weight” to mean “what a scale says when you put a mass on it”. That’s why physicists et al use the term mass and not weight. But this variation is only relevant if you’re talking about moving the mass from the surface of the planet to far above it, like taking something from Cape Kennedy to the ISS with the space shuttle. I’m quite sure that moving something from, say, a sea-level freight dock on the coast of China to Boulder, where the official altitude is 5430 feet, would not produce a measureable change in its mass. Moreover, that change in altitude most certainly wouldn’t produce a change in weight that would register within the stated accuracy of this cheap scale (which is seemingly two grams, although it’s not clear whether the figure stated in the Specifications is accuracy or resolution, but I digress).