No. Sea level is (approximately) an equipotential surface. That means that the gravitational potential is the same at all points at sea level. But what we’re interested in is not the potential, but the gravitational field, which is the gradient of the potential. Except for some special cases with high symmetry, the field will not in general be the same at different points on an equipotential surface.
To bve honest Chronos, you lost me. Ignoring the effect of tides, are you saying that my registratable weight would not be the same anywhere in the world at mean sea level? ( I do understand that the gravitational field varies with latitude and even longitude as per **Squinck’s ** cite.
That is correct. The sea-level value of g is indeed different at different latitudes (as well as the smaller perturbations due to geology etc as shown in the “bumpy Earth” map above). It’s been measured pretty accurately – I quoted some figures to several decimal places above.
Flying Dutchman
I think this is the point that mangetout made initially.
For a moment let’s assume the Earth is perfectly spherical and is not rotating.
Now let’s further imagine that the Northern Hemisphere of the Earth is 100% aluminum and the Southern Hemisphere consisted of 100% lead. Aluminum is less dense than lead, and so on this “imaginary Earth”, your weight at the North Pole would be significantly less than your weight at the South Pole.
Granted, in reality, the Earth does not have such extreme delineations of geologic composition, but I’m sure you can see that areas of the Earth that have a higher density would have a greater value of ‘g’ than those areas of Earth with a lower density (or specific gravity).
So if something that is priced by weight is shipped from a heavier place to lighter place would the receiver potentilaly think the sender had cheated them if it’s .05% shy on the receiving end?
astro
Darned good point.
In order to measure mass accurately, some type of “double pan balance” arrangement has to be made. Anything employing springs is measuring force and not mass. I don’t know how the Toledo Scale Company accomplished this but remember their slogan? “No Springs - Honest Weight”
So, in my “imaginary Earth” world, a kilogram of potatoes would show the same mass if you were on the aluminum side or the lead side - provided you used a double pan balance or a Toledo scale or anything else that determines mass.
As wolf-meister has already said the mass doesn’t change, but the force it exerts onto a scale will change.
If both the sender’s scale and the reciever’s scale are properly calibrated than they will both get the same result.
If you on the other hand take your old bathroom scale and weigh yourself once at the north-pole and once on the equator without recalibrating it for the new location you might get a noticeable difference.
I’m just curious how a Toledo Scale “No Springs - Honest Weight” measures mass.
It’s easy to see that a double pan balance has a mass on one side which will counterweight (actually “countermass”) the other side when the masses in both pans are equal.
The single pan balance is also easy to visualize. (A doctor’s scale is a good example.) You stand on the single pan (the platform) and then the masses on that beam, when properly adjusted, display your weight. (mass actually).
Anyway, how does a Toledo scale work because it is hard to visualize the counterweight[sup]1[/sup] system being linked to that weighing platform.
1 - Yes I know it is a countermass system.