Friday, 24 March 2017

earth - Is effective gravity constant over the surface of the ocean?


According to Wikipedia:



The Earth is not spherically symmetric, but is slightly flatter at the poles while bulging at the Equator: an oblate spheroid. There are consequently slight deviations in both the magnitude and direction of gravity across its surface. The net force (or corresponding net acceleration) as measured by a scale and plumb bob is called "effective gravity" or "apparent gravity".



and



In combination, the equatorial bulge and the effects of the surface centrifugal force due to rotation mean that sea-level effective gravity increases from about $9.780\,{m/s^2}$ at the Equator to about $9.832\,{m/s^2}$ at the poles, so an object will weigh about $0.5\%$ more at the poles than at the Equator.



But I don't see how this is physically possible.



If the force on a unit of water at the poles was greater than the force at the equator, shouldn't the ocean fall at the poles and rise at the equator? For the same reason that when I step into the bath the water falls where my foot is pressing down on it and rises elsewhere. Surely the force at the surface of a body of water in equilibrium has to be constant.


So is my physical argument wrong, or is the net force on a body actually the same at the poles and equator?



Answer



You suggest that for a body of water to be in stable equilibrium, i.e. to have minimum energy, it should have the same gravitational field everywhere at its surface, as otherwise we would be able to move the water around to lower the energy. This sounds intuitive, but it's just not true.


As an extreme example, consider a puddle of water on Pluto. The gravitational field is weaker there, so by your argument we should be able to harvest energy to sending water to Pluto. But that's completely wrong: it would actually cost an enormous amount of energy to do this.


The right statement is that the gravitational potential is the same everywhere on the surface of water. That has nothing to do with whether the field is the same.


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