Centrifugal force is exactly as real as gravity, and both only exist in particular reference frames. It is not a question for a scientist to say just how real that is, as long as one treats both in the same way. It is perfectly valid to say that neither exists, and that the atmosphere at the equator is just doing a better job of moving in a straight line, but it’s also perfectly valid (and in many cases, including this one, simpler) to say that both do exist as “real” forces.
I would also like to add that the density of the air at the poles is greater than at the equator. This would make it more compact and therefore closer to the Earth’s surface.
You know, the atmosphere is really a lot less spherical than the Lithosphere, not even including the hydrosphere. The outer reaches of the atmosphere are distorted from spherical by solar wind, and magnetic influence. (I think someone mentioned the Van Allen Belts already, and even the stratosphere changes shape every day.) And there are tidal effects of both the sun and moon. Since it is a fluid, as opposed to the solid earth below it, it responds much more to these forces, and consequently must be less perfectly spherical. Temperature and pressure in the Troposphere varies as we all know, but the upper levels of the atmosphere are not static either.
Tris
My gut feeling is that–even neglecting effects from solar wind, tides, and uneven heating–the atmosphere would have a similar shape to the solid Earth. It’s the same reason that the oceans from a surface that follows a near-ellipsoid like the crust. Using the OP’s words, the water on the Earth’s surface shoudn’t “care” about the shape of the land it has to flow around. If it saw the gravitational potential as being equal at all points equidistant from Earth’s center, it woud have no problem forming itself into a sphere superimposed on the lithospere. So the oceans would be really deep at the poles and the equator would be dry.
But this doesn’t happen, because the oceans are attracted not just to the center of the Earth as a point mass, but to the entire mass of the Earth as it is distributed. The non-spherical shape of the earth creates equipotential surfaces for gravity (the one at seal level being called the geoid) that are roughly similar in shape to the planet itself. So the oceans lay on top of the crust with a mostly uniform thickness (if you ignore local topograhpic excursions like trenches and mountains).
This logic for water can be equally well adapted for air. Absent any other influences, the atmosphere, however you choose to bound it, should form a near-ellipsoid, much as mean sea level does. Like the geoid, it will have variations due to local maxima and minima in the Earth’s mass distribution. But it will also not form itself into a perfect sphere.
If you had a pool ball sized Earth, could you feel the mountains with your fingertips? See them with the naked eye (and they appropriate lighting)?
I would think you could. Let’s pick a specific steep-sided feature – the Grand Canyon. It’s approximately a mile deep; translated to a pool ball that’s about 0.0003". Sounds small, but surface finish is measured in microinches (millionths of an inch), and 0.0003" is 300 microinches. Check out this handy chart: 300 microinches corresponds to the finish you get from sawing or very rough milling. Easy to feel with a fingernail, and easy to see (with enough contrast).
For mountains in general, I would think slope becomes important. The Himalayas and the Alps and the Rockies are large enough to be noticable, I would think, but it would be easier to detect a sharp cliff than a gradual decline.
A real machinist would be able to give a better answer, but my sense is that you could probably feel any surface finish over about 63 (a quarter mile scaled up to the Earth) with a fingernail, and see machinging marks down to a surface finish of 8 (about 150 feet). However, the repetative pattern of a normal machining process would be much easier to detect than a single feature. (A thousand parallel scratches is easier to see than just one, right?)
Great response, zut. Your last point might be the deal, though. Thousands of identical parallel machine marks might feel different than a single feature.