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#1
Old 10-06-2007, 04:06 PM
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The Earth is not a sphere; but is the Earth's atmosphere a sphere?

The Earth is a little bit flattened at the poles (or conversely, a little bit bulged at the equator). But is the atmosphere also flattened at the poles? The atmosphere shouldn't "care" about the shape of the Earth, should it? I mean, the atmosphere should end (for the purposes of this question, let's say the atmosphere "ends" when atmospheric pressure becomes immesurably small) at the same distance from the center of the Earth, regardless of how much rock is underneath it. Right?

If this were true, we'd see higher-than-expected air pressures at the poles, and my brief unscientific research seems to bear this out:

The elevation at the South pole is roughly 2835 meters.cite
The standard barometric pressure at that altitude is 548mmHg.cite
The actual pressure at the South pole runs between 670-685.cite
{I'm totally prepared to be corrected on any of this. Including my math or the soundness or my reasoning.}

So is it true? Is the Earth's atmosphere much closer to a true sphere than the Earth itself?
#2
Old 10-06-2007, 04:35 PM
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Just a guess, but since the atmosphere spins more-or-less in synch with the earth, I would assume it bulges for the same reason. I would say centrifugal force, but some clown is certain to tell me it doesn't exist (neither is there a gravitational force, in exactly the same way) so I will say that the air molecules above the equator are a bit more successful moving in a straight line than those at the poles.

Actually, the prevailing winds slightly counterbalance this, but they don't go 1000 mph as the earth's surface at the equator nearly does. So it ought to bulge a bit less.
#3
Old 10-06-2007, 05:28 PM
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Quote:
Originally Posted by Hari Seldon
Just a guess, but since the atmosphere spins more-or-less in synch with the earth, I would assume it bulges for the same reason. I would say centrifugal force, but some clown is certain to tell me it doesn't exist (neither is there a gravitational force, in exactly the same way) so I will say that the air molecules above the equator are a bit more successful moving in a straight line than those at the poles.
Centrifugal force exists, but only in the rotating reference frame. Its counterpart, centripetal force, exists in the stationary or "lab" frame. The gravitational force most definitely exists in all reference frames, even if some of them aren't experiencing it at certain moments.

Dunno about the atmosphere question though.
#4
Old 10-06-2007, 05:31 PM
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Quote:
Originally Posted by Spatial Rift 47
Centrifugal force exists, but only in the rotating reference frame.
Dr. Brantley would be very angry with me if I didn't say the following:
Quote:
There is no such thing as centrifugal force. It's inertia.
#5
Old 10-06-2007, 05:36 PM
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IIRC, the Earth is the closest thing to a perfect sphere on Earth. The ratio of the long diameter at the equator to the short ones at the poles is small compared to lots of other objects we consider spheres, like balls, bubbles, etc...
#6
Old 10-06-2007, 05:56 PM
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The atmosphere takes its shape from the shape of the gravity well its in, not from the shape of the dirt ball in the middle of that gravity well.

If Earth had much stronger gravity on one side than the other (say a small neutronium deposit) the atmosphere would react to that, even if the planet itself was perfectly spherical.

So I'm gonna suggest that the shape of the "top" of the atmosphere matches roughly the shape of the gravity well, net of centrifugal/centripetal forces. Also net of electromagnetic forces on the ions created & moved by the solar wind.
#7
Old 10-06-2007, 06:59 PM
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How are you defining the top of the atmosphere? 'Immeasurably small' doesn't cut it. Do the radiation belts count as part of the atmosphere?
#8
Old 10-06-2007, 07:23 PM
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Quote:
Originally Posted by bouv
the Earth is the closest thing to a perfect sphere on Earth.
I don't think so. This wiki page on earth radius says the difference between poles and equator is just under 22km, for a variance of about 1 part in 300.

Here's a link to a place that sells tungsten-carbide balls that are claimed to be spherical within 0.000025 - for a 1/2" ball, that's one part in 20,000.
#9
Old 10-06-2007, 07:33 PM
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Quote:
Originally Posted by Quartz
How are you defining the top of the atmosphere? 'Immeasurably small' doesn't cut it. Do the radiation belts count as part of the atmosphere?
I think you understand my question. How, for the purposes of my question, would you define the "top of the atmosphere"?

Do you really think the radiation belts qualify for the purposes of this question? Really?
#10
Old 10-07-2007, 02:09 AM
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Quote:
Originally Posted by Xema
I don't think so. This wiki page on earth radius says the difference between poles and equator is just under 22km, for a variance of about 1 part in 300.

Here's a link to a place that sells tungsten-carbide balls that are claimed to be spherical within 0.000025 - for a 1/2" ball, that's one part in 20,000.
IIRC the Earth is more of a sphere then the tolerance for billiard balls.
#11
Old 10-07-2007, 02:16 AM
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I've seen footage of experiments with flame aboard the space shuttles, and candle flame always looks spherical. Would the same forces or lack thereof involved in that make Earth's atmosphere spherical?

Last edited by Siam Sam; 10-07-2007 at 02:17 AM.
#12
Old 10-07-2007, 02:49 AM
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Quote:
Originally Posted by LSLGuy
If Earth had much stronger gravity on one side than the other (say a small neutronium deposit) the atmosphere would react to that, even if the planet itself was perfectly spherical.
The only way to have greater gravity on one side of the planet is to also have greater density. The Earth rotates around an axis that passes through its center of gravity. An unbalanced Earth would wobble like an unbalanced tire as it turned. I don't know all the effects that would have, but I suspect that atmosphere density would be the least of our worries.
#13
Old 10-07-2007, 03:58 AM
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Jeez a dozen posts and nobody has mentioned the obvious point?

The atmosphere has tides. Aside from the pull of the moon and sun the atmosphere swells as it heats up and shrinks as it cools. That all causes the depth of the atmosphere to change constantly.

So no, that atmopshere is certainly not spherical.
#14
Old 10-07-2007, 06:31 AM
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Parts of the atmosphere certainly aren't spherical. The troposhpere where most of the weather happens is much thicker at the equator copared to the poles.

Quote:
The actual pressure at the South pole runs between 670-685
Those figures are in mb not mmhg. They are equivalent to 502 - 514 mmhg. This would suggest the atmosphere is thinner at the poles. It should also be pointed out that the "standard atmosphere" has no particular bearing on reality, particularly when considering an extreme part of the Earth.

Also from http://aerospaceweb.org/question...re/q0090.shtml

Quote:
Along the equator, the atmosphere tends to bulge outward more so than at the poles due to the centrifugal effect of the planet's rotation as well as the gravitational attraction of the Moon.

Last edited by Richard Pearse; 10-07-2007 at 06:34 AM.
#15
Old 10-07-2007, 06:40 AM
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Quote:
Originally Posted by ChrisBooth12
IIRC the Earth is more of a sphere then the tolerance for billiard balls.
This site says a typical billiard ball is 2.25" in diameter, with a tolerance of .005". That gives a variance of 1 part in 450, compared to 1 in 300 for the Earth. So the billard ball wins here.
#16
Old 10-07-2007, 07:52 AM
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This site on the South Pole Station says:
Quote:
The station is at an elevation of 9,300' (2900m), however the equivalent pressure elevation, based on polar atmospheric conditions, will vary from 10,800(3300m) to 13,120 (4,000m).
Which is another way of saying that the atmosphere is not as thick there.


Another important point is weather: the atmosphere regularly develops bulges (high-pressure areas) and depressions (low-pressure areas). These make it non-spherical over areas spanning hundreds of miles.
#17
Old 10-07-2007, 08:47 AM
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The usual bit about the earth being smoother than a billiard ball is talking about surface finish, not overal sphericity.

The bumps on the Earth, from the-trench-which-shall-remain-nameless-and-I-HOPE-unvisited-in-a-future-post to the peak of Everest, represent a surface roughness of ~12 miles on a sphere of diameter ~8000 miles.

Overall, that's pretty smooth. But as others have pointed out, that ignores the fact that the ball might be real smooth, but it isn't really all that round.
#18
Old 10-07-2007, 11:28 AM
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Quote:
Originally Posted by LSLGuy
The usual bit about the earth being smoother than a billiard ball is talking about surface finish, not overal sphericity.

The bumps on the Earth, from the-trench-which-shall-remain-nameless-and-I-HOPE-unvisited-in-a-future-post to the peak of Everest, represent a surface roughness of ~12 miles on a sphere of diameter ~8000 miles.

Overall, that's pretty smooth. But as others have pointed out, that ignores the fact that the ball might be real smooth, but it isn't really all that round.
Yes, that's correct. However (to continue the hijack), the surface finish of the Earth (12 parts in 8000) equates to a surface roughness on a pool ball of over 3 thousandths of an inch. That's extremely rough when you're talking about a manufactured product.

So, the upshot is:
Sphericity: A pool ball is slightly more spherical that the Earth
Surface Roughness: A pool ball is substantially smoother than the Earth.
#19
Old 10-07-2007, 12:54 PM
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Quote:
Originally Posted by 1920s Style "Death Ray"
Those figures are in mb not mmhg. They are equivalent to 502 - 514 mmhg. This would suggest the atmosphere is thinner at the poles. It should also be pointed out that the "standard atmosphere" has no particular bearing on reality, particularly when considering an extreme part of the Earth.
Gah! I knew I shouldn't have attempted any reasoning. Especially anything involving math.
#20
Old 10-07-2007, 03:23 PM
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Quote:
Originally Posted by Spatial Rift 47
Centrifugal force exists, but only in the rotating reference frame.
I refer you all to this xkcd strip.
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#21
Old 10-07-2007, 04:08 PM
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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.
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#22
Old 10-07-2007, 09:39 PM
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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.
#23
Old 10-07-2007, 09:56 PM
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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

Last edited by Triskadecamus; 10-07-2007 at 09:57 PM.
#24
Old 10-08-2007, 02:19 AM
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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.
#25
Old 10-08-2007, 06:11 AM
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Quote:
Originally Posted by zut
Yes, that's correct. However (to continue the hijack), the surface finish of the Earth (12 parts in 8000) equates to a surface roughness on a pool ball of over 3 thousandths of an inch. That's extremely rough when you're talking about a manufactured product.

So, the upshot is:
Sphericity: A pool ball is slightly more spherical that the Earth
Surface Roughness: A pool ball is substantially smoother than the Earth.
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)?
#26
Old 10-08-2007, 07:43 AM
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Quote:
Originally Posted by Sapo
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?)
#27
Old 10-08-2007, 05:07 PM
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Great response, zut. Your last point might be the deal, though. Thousands of identical parallel machine marks might feel different than a single feature.
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