If Earth's atmosphere were frozen into a solid sphere, what would be its diameter?

Answer 1

I think you are asking about what the thickness of a spherical shell would be were the atmosphere to condense into a non-compressible state.

The mass of the atmosphere is approximatelty 5,000 trillion metric tons. According to the National Center for Atmospheric Research, "The total mean mass of the atmosphere is 5.1480×10^18 kg" (see: http://en.wikipedia.org/wiki/Earth's_atmosphere#Density_and_mass )

Now, liquid air has a density of 870 kg/m3. If liquid air is frozen solid, the density will be similar. (wiki)

So: 5.1480×10^18 kg * m^3/870 kg = 5.92*10^15 (m^3)

The surface area of the earth is 510,065,600 km². (wiki)

5.10*10^8 (km^2) * 10^6 (m^2/km^2) = 5.10 * 10^14 m2

So to get the depth of the frozen atmosphere on the surface of the earth, divide the volume of atmosphere by the area of the earth's surface:

5.92*10^15 (m^3) / 5.10 * 10^14 (m^2) = 1.16 *10^1 meter

This is about 11.6 meters, as a spherical shell sitting on the surface of the earth.

*[Note: if you are talking instead about removing all the atmosphere to a remote location and making a sphere that consists of *only* condensed atmosphere, use the formula for the volume of a sphere, and solve back for the diameter.

V= 5.92*10^15 (m^3) = 4/3 pi * r^3

5.92*(10^15) * (3/4) / pi = r^3

1.41*10^15=r^3

1.12*10^5 =r

2.24 * 10^5 meters = 224 km = diameter of the sphere made from condensed atmosphere. ]*

Answer 2

This is not a good question because it does not have a precise answer, since the atmosphere gets less dense as you go up in altitude, but it never quite goes to zero. That said, the atmosphere is about 800 miles thick, which yields the following:

Polar Diameter of the Earth: 7900 miles
Equatorial Diameter of the Earth: 7926.41 miles
Thickness of Atmosphere: 800 miles

Thus:

Estimated Polar Answer: 9500 miles
Estimated Equatorial Answer: 9526.41 miles

Yes?

Answer 3

To answer such a question, you need to presume that the atmosphere has an obvious end, and is equal in all places.

Let's presume that the atmosphere ends 800 miles above us, and the earth's circumference is 25,000 miles, If the atmosphere was frozen, I would imagine the diameter would be about...

20,000 miles

You have to take into account, that this will never happen...

This is just a REALLY ROUGH ESTIMATE and do not ask me the maths involved as it is too complex to write down.

I must however stress that I may be wildly wrong.

Answer 4

Hi. First we need an estimate of how much atmsophere we have. Since the air 'weighs' 14.7 pounds for every square inch on the Earth's surface, we need to know how many square inches the Earth has (figure this out) the result of the number of inches times 14.7 will give a pretty good estimate of the atmosphere's weight. Find the density of frozen 'air' and multiply by the estimate and you'll have a mass and volume. Calculate a sphere with that volume and 'Bob's your uncle.'

Answer 5

If the earth's atmosphere were frozen solid it would be hollow. If you want the diameter of the earth including its atmosphere that would be between 8500 and 9000 miles, depending on your location. It's flatter at the poles and thicker at the equator.

Answer 6

The mass of atmosphere above a square meter of surface is given by m=P/g where P is surface pressure 100,000 Pascals for Earth and g = 9.8 m/s^2. Then m=10,000 kg/m^2 = 10 tons/m^2 = 1 kg/cm^2.

If the frozen density is 1 g/cm^3 (solid nitrogen), 1 kg will be 1000 cm^3, and the shell will be 10m thick

Answer 7

If the atmosphere was frozen solid you could probably measure it's depth in feet.

Answer 8

We're supposed to know that how...?