Purpose: Discussion of average density using understandable units of total mass and volume of the Earth
Supplies: Can of Beer or Soda, 1-pound Bag of Pretzels
Background and Demonstration:
The average density of the Earth may be found from the total mass and volume of the Earth. The volume is obtained from the radius, reasonably accurate estimates of which were made at about 200BC by Eratosthenes. The details of this method may be found in Earth Science texts, but a modern estimate of the average radius of the Earth is 6371km. Assuming the Earth is a sphere (which is a good approximation to 99.8% accuracy in radius), the volume of the Earth is 1.08 x 10^12 km^3. However, I have yet to encounter any person who has a good intuitive feel for what a km^3 is. Therefore to put this in readily understandable terms, we may define a new unit, the CB unit ("Can of Beer") [Feel free to change the name; the CB unit appeals to college students.] At this point, you dramatically display your CB. Now,
1 CB = 12 oz. = 21.65 in^3 = 355 cm^3 = 3.55 x 10^-13 km^3
The Earth's volume, in our units is
V = (1.08 x 10^12 km^3) / (3.55 x 10^-13 km^3/CB) = 3.0 x 10^24 CB
= 3,000,000,000,000,000,000,000,000 CB (24 zeros)
= 3 trillion trillion Cans of Beer [An intoxicating concept!]
The total mass of the Earth may be determined by measuring the acceleration of gravity at the Earth's surface (Galileo's experiment) or by measuring the orbital period of satellites. The result is that the total mass of the Earth is 5.97 x 10^24 kg. Once again, American's have a poor understanding of the kg, and I don't think anyone has a good feeling for what this number represents. Therefore, to put the mass of the Earth in more understandable units, and appropriate to our previous choice of units, we will define the BP unit ("Bag of Pretzels"), once again dramatically displayed. In the US, we still buy pretzels in bags of a certain number of ounces, but ounces are confusing since that term is used for both weight or volume. Although difficult to find, I use a 1-pound bag of pretzels as my BP unit. In this case,
1 BP = 1 lb. = 0.455 kg (at least at the Earth's surface)
Then the mass of the Earth may be expressed as
M = (5.97 x 10^24 kg) / (0.455 kg/BP) = 1.3 x 10^25 BP
= 13,000,000,000,000,000,000,000,000 BP (24 zeros again)
= 13 trillion trillion Bags of Pretzels [Feed the world!]
Finally, we may obtain the average density of the Earth by dividing total mass by total volume.
Avg. Density = M/V = (5.97 x 10^24 kg) / (1.08 x 10^12 km^3)
= (5.97 x 10^27 g) / (1.08 x 10^27 cm^3)
= 5.52 g/cm^3
You can put this into perspective by noting that the density of water is about 1 g/cm^3, the density of rocks at the Earth's surface (granite) is about 2.7 g/cm^3, and the density of rocks in the upper part of the mantle (peridotite) is about 3.4 g/cm^3. If the average density is so much greater than the density of surface rocks, the density of the Earth's materials must increase dramatically toward the Earth's center.
Of course, to give the average density an even more realistic perspective, we express it in our new units:
Avg. Density = (1.3 x 10^25 BP) / (3.0 x 10^24 CB)
= 4.4 Bags of Pretzels / Can of Beer
Imagine how it would feel to consume pretzels and beer (or soda) in those proportions! Or, imagine trying to fit 4.4 bags of pretzels into an empty beer (or soda) can. On average, the Earth is clearly very dense.
Jeffrey S. Barker (SUNY Binghamton) Demonstrations of Geophysical Principles Applicable to the Properties and Processes of the Earth's Interior, NE Section GSA Meeting, Binghamton, NY, March 28-30, 1994.
Questions or comments: jbarker@binghamton.edu
Last modified: March 18, 1996 (content), June 6, 2021 (reformatted and moved to Google sites)