Re: How deep would the ocean be if the solid earth formed a perfect sphere?

Hi Greg,

If the solid Earth were a perfect sphere, covered evenly by the ocean, then the ocean would be about 2.6 km (1.6 miles) deep.

To work this out requires some facts. Earth isn't exactly a sphere, but it's close, and its average radius, r, is about 6,370 km. So Earth's volume is about (4*pi/3)*r³, or about 1,082,700,000,000 cubic kilometers (km³). The ocean's total volume, according to my encyclopedia (Columbia, 1995), is 1,347,000,000 km³. In other words, the volume of the ocean is only about 1/1000 of the volume of the Earth!

What we want is the depth d of the ocean on a perfectly spherical Earth. There are many ways to work this out. The way I did it is to think about two concentric spheres, the inner one being just the solid earth, with radius r, and the outer one holding both the solid earth and the ocean, with radius r+d. The volume of the outer sphere minus the volume of the inner sphere must equal the volume of the ocean, which gives us an equation to solve:

This was a pretty simple approximation for the true value of volume of the solid Earth: the volume of a sphere with radius 6370 km is probably closer to the volume of the solid earth plus the ocean. But taking that into account changes the answer by less than two percent.

As your question acknowledged, the real Earth has continents which confine the ocean to a smaller area. Therefore the ocean needs to be deeper to hold the same volume. The average depth of the real ocean is about 4 km (2.5 miles). Its deepest point is over 11.5 km (7.2 miles) deep, enough to submerge Mt. Everest and still have 2.6 km (1.6 miles) of ocean above it! As deep as the oceans are, however, their depths are tiny compared to their widths. For example, the the ratio of the width of the Pacific Ocean (11,000 km) to its thickness is about the same as a piece of typing paper (Pickard and Emery, 1990). For oceanographers studying ocean currents, this is a very important fact, because it often means that currents can be thought of as primarily horizontal. Not having to worry too much about vertical motion makes the physics a lot simpler.

A good place to go for further ocean information is the question and answer page maintained by the Woods Hole Oceanographic Institution.

Hope this answered your question!

References:

• Concise Columbia Encyclopedia, Columbia University Press, 1995
• Pickard G L and W J Emery (1990) Descriptive Physical Oceanography: An Introduction, Pergamon Press, Oxford, 320 pp.

Dan Goldner
goldner@mit.edu
MIT/ Woods Hole Joint Program in Oceanography