Sometimes you are sailing uphill

Question: I read with interest the recent article on chart projections (“Dealing with distortion,” Issue No. 112, March/April 2001). However, not being a physicist, I can’t understand a point being made and wonder, as a layman, if it was presented backwards? The article notes that “gravity is so weak in the central Indian Ocean that sea level is 328 feet (100 meters) lower than the ellipsoid would suggest … ” If gravity, which pulls us toward the center of the earth, is weak, wouldn’t the effects of centrifugal force pull the water up, away from the center of the earth, and, as a consequence, sea level would be higher? I’m hoping to learn something new. Vin PicaNew York City Answer: I had exactly the same reaction, some 20 years ago, when I first heard this! The reason for the odd behavior lies in the way the oceans and gravity react. Ignore, for a moment, storms and tides, and imagine a spinning earth. The water level is set by the combination of surface tension, centrifugal force (minor) and earth’s gravity. The sea surface lies at a place where all three of these are in balance. Now imagine a place where gravity is stronger than normal. The ocean level will adjust to a place where the gravitational force is the same as everywhere else - and that place will be further from the earth’s center. That is, it will be higher! Likewise, in a place where the gravitational force is lower than normal, the sea level will adjust to a place where the gravity is stronger - closer to the earth’s center. So, we get the (seemingly backward) result that the geoid is high where gravity is high, and low where gravity is low. Other effects also play a role. The topography of the sea bottom also affects gravity, and one can actually “see” seamounts, trenches, and islands beneath the sea surface from their effects (via gravity) on sea level. A few years ago a German researcher actually discovered an entire mountain range that had gone unseen using this gravity technique. See www.luau.ucsd.edu/marine_topo/ for a technical but very readable introduction from the masters of the field.