Eyeing 'pear-shaped Earth' to understant its wobbles

Remember the "pear-shaped Earth," the asymmetry of our planet's figure revealed by small changes in satellite orbits? Scientists who study the shape of the Earth have redone their measurements and find the planet to be even more pear-shaped than they had thought.

The North Pole is 45.1 meters farther from Earth's center than is the South Pole. The previous estimate was 44.7 meters.

This slight refinement may seem unimportant except for specialized uses. But it highlights the fact that space geodesy -- the science of measuring our planet's shape with the help of reference points in space -- is reaching such precision that it can have a major impact on our knowledge of earth.

For the first time since this kind of space science was started by the ancient Greeks (that's right, the Greeks), it promises:

* Precise enough measurement of fault slippage and other surface movements to help anticipate earthquakes and track the slow drift of continents.

* Accurate tracing of small motions of the poles which are related to shifts in the way the atmosphere is distributed over the planet and to earthquakes (each one of which rattles the polar axis).

* Finely detailed monitoring of minute changes in Earth's rotation that reflect the drag of the winds and the coupling between the planet's outer shell and its liquid core.

Desmond G. King-Hele of Britain's Royal Aircraft Establishment has explained: "The twitches in the Earth's rotation, expressed by the polar motion and changes in the Earth's rate of rotation, may themselves be a source of geophysical events, because they make the Earth throw its enormous weight around jerkily. . . . The Earth is a self-exciting earthquake generator, and it looks as though satellite geodesy may in the end offer the key to the origins of the excitement."

However, as Dr. King-Hele and C. J. Brookes and G. E. Cook of the University of Aston (Birmingham, England) note in reporting their new estimates of Earth's figure in the journal Nature, scientists need a highly accurate map of Earth's gravitational field to make the most of the new geodesy. And that is what their concern with "the pear-shaped Earth" is all about.

In talking about Earth's shape, geodesists aren't interested in mountains and valleys. They are concerned with a kind of idealized sea level surface called the geoid. It's the shape our planet would have if entirely covered by water whose surface is molded by the balance between the inward pull of gravity and the outward tug of centrifugal force due to Earth's rotation.

This rather abstract, academic notion is highly practical. It is the underlying basis of maps -- the reference level for mountain heights or sea floor depths. It also is the reference level for charting the detailed structure of Earth's gravitational field which affects satellite orbits -- hence the ability of Dr. King-Hele and his colleagues to determine the geoid's shape from satellite observations.

Indeed the concept of Earth's underlying shape has fascinated people for millenniums. Remember reading about those emotional debates over whether Earth is round or flat? It also inspired what Dr. King-Hele calls "one of the finest achievements" of ancient Greek science.

Some 2,200 years ago, Eratoshtenes of Alexandria used the fact that the midsummer sun was directly overhead at Aswan but was 7.2 degrees off the vertical at Alexandria to infer that the two sites were 1/50th of a circle apart on Earth's surface. He assumed Earth had the celestially ideal shape of a shpere. Earth's circumference, therefore, would be 50 times the distance between Aswan and Alexandria. On this basis, Eratosthenes estimate could have come within 1 percent of the correct figure. It was, Dr. King-Hele notes, "the first example of space geodesy, with the sun as the reference object in space."

Many centuries later, Newton refined the concept of a spherical Earth by showing that the centrifugal force of rotation would make the planet bulge at the equator and flatten a bit at the poles. The planet's average profile would be an elipse -- a slightly squashed circle flattened by about one part in 298.25 , to use the current estimate.

This is by far the most important departure from a truly spherical figure. Its gravitational effect is a thousand times larger than that of the other departures, such as the pear shape tendency, which reflect the planet's internal structure.

Although they are small, all of these departures from sphericity have their influence on orbiting satellites. The equatorial bulge, for example, makes the plane of the orbit rotate around the Earth so that the point where the orbit crosses the equator slips several degrees a day.North-South assymetries, such as the pear-shape, can make perigee (the point of the orbit nearest Earth) move up and down by substantial amounts.

Scientists can work backward from observations of these orbital changes to calculate the shape the geoid has to have to produce them. In this way, Drs. King-Hele, Brookes, and Cook produced their new measurement of the pear-shaped profile.

In all of this work, scientists are struggling to attain the accuracy that is inherent in modern techniques of satellite tracking, especially laser tracking systems. These already can measure the line-of-sight range to a satellite to within 10 centimeters and promise to cut that uncertainly to as little as one centimeter. This allows geodesists to do long-distance surveying using satellite triangulation. They expect to follow the motion of continents that drift a few centimeters a year and to monitor the sliding of faults. However, the technique requires equally precise knowledge of the geoid shape. And that still is lacking.

Dr. King-Hele and his colleagues think their latest pear-shape profile is accurate to about 50 centimeters up to latitude 86 degrees and accurate to within 150 centimeters north and south of that. They point out that this is not good enough to match the accuracy of laser tracking. There are stubborn uncertainties to be overcome both in the theory and in the computer computations that connect Earth's shape with satellite motions.

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