Terrestrial gravity measurements challenge engineering, Einstein

Richard Feynman once described gravity as “damned weak, but not negligible.” Gravity is the weakest of physics’s four fundamental forces, and measuring it accurately can be an engineering challenge, one tackled by University of Colorado alumnus Dr. Tim Neibauer and his company, Micro-g LaCoste.

Accurate measures of Earth’s gravity are useful for geophysics applications like measuring sea levels and volcanoes, for commercial applications like prospecting and monitoring reservoirs, water tables, and geothermal sources, for standards applications like calibration and Watt balance measurements, and military detection guidance and navigation applications. Thus, accurate measures of gravity are financially worthwhile.

Prospecting applications require an accuracy of at worst 1milliGalileo (mGal), but Neibauer explained that Micro-g LaCoste’s instruments are designed to work at the level of micro Galileos (u-Gal), which is about the gravitational force from a three millimeter height variation. Neibauer described this as the amount of gravitational attraction “If you’re standing next to someone you like.”

There are a number of methods of measuring the Earth’s gravitational field. Relative measurement tools became available in the 1930s and consist of a spring-mass system. While inexpensive, these tools are also indirect measurements and generally unsuitable for the micro-Gal range. Another classic method of measuring gravity is borehole gravity, which measures the apparent bulk density of a material for measurements made at discrete vertical depth intervals. A more unusual method of measuring gravity, currently being pursued by NOAA’s GRAV-D program, entails measuring differences in GPS readings from the air.

The method Neibauer focused his concerns on, though, was absolute gravity. This method entails dropping an object, recording how fast it fell, the time and distance it traveled at its 0 crossing, and solving its equation of motion. In a general sense, the absolute gravimeter consists of an interferometer with one moveable mirror. When making a measurement, the mirror is dropped, and the change in photodetector output allows the machine to measure the motion of the mirror.

In analyzing results from these detectors, though, standard procedure is to use a retarded time correction, which accounts for a phase shift and doppler shift, correcting for the speed of light. However, Neibauer’s work indicated that this standard method overcorrects for the speed of light. By analyzing with a double doppler shift, Neibauer’s results improved over measuring with the retarded time. He noted, however, that this result was controversial as it was not fully compatible with Einstein’s General Relativity.

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