# Comment On The Normal Height Differences Determination From Geopotential Differences

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Tatyana,

I like your paper a lot, but wish it were an online calculator simulator, not just mathematical equations on paper (PDF is the same as paper).

The only problem I have with using “direct gravitational potential” differences is that the direct methods like LIGO, atomic clocks, and Mossbauer are usually bigger, more costly and fewer.

That is why I have spent so much time over the years following and encouraging gravimeter and gradiometer approaches (gravitational potential gradient measurements). If you have atomic clocks, that’s great. But most people don’t.

Maybe it was because of Newton there are a LOT of force based measurement methods (acceleration) and now the position and velocity instruments are either integrating the signal processing into the instrument to also report acceleration, or storing and processing later.

You might want to look at using three axis gravimeters with high sampling rates. The high sampling rate sets the spatial resolution for distances to various sources. Using the sun and moon as references (10 meters in 1 astronomical unit is 100 parts per trillion) and there are a lot of measurements to improve by statistics. The mass of the sun does not change much, and the response of the earth (for position and orientation of the instrument) over time are fairly stable.

If you have ever used “Gain bandwidth product” to characterize the quality and sensitivity of an amplifier or circuit element, the “bits per reading” and “readings per second” for instruments is a good indicator. It is the log2 (bits) version of the gain bandwidth product.

Using a three axis instrument (or a full tensor gradiometer can give an absolute reference at a location. Rather than measuring the potential which is about the same as measuring a pressure or energy density, measuring the force or momentum flow and its spectrum is usually faster, less expensive and smaller.

I would like to see you do the experiments and set up permanent gravitational potential measurement sites. If you sample at high rates (higher than LIGO 16,384 readings per second, which is about 18 kilometer resolution), then the location of sources of variation (seismic waves, ocean waves and currents, atmospheric density variations and currents) can be imaged and characterized and compared to models with input from many global sensor networks.

Atomic clocks are not that expensive – if you make “low cost” and “affordable to all countries and groups” a criteria. I know there are atom interferometer gravimeters and gradiometers, but those usually just get experiments done for academic exercises and don’t ever seem to get into operating networks. The GPS and GNSS times are a bit dicey. Not that hard, just tedious. Dual and multiple frequency methods help. But ultimately the problem is that electromagnetic signals are attenuated, refracted, reflected, absorbed.

And gravitational signals are NOT, or not as much. Your gravitational time dilation equations show that the rate of clocks depends on location (potential at the location) and it depends on time and date (the sun and moon and planet variation, particularly because the station is moving as the earth rotates and oscillates with earth tides) — that can be interpreted as a change in the local index of refraction.

That is what I do usually – calculate the sun moon earth gravitational potential at some location over time from JPL and Geopotential models – let that set the local rate of clocks via the index of refraction changing the local speed of light and gravity. Then use local speed of light and gravity for regional comparisons.

But, no one is operating real time global gravimeter networks that are three axis high sampling rate. I cannot afford to make them and operate them. I just keep encouraging people and groups to go in that direction.

The superconducting gravimeter is only 0.1 nanometer per second squared at 1 sample per second. In bit terms that is 10^10 or 2^33. Acoustic ADCs routinely get that precise. Stages of amplifiers with external calibration can get there. The MEMS gravimeters could all be calibrated and get there. About 10 kinds of gravimeter and many groups could get there. Mossbauer gravitational sensors could get there. Atomic microscope method gravimeters, quantum and Bose Einstein gravimeters can get there.

Richard Collins, The Internet Foundation