Calculating Reference Gravitational Acceleration Signals for High Sensitivity Gravimeters from Simple and Complex Targets
Can you make a wireframe cylinder handing from a thread. Let it turn and wobble. The turn is 360 in the horizontal frame. The wobble is +/- 15 degrees referenced to the horizontal plane. I need this so I can calculate and show a group how to calibrate their gravitational sensor.
I have two ways to calculate the gravitational acceleration signal at the detector(s) a few centimeters or meters away, or further as they increase their sensitivity and sampling rate. At first they won’t even know they are getting a signal until their measurements and signal are exactly calibrated. Then with that as a reference, they need to increase the gain, increase the sampling rate and try for greater precision.
This is a real problem. There are about 50 labs that can do this experiment. And hundreds more once they know how easy it is (assuming you already are working on sensitive gravimeters for the next generation LIGO or geophysics or quantum detectors or things that require high resolution, high sensitivity detectors at high data rates).
Robert Forward talked about and showed examples of these kinds of signal generators more that 50 years ago. It is only in the last few years that the detectors and data collection systems are sufficient to actually do it.
Below is two masses. One is 6 kg and the other is 20 kg. They are held together by a bar and suspended from their balancing point (0.3 meter from the 20 kg mass and 1 meter from the 6 kg mass)
The pair is being rotated at a specific speed. Cameras and sensor monitor the motion precisely. A stepper motor rotate the pair. The detector is a simple 0.1 nanometers per second squared sensor at 1 Hz detector. So that vertical scale (nm/s2) that goes from 0 to 60 is broken up into 600 steps of 0.1 nm/s2. The turn rate can be anything. If it is one turn every 6 minutes that is 360 seconds, or 360/360 = 1 degree per second. This is a three axis signal. I only calculated part of it to get it set up. The detectors are relatively cheap – modified MEMS gravimeters and purpose built nanodetectors. So three for the three direction of the acceleration signal, and several sets of three axis detectors for redundancy and verification.
Because there is a very very precise reference signal the noise does not matter. You know the equations and the absolute values. The sensors are first calibrated against this basic test, then the gains on the detectors can be cranked up and the sampling rate increased. Double the gain and double the sampling rate for a given signal strength and sensitivity and you get roughly the same results. I have tried this with the high frame rate cameras. I know how to correct for variations.
This lab signal source used “Big G”, the gravitational constant. But on the surface of the earth, gravity is never constant, nor the properties of the gravitational potential field. You might better talk about “gravitational weather” at some place. So the G that you get from the labs will vary from the reference value that NASA JPL solar system ephemeris system network produce. I envision a constant global community that gradually resolves the differences and helps all groups see the latest work – with the models, equations, assumptions, context, workers, and raw data streams ALL available verification, to save people reinventing the wheel, for classrooms and training. These things are so simple, many people can afford to try. And all the countries in the world with few instruments of their own, SHOULD all have access to any global data collection – in formats and way they can use. With raw data and human-computer readable formats anyone can tackle hard global problems. You know that all the hard problems in the world are not solved because the solution is not where people are looking.
I want to show people – an aluminum cylinder rotating and bobbing vertically (because of Joe Weber’s cylinders, here he is exactly as I remember him in his lab – https://en.wikipedia.org/wiki/Joseph_Weber – https://en.wikipedia.org/wiki/Weber_bar )
A flat steel plate 1 cm thick 25 by 25 cm hanging by one corner. Same out of aluminum (harder to detect). The same aluminum with a pattern cut out of the center.
A pyramid with a rectangular base about 25 cm tall and 20 cm on the base side. Made of marble or steel or plaster or wood – pointing horizontally and hanging from its balancing point.
All the models need to rotate in the horizontal plane, and also wobble in the vertical plane. Those extra motions are to calibrate all three axis at once. And the asymmetric shapes help to test sensitivity.
A collection of bars at random sizes and directions. As long as you can monitor it with sensors and camera and track it in 3D, then calculating the signal is simple. If you can get me the objects, their locations and directions, I can calculate each contribution to the signal. From my experience with the superconducting gravimeters the signals will lie so close on the measurements (one a preliminary calibration sets the size) that you will not be able to see any differences when the two curves are overlaid one pixel wide plot. Except for noise, which is usually something real that you want to look more closely at, once you subtract the large signal.
A person (3D model with skeleton) the skeleton has precise location and limits, even when the body changes. This is to encourage people to develop 3D scanners for many purposes that involve detecting, tracking, scanning humans, mammals (cows, sheep, horse, dogs, cats).
These are all passive detectors. At very high sampling rate and sensitivities, you can strike the aluminum cylinder and detect the acoustic modes. That is what Joe Weber described to me all those years ago. But it has taken me 40+ years to wait for the technology to be able to do that. And it still needs software and data gathering systems that have not been built yet. The theory is trivial – Newtonian gravity. The gravimeters (measuring the acceleration field) took that long to come down in price.
The superconducting gravimeters I started with 20 years ago still cost $200,000. The MEMS gravimeters are MEMs integrated devices and cost a few pennies? dollars? in large numbers. They were adapted from cellphone MEMS accelerometers and could simply replace all the low resolution accelerometers with gravimeters. People could at least use them at stationary locations for “gravitational GPS” as or more precise than VLBI. That was my target sensitivity and resolution.
I call something a “gravimeter” when it can track all three axes of the sun moon signal anywhere on the earth or under it. The signal is +/- 1000 to +/- 500 namometers per second squared (nm/s2) so 10,000 time larger than the detector sensitivity. But with lab reference signals and the sun and moon reference signal for global calibration and coordination, any lab or group or individual can increase the gain , and increase the sampling rate. Push the gain, improve the device, push the gain, improve the device. At picometer per second squared (pm/s2), you can detect people and cars and packages. If near a beach, you can use the 3D wave shapes over time to calculate the signal and try to image complex changing shapes precisely. At femtometer per second squared (fm/s2) you can detect distant earthquakes and global networks can track Venus and Jupiter. And scan the interior of the earth. At attometer per second squared (am/s2) you can monitor solar mass eruptions and the fine signals from spicules on the sun.
There are MEMS gravimeters that are low cost, but not yet sensitive. Cheap to use in arrays. Atom inteferometer gravimeters are pretty far along but expensive clumsy and academic lab bound. Atom interferometer chips and integrated devices are dropping the cost and size everywhere. Many groups and methods are already at GravityNotes.Org and I will be profiling and organizing that because it has expanded so much and so quickly.
But the basic moving shapes, that Robert Forward envisioned, need to be calculated – by finite element methods and stochastic integrals, or by basic integral calculus. I want to get some 3D tomographic, neutron scrattering, electron microscope, x-ray, gamma ray, acoustic and other 3D datasets for real objects. Those port scanners for trucks and containers – they can be used to estimate mass, and the detectors can verify. Calibrate the two and the gravitational scanners can replace the somewhat dangerous gamma ray sources. The methods used for gravity in simple terms mean pushing detectors form electron volts down to nano and pico electron volts. Most of those technologies have already been developed – just not for detection of small, nearly chaotic signals.
I have had to allow for the gravitational potential itself to flow, to cavitate, to have fluctuations, for flows to intermingle, for small regions to rotate and have vorticity, for blobs to be as diverse and complex as the clouds in the sky, or the waves on the beach, or the motions and processes on the surface and interior of the sun, or as complex as thunderstorms and tornadoes. Only that encompasses the wide range of things that people describe when they talk about the gravitational potential field, potential fields in general, and high energy density and tiny processes in general.
I calculated the mass and size and number of the gravitational potential field fluctuations at the surface of the earth. I will write about that separately, but for ever mole of molecules in air, there are millions of moles of gravitational fluctuations. A good working mass is about one 7 millionth the mass of the electron. The average velocity is the speed of light and gravity, but that is just the average.
Richard Collins, Director, The Internet Foundation