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In the future, a variety of different technologies to evade detection are employed, such as harmful sensory input that renders one incapable of perceiving the object that attempts to evade detection even if his/her eyes are looking directly at it, early experiments in light-bending, or just "Stealth aircraft, but better". New technologies are employed to counter this. What I am wondering is whether gravimetry is a potential solution for a military counter such stealth technologies.

Can a set of sensors that detect gravitational fields be used to accurately determine whether something is present in an area that is not supposed to be there? For instance, could a setup like what LIGO used, but miniaturized to be mounted on a truck-sized platform provide data such as "There's a human-sized object with a mass of around 1 ton two kilometers from here", or "multi-ton aircraft having such-and-such altitude is located 30 kilometers from here and is moving in such-and-such direction" with enough precision to guide either a conventional or nuclear missile to the location of the object, or are gravitational sensors incapable of being precise enough for this task?

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    $\begingroup$ It has to visible to some form of light otherwise it is not emitting any light which means it cannot get rid of any heat, meaning it will quickly heat up to the point it destroys itself. "we're turning on the cloak, we have one minute until the interior of the plane reaches the melting point of lead" anything with an engine is just a bomb without a way to lose heat. $\endgroup$
    – John
    Jul 14, 2023 at 12:58
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    $\begingroup$ @Aetol and they would be even more visible to infrared. $\endgroup$
    – John
    Jul 14, 2023 at 15:15
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    $\begingroup$ You're better off detecting something using a spectrum that's not as susceptible to stealth/mimicry, like a craft of dense material blocking the background radiation of the sky in a way it can't reproduce, or infrasound. $\endgroup$ Jul 14, 2023 at 17:05
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    $\begingroup$ Presently they use Muon detectors to generate images of stuff underground. It works because an object slightly displaces the muons. These minute difference can be detected, although I don't know how portable/fast they work. Some aren't portable. $\endgroup$
    – cybernard
    Jul 14, 2023 at 18:42
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    $\begingroup$ @John Stealth aircraft and ships are faceted so that all reflections are at known angles- and away from any point source of radar or illumination. Even for some sort of passive spotting technology, a cylindrical cloak might work, with all heat etc. directed at right angles to the line of sight. $\endgroup$ Jul 15, 2023 at 6:50

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According to this source, the amplitude of a gravitational wave from two masses rotating around their common mass center scales with second power of distance between masses, fourth power of rotation frequency, first power of mass (total, the formula provided uses two equal masses) and minus first power of distance to the object. The problem here is that LIGO detects waves that originate from objects whose masses are multiple of the Sun's, over distances which are nowhere as long, and of frequencies that are decent, astronomy wise (1Hz or more). So, a gravitational wave caused by a moving human against a stationary human would differ from those that are detected by LIGO by (-31+16-4*1-6*2) = -30 orders of magnitude. Here first -31 is mass difference in orders of magnitude, +16 is distance difference, rough estimate, -1 is frequency difference, considering that a human moving past could be a part of him walking in a circle around the other one, and this actually depends on distance to that human at (-1) power, thus the distance between humans gives a power of -2 to the amplitude of resultant gravitational wave, and -6 is radius difference. So while the gravity waves of a traversing objects do exist, detecting them would require detectors that are 30 orders of magnitude better than existing. But, the gravity wave from Earth revolving around the Sun, not speaking of any binary star, would be about 12 orders of magnitude larger than what you expect to detect, leading to any detector capable of detecting moving humans be completely overloaded by background gravity waves coming from everywhere.

That means, no practical detector could exist to detect stealth objects by gravity waves. You might try a different principle, such as using Earth's magnetic field as current initiator in humans walking somewhere, and detecting those currents from afar. I expect such detectors to require at least 10 orders less efforts to detect. Yet they would also find and track all of your own unprotected people... And currents created by other magnetic fields would also make them overloaded.

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    $\begingroup$ Well, it's possible to precisely predict the gravity waves from Earth revolving around the Sun and any other stellar sources, so it's possible to subtract them out from the signal. The detector could also make use of parallax in a moving truck to filter signals by distance. Still, just getting that much sensitivity is probably impossible. $\endgroup$
    – causative
    Jul 14, 2023 at 11:04
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    $\begingroup$ Hey mind you, a moving truck is its own source of gravity waves! Spinning engine, moving pistons, just the rotor if the truck is electric, whoever walking inside close to the detectors, their own thermal oscillations - all this causes gravity waves, so you'd want to either filter some of them out by frequency, or somthing alike... Yet, a piece of debris on an unpredicted orbit also causes some serious gravity waves, as it's moving at quite a speed around Earth and all the humans down here, with freq about the one sought, range 4-6 orders larger, mass 4-0 orders smaller - quite a signal! $\endgroup$
    – Vesper
    Jul 14, 2023 at 12:23
  • $\begingroup$ Though a great answer, as we're talking about 'future technologies' where full stealth is possible we can probably allow some magical thinking. Our computers used to be room sized with the calculating power of a potato, now we have a phone in our pocket billions of times stronger that can last a day on a battery. An underground kilometers long facility might become a container on a truck as a new form of radar. $\endgroup$
    – Trioxidane
    Jul 25, 2023 at 6:49
  • $\begingroup$ @Trioxidane well, even with some far-future tech advancements, it would still be hard to amplify detection power by thirty orders of magnitude, and then filter out an unpredictably large set of signals from any kinds of moving parts around the planet. Especially if there exists a kind of movement that is quite common and produces signals of about 10 orders of magniture larger than those sought. $\endgroup$
    – Vesper
    Jul 25, 2023 at 13:56
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Gravimetry is the measure of gravitational force, LIGO does measure gravitational waves, which are propagating distortions of space time caused by moving masses.

The two things are not the same.

Why gravitational waves won't do for your use case, you have already been told by Vesper in their answer, which I won't repeat.

Similar reasoning applies for gravitation force: gravity, being so pervasive, creates a mess of background noise in which what stands out is the contribution of the largest/closest object.

Since gravity scales with the square of the distance, 1 ton at 2 km distance has the same gravitational effect of $1000000000/(2000)^2$=250 mg at 1 meter. In other words a sandwich, a phone or a walking rat could easily fool and blind your detection system.

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    $\begingroup$ You would need a gravitational lens, but that is a serious piece of tech. Near Clark tech. If you could pull one off, you have no need for tech like airplanes or nukes. You would likely have starships, or something better than starships. $\endgroup$
    – DKNguyen
    Jul 14, 2023 at 14:27
  • $\begingroup$ @DKNguyen speaking of which, this tech would make a lot more sense for use on large starships in deep space. More mass, less interference, right? $\endgroup$ Jul 14, 2023 at 21:10
  • $\begingroup$ @JoannaMarietti Yeah. especially If you're trying to detect planet massed super cloaked space ships. $\endgroup$
    – DKNguyen
    Jul 14, 2023 at 21:15
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    $\begingroup$ So if we consider something like Cavendish's experiment using a torsion balance, and ignore (for the moment at least) noise due to vibration conducted through the support, I wonder what the limits to sensitivity are? There's obviously going to be a rate-of-change limit with an extremely small force striving against the inertia of the support beam, but I wonder whether a support wire or fibre twists uniformly or is susceptible to some sort of quantisation... $\endgroup$ Jul 15, 2023 at 6:59
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Commercial available gravimeter

Current commercially available gravimeter used for the purpose of geophysics.

Typically used to measure down to milliGal range or 1e-5 m/s^2 or one millionth of one g. To reduce error users aim for knowing the position of sensor down centimeter or better via differential gps. A good DEM 2m resolution near the measurement point with less resolution further away is needed to correct for local topography/hills.

In geophysics context they are used to find ore bodies. For submarines they can find mountains.

Locating a target

Where as attempting to locate a 1 tonne target $M_t$ at a distance of 2000 m $r$ would have a 'g' of $g=G*M_t/r^2$ ~= 1.6e-14 1e-14 vs 1e-5 is a considerable gap of sensitivity.

This of course assumes you have a large grid array of gravimeters spaced apart so that your distance to target is approximation 2000m from some part of the array.

An array is needed since point measurement gravimeters like the linked cg6 does not tell direction and it is impossible to get direction from a single measurement to get a direction of something that is moving you need multiple simultaneous measurements.

A LIGO style sensor can certainly up the precision(mostly by increased size and directionality), its not going to up the precision by nine orders of magnitude.

Why not try some seismic?

What would be more plausible is detecting a moving multi tonne object by seismic/acoustic. That is one of the sources of noise for the LIGO project. Geophones and or seismometers are much less expensive then gravimeters and over much better odds of tracking moving vehicles or people depending on terrain.

Gravimeter are not precise enough.

Outside of magic/ pure narrative declaration of it being so. Using gravity to detect light objects is not practical and probably physically impossible due to near impossibility of controlling for all sources of noise ie its raining so now there could be tonnes of mass moving all around the sensors.

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Military submarines use gravity gradiometry to prevent collisions with underwater objects. That clearly shows that detecting nearby objects with gravity is possible. I don't know how precise such technology can be, but considering these were used in the 80s and your world is set in the future, I doubt what you want would seem implausible to most readers, particularly if you include a short description of how the technology evolved over time.

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