[evan_au (OP)]

This was split off from another "New Theories" thread, sparked by the following comment:

If dark particles can somehow aggregate (praps gravitationally) then they can form dark planets...

The most popular current theory of Dark Matter is that it consists of some subatomic particle which almost never interacts with normal matter (even less than the ghostly neutrinos).

These hypothetical Dark Matter particles would feel the tug of gravity, but that is not enough to cause them to aggregate - you need one or more forces which can cause Dark Matter particles to interact with each other, and radiate away the energy of their gravitational aggregation.

This theory cannot tell us if there is such a "Dark Force" which is felt by Dark Matter, but not by normal matter. But if such forces existed, then you could produce a "Dark Planet" or a "Dark Periodic Table".
See: https://en.wikipedia.org/wiki/Dark_matter#Dark_matter_aggregation_and_dense_dark_matter_objects

[evan_au (OP)]

The Hypothesis
If we continue with the idea that Dark Matter particles might feel a "Dark Force" that is not felt by normal matter..
- It is speculation: As yet we have not identified any Dark Matter particles, let alone characterise what forces they may experience with other Dark Matter particles - eg their range
- But as I suggest below, if such forces exist, we may be able to detect aggregations of Dark Matter "planets" by their gravity alone.
- This implies the following line of reasoning:

What we know about Dark Matter
Studies of galaxy gravitational lensing and anomalous gravitational rotation curves suggest that there is a sphere of Dark Matter orbiting the galaxy, gravitationally attracted to it, but not interacting strongly with it.
- However, this large-scale behavior does not prevent subatomic-sized Dark Matter particles from clumping into larger lumps that we might describe as being on the scale of a "Dark Matter atom", a "Dark Matter molecule", "Dark Matter dust", "Dark Matter planets" or even "Dark Matter stars".
- Studies of microlensing events in the plane of the Milky Way does put a constraint on the latter two: They suggest that there are not enough microlensing events to account for much of the predicted Dark Matter - this rules out free-floating large planets, burnt-out stars or black holes as a major contributor to Dark Matter. This also puts a constraint on the number of "Dark stars" and larger (Jupiter-sized) "Dark planets".

The possibility of Dark Planets in our Solar System
Any clumps of dark matter would feel a gravitational attraction to clumps of normal matter - like the Sun, Jupiter or Earth.
- If the relative velocity were low enough, a clump of normal matter could have a clump of Dark Matter orbiting it's average location.
- So the Sun (normal matter) could have a clump of Dark Matter orbiting within or around it; they would effectively both be orbiting their common barycenter.
- When we measure the mass of the Sun (by timing the orbits of the planets, for example), we would effectively be measuring the mass of the Sun + the mass of any Dark Matter clumps caught in its gravitational field
- I imagine that Dark Matter could not make up a large percentage of the Sun's mass, as that would distort measures of the Sun's density, as determined from helioseismology, for example.

Similarly, the Earth could have captured some of these hypothetical Dark Matter clumps in its gravitational field.
- So when we measure the Earth's mass by timing the orbit of the Moon, or by gravitometers on the Earth's surface, we are measuring the mass of the Earth + the mass of any clumps of Dark Matter captured in its gravitational field.
- Any Dark Matter clumps orbiting the center of the Earth (but beneath the surface of the Earth) would have an orbital period of somewhere around 80 minutes.

Detecting Dark Planets near Earth
A team have produced a very sensitive gravitometer that can measure the daily tidal influence of the Moon - about 1/80 the mass of the Earth, at a distance of 380,000 km.

By having a 3-axis gravitometer in one place, or a network of vertical-axis gravitometers dotted around the Earth, it should be possible to detect the motion of a (speculative) clump of Dark Matter with a mass of 0.1% of Earth's mass, orbiting the Earth's core (about 7,000km away).
- Rather than looking for the known tidal influence of the Moon (with a period slightly over 12 hours), they would have to search for periodic variations below 90 minutes.

Another (even more speculative) possibility is that while Dark Matter might share the average position of the Solar System, it may have condensed from a Dark Matter cloud with a slightly different axis of rotation.
- This would mean that the plane of the planets is at an angle to the plane of the Dark Planets.
- So they would interact strongly for only a few days, every 6 months...
- But I am sure that this would produce gravitational interactions between normal planets and Dark Planets that would cause their orbits to align, over time...   

See: https://spectrum.ieee.org/energywise/energy/fossil-fuels/stampsized-gravity-meter-could-have-big-impact-on-oil-exploration

All comments are welcome...

[Petrochemicals]

Like the idea, it wouldbe useful to know if it had clumped.

Would not this gravity meter be better done from orbit or the moon ?

What do we know about dark matter other than it affects the normal matter ? Is there any reason to believe that it itself possesses attractive qualities?

[evan_au (OP)]

Would not this gravity meter be better done from orbit or the moon ?

Sensitivity to small changes in the distribution of mass is improved if you are closer.to the object you are studying.
- So you wouldn't study the distribution of mass inside the Earth from the Moon or from Lunar orbit

Searching the distribution of mass inside the Earth has been done from Earth orbit, with the GRACE (pair of) spacecraft, see: https://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_Experiment
- With a separation of around 220km, GRACE would have been most sensitive to variations in density of the Earth near the surface, 500km away. Hypothetical Dark Matter masses would be orbiting the Earth's core, 8000 km away, where GRACE is much less sensitive.
- With an orbital period of 97 minutes, it is difficult for GRACE to detect the motion of hypothetical Dark Matter clumps with slightly shorter orbital periods around 80 minutes.
- I expect that most of the analysis from GRACE would have focussed on correlations with the surface of the Earth, passing 500km below. However, a careful re-analysis may reveal changes with a different periodicity.
- The GRAIL spacecraft also did a similar study of the Moon, see https://en.wikipedia.org/wiki/GRAIL
 
I expect that a network of sensitive gravitometers fixed to the Earth's surface, rotating with the Earth every 24 hours would be better placed to pick up periodic variations with an orbital period of around 80 minutes. 

What do we know about dark matter other than it affects the normal matter ?

The one thing that cosmologists expect is that it doesn't affect normal matter very much at all (except by gravity).

Is there any reason to believe that it itself possesses attractive qualities?

From relativity, we expect that any particle with energy will experience the attraction of gravity.

Beyond that, you really need to isolate a particle to determine what it interacts with:
- It wasn't until electrons were isolated in a vacuum tube that it was possible to determine their charge, and response to magnetic fields, and charge/mass ratio
- It wasn't until α, β and γ rays could be separated that their unique properties could be studied
- It wasn't until protons were isolated that their properties could be studied
- Once neutrons could be produced on demand, they could be studied

Since to date we have failed to separate out any individual Dark Matter particles, I suggest that it may be worth checking for possible clumps of dark matter, as another avenue to narrow down that it exists, and in what quantities.