This new, super-accurate way to pinpoint our solar system's center may help spot monster black hole crashes

An important astronomical measurement, going back to Jupiter :) Here is a bit more from the NASA ADS site,
https://ui.adsabs.harvard.edu/abs/2020ApJ...893..112V/abstract, 'Modeling the Uncertainties of Solar System Ephemerides for Robust Gravitational-wave Searches with Pulsar-timing Arrays, April 2020. “1. INTRODUCTION Pulsar timing exploits the remarkable regularity of millisecond-pulsar emissions to extract accurate system parameters from time-of-arrival (TOA) datasets (Lorimer & Kramer 2012), by fitting precise timing models that account for all pulse delays and advances, from generation near the neutron stars to detection at the radiotelescopes (Lommen & Demorest 2013). The largest time-dependent term in the model is the Rømer delay (Rømer 1676) due to the motion of Earth around the solar-system barycenter (SSB), with magnitude ~ 500 s. Solar-system ephemerides (SSEs), such as those produced by the Jet Propulsion Laboratory (JPL; see Folkner et al. 2009, 2014; Folkner et al. 2016; Folkner & Park 2016, 2018), are used to convert observatory TOAs to the notional coordinate time of an inertial frame centered at the SSB. It follows that errors in our estimate of Earth’s trajectory around the SSB produce a time-dependent bias in the TOAs.”

Interesting, dark matter does not play a role here but the motion of the Earth shows up. I plan to observe Jupiter tomorrow morning early around 0100 EDT using my telescopes. Jupiter is approaching opposition this month on 14-July and Saturn follows 20-July. Good to see studies testing ephemerides using Jupiter and pulsar timing :)
 
Interesting, dark matter does not play a role here but the motion of the Earth shows up. I plan to observe Jupiter tomorrow morning early around 0100 EDT using my telescopes. Jupiter is approaching opposition this month on 14-July and Saturn follows 20-July. Good to see studies testing ephemerides using Jupiter and pulsar timing :)

Dark matter should not play a role here - our system has an asteroid's worth of it and instruments are 10^5 times too insensitive to catch that - so that is honestly more (albeit weak) evidence.

Good luck with Jupiter! A teacher once took us out to see the Galilean moons, long before light pollution was too much of a bother.
 
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By definition, the Solar system's barycenter cannot "constantly change position as the planets move around the Sun." The NASA Space Place link inside this article (https://spaceplace.nasa.gov/barycenter/en/) is inconsistent and flawed. This Space.com article promotes a misconception.

Of course it changes position since our system orbits the Milky Way. And even from the reference point the NANOGrav project uses it could (and apparently does).

"In astronomy, the barycenter (or barycentre; from the Ancient Greek βαρύς heavy κέντρον center[1]) is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit. ...

The distance from a body's center of mass to the barycenter can be calculated as a two-body problem.

If one of the two orbiting bodies is much more massive than the other and the bodies are relatively close to one another, the barycenter will typically be located within the more massive object. In this case, rather than the two bodies appearing to orbit a point between them, the less massive body will appear to orbit about the more massive body, while the more massive body might be observed to wobble slightly. ...

When the less massive object is far away, the barycenter can be located outside the more massive object. This is the case for Jupiter and the Sun; despite the Sun being a thousandfold more massive than Jupiter, their barycenter is slightly outside the Sun due to the relatively large distance between them.[2] "

[ https://en.wikipedia.org/wiki/Barycenter ]

Seems the new observations has enabled scientists to model it to lie within the Sun (for whatever reference system NANAOGrav uses), when all planets are considered and way-out-of-system references are used.
 
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The barycenter of the Solar System does not move as the result of the revolution of its own planets, etc. Yes, this position is the center-of-mass of the entire Solar System - the Sun, too, moves around it even though that position lies outside the Sun's volume. (BTW, this is one technique [astrometry] used to detect exoplanets.) However, just like the pivot point of a teeter totter doesn't move as two people bob up and down, neither does the barycenter of the teeter totter move. Yes, the Solar System's barycenter moves within the Milky Way galaxy but that is not the subject of this article.
 
Dark matter should not play a role here - our system has an asteroid's worth of it and instruments are 10^5 times too insensitive to catch that - so that is honestly more (albeit weak) evidence.

Good luck with Jupiter! A teacher once took us out to see the Galilean moons, long before light pollution was too much of a bother.

Torbjorn Larsson, I enjoyed excellent views of Jupiter early Friday morning. I was out from midnight until 0530 EDT before sunrise viewing Saturn, Jupiter, Mars and the waxing gibbous Moon very bright (later hunt for comet NEOWISE and Venus brilliant). I used a 90-mm refractor telescope and 10-inch Newtonian at 158x views. Ganymede transited (I could see the moon) and Ganymede shadow transit too along with the Great Red Spot passing by. I enjoyed the reference in the space.com article to Jupiter because so much happened in astronomy there. When I view the Galilean moons moving around Jupiter and various Galilean moon eclipses using my telescopes, I am reassured that there is no dark matter there holding them in place :)
 
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The barycenter of the Solar System does not move as the result of the revolution of its own planets, etc. ... Yes, the Solar System's barycenter moves within the Milky Way galaxy but that is not the subject of this article.

But it was, since the pulsar references are situated in the Milky Way so the common barycenter of the system moves in relation to them, and Earth moves in relation to the common barycenter of the system. Their reference system has to account for the relative movements.
 
No, dark matter is more holding systems together on the scale of dwarf galaxies up. That's one reason Newton didn't know about the stuff. :D

Good observation but note that Einstein in GR did not use DM either. My trusty book, 'Relativity The Special and the General Theory, A Clear Explanation that anyone can understand', 1961 does not show DM used in equations for GR, e.g. the principle of equivalence, inertial mass and gravitational mass. The space.com article in this discussion, 'This new, super-accurate way to pinpoint our solar system's center may help spot monster black hole crashes', is a good measurement for the barycenter of the solar system, the SSB. The Galilean moons do not show DM or need DM to predict their orbits and motion, neither does precise measurements for determining the SSB today. Dwarf galaxies (especially with fast stars in them) and spiral galaxy rotation curves apparently need the DM - assuming they have been in motion for billions of years.
 
Good observation but note that Einstein in GR did not use DM either. ... a good measurement for the barycenter

General relativity describes all energy (and stress) as well as space time curvature - Einstein didn't include dark energy either.

Yes, if dark matter density is 10^-5 times from being observable in our measurements it can safely be ignored in modeling the system barycenter.
 
Again, we see no DM in the solar system, at the Galilean moons or the SSB sensitive measurements now. I am also not aware of DM used in Einstein GR equations or dark energy for space time curvature, e.g. neutron stars and objects creating gravitational waves. The space.com article is titled "This new, super-accurate way to pinpoint our solar system's center may help spot monster black hole crashes"

Astronomy began at Jupiter, it is always good to go back to Jupiter and observe :)