[jasonhocky (OP)]

Has anyone ever calculated this value? If so what value was approximated?
Jason

[yor_on]

That's an impossible question to answer I think. What one see looking out is stars, not planets. One can guess on planets by perturbation of stars but knowing all planets? As Space is supposed to be isotropic and homogeneous it might be possible to take a 'statistic sample' though of our closest neighborhood and then apply it on the rest of the 'observable universe' as we have a defined distance in Light years (13.7~ ly all around you). Presuming that everything is much the same at any other 'patch' of our universe as it is at ours. Then there is theoretical definitions of course of dark mass etc to consider too if wanting to get to some 'density' of it.
=

This one discuss the mass but knowing the volume of 'space', then also considering the accelerating expansion, you might be able to reach a number of the mass density, presuming now you meant mass relative space. if you meant average density of 'all mass' it becomes different.

https://hypertextbook.com/facts/2006/KristineMcPherson.shtml

[evan_au]

Do we know the mass density of the observable universe?

Yes, this is something that astronomers have attempted to measure and calculate many times over the past century.
- This is an important parameter in Einstein's General Theory of Relativity, since it dictates the future of the universe:
- Collapse back into a "Big Crunch"
- Or expand forever in a darkening sky

With increasingly powerful telescopes, it is possible to survey large parts of the universe for glowing gas - powered by stars
- Examination of the rotation rates of nearby galaxies showed that there was far more mass than could be accounted for in stars
- Radiotelescopes can detect clouds of neutral hydrogen at various distances in intergalactic space between us and distant quasars
- There have been surveys using gravitational lensing looking for black holes or free-floating planets. Some have been found, but not nearly enough to account for the missing mass
- We now call this missing mass "Dark Matter"
- Studies of nuclear processes in the Big Bang, and today's Cosmic Microwave Background Radiation allows cosmologists to place fairly tight limits on the density of matter in the universe, both normal matter and Dark matter

In all the studies, the density seems to be just above the magic value that would prevent a Big Crunch.

However, the more recent discovery of the accelerating expansion of the universe (attributed to Dark Energy) means that the density of matter in the universe is today not the dominant factor determining the future of the universe.

But astronomers are still looking for ways to determine the density of the universe, and the nature of Dark Matter and Dark Energy.

[evan_au]

Yesterday I read a technical description of the new CHIME radiotelescope (arXiv:1803.11235v1 [astro-ph.IM] 29 Mar 2018).

The original concept was to monitor the transition from inertia-driven expansion of the universe (matter+dark matter) to Dark-Energy-driven expansion. This occurred around the time that the redshift (abbreviated z) was around 0.25-0.8.
- They do this by monitoring the neutral Hydrogen line at 21cm/1.4GHz.
- Due to cosmic redshift, this is brought down to a frequency of 0.4-0.8GHz, which they are actually monitoring.
- In the next 3 years, this telescope will map the density of Hydrogen in the universe over the biggest volume of space ever surveyed - more than can be mapped by looking at visible galaxies
- They will be able to measure Hydrogen in galaxies and between galaxies, as these frequencies pass through dust clouds quite well (unlike visible light).
- They won't be measuring hydrogen in stars, as this is an ionised plasma, rather than neutral hydrogen atoms.
- They should be able to detect any large-scale structure to the universe, like voids and membranes

Once they had the basic telescope design in place, they added specific processors looking for Fast Radio Bursts (they have found lots), and other processors intensively monitoring pulsars and other periodic sources in the sky.

They kept the cost down by:
- making the telescope non-steerable (the Earth's rotation scans it's beam around the Northern sky every 24 hours, monitoring a patch of sky which is about 100 degrees North-South and 2 degrees East-West. This is a huge area compared to most telescopes)
- Using components from Mobile base stations
- Using components from high-end computer games

See: https://en.wikipedia.org/wiki/Hydrogen_line
https://en.wikipedia.org/wiki/Canadian_Hydrogen_Intensity_Mapping_Experiment