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nick1o2
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I was reading up on critical density, and found the "current" number for it, but can't fine any past records or graphs to show how they have changed over time. Any help?
nick1o2 said:I was reading up on critical density, and found the "current" number for it, but can't fine any past records or graphs to show how they have changed over time. Any help?
nick1o2 said:The Average Critical Density of the universe. Sorry should of made that clear.
marcus said:If you're familiar with Friedman eqn. then you remember that
H2 = (8πG/3c2)ρ
with ρ expressed as an energy density (if you like it as a mass density then omit the c2)
So solve for ρ:
ρ = (3c2/8πG)H2
Are you familiar with the Hubble time? It is simply the reciprocal of the rate:
THubble = 1/H
Let's denote it by Θ so we don't have to write the subscript
Θ(t) = 1/H(t)
So if I can show you a table of the past history of the time Θ(t) you can calculate ρcrit!
ρcrit = 3c2/(8πG Θ2)
Here's a table of past values of the Hubble time Θ listed in billions of years.
[tex]{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline T (Gy)&\Theta (Gy) \\ \hline 0.473&0.7105\\ \hline 0.566&0.8504\\ \hline 0.678&1.0176\\ \hline 0.811&1.2173\\ \hline 0.971&1.4558\\ \hline 1.162&1.7401\\ \hline 1.390&2.0787\\ \hline 1.663&2.4807\\ \hline 1.988&2.9566\\ \hline 2.375&3.5172\\ \hline 2.835&4.1732\\ \hline 3.380&4.9340\\ \hline 4.023&5.8050\\ \hline 4.777&6.7856\\ \hline 5.654&7.8652\\ \hline 6.666&9.0202\\ \hline 7.819&10.2134\\ \hline 9.114&11.3964\\ \hline 10.549&12.5168\\ \hline 12.111&13.5285\\ \hline 13.787&14.3999\\ \hline \end{array}}[/tex]
This takes you from around year 470 million (first stars and galaxies were forming) up to around year 13.8 billion (the present).
You can use google calculator to convert the Thetas to nanojoules per cubic meter. for example to get the present rho_crit just paste this into the google box:
3c^2/(8 pi G (14.4 billion years)^2))
Google will say 0.778 nanopascal which is the same as 0.778 nanojoule per cubic meter (when you sort the units out.)
Or if you want the density when the first stars were forming just paste this into google box:
3c^2/(8 pi G (0.7105 billion years)^2))
Google will say 319.8 nanopascal which is equivalent to 319.8 nanojoule per cubic meter.
Historical critical density data refers to the information and measurements collected over time about the density or mass per unit volume of a substance or material. This data can provide insights into the physical properties and behavior of a substance, and can be used for various scientific and engineering purposes.
Finding historical critical density data is important because it can provide valuable information for research and development, quality control, and safety assessments of materials. It can also help in understanding the changes in physical properties of a substance over time and can aid in making predictions for future behavior.
There are several sources where historical critical density data can be found, such as scientific databases, research papers, government agencies, and industry organizations. You can also contact experts or researchers in the field for access to relevant data.
Historical critical density data is typically measured using specialized instruments such as hydrometers, pycnometers, or densimeters. The measurements are recorded in standard units of mass per unit volume, such as grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3). This data is then usually organized and presented in tables, graphs, or charts for easier analysis.
While historical critical density data can be found for a wide range of materials, it may not always be available for every substance. The availability and accuracy of data may also vary depending on the material and the time period in which it was collected. Additionally, certain materials may require specialized measurement techniques, making it more difficult to obtain historical critical density data.