Pete wrote:iamlucky13 wrote:
A light-year is 9.5 x 10^9 km.
So the volume of a 1 light-year sphere is 4.5 x 10^29 cubic kilometers.
Caution! A light-year is 9.46
trillion kilometers: 1 ly = 9.46 x 10^12 km, and a sphere of radius 1 ly encloses a volume of 3.5 x 10^39 km^3. A 25-solar mass sphere would have a mean density of
1.4 x 10^-17 kg / m^3, one hundred million billion (10^17, but you have to
say it like Dr. Evil from Austin Powers!) times less dense than air at sea level, which has a density of ~1.2 kg / m^3.
Taking the Milky Way's mean interstellar medium density to be something like 10^6 gas (hydrogen) atoms per cubic meter, or roughly 7 x 10^-21 kg / m^3, a hypothetical 25 solar mass, 1-ly Bok globule would be roughly 2,000 times denser than typical ISM. That's still far less dense than the best possible lab vacuum, making it difficult to get an intuitive sense of the densities of objects like the Dark Tower.
This is about right although the problem as posed:
Neufer wrote:Knowing the density of the sun and it's diameter in light seconds;
how dense would a 25 solar mass Bok globule be
contained in a sphere the diameter of a light year?
Using that estimate how dense should The Dark Tower be?
Discusses a Bok globule with DIAMETER (not radius) of a light year.
I was hoping that some would know that
there are about 30,000,000 seconds in a year
and that the sun is about
a million miles (~ 5 light seconds) in diameter .
So 1 sun (with an average density of water)
would be expanded 6,000,000 times linearly
or 216 x 10^18 in volume.
A 25 solar mass Bok globule:
25 suns/ (216 x 10^18) ~ 10^-19 water density.
1000 cc's of water & 1 cubic meter of air STP both weigh
about 1 kg so we are dealing with ~10^-16 air density.
Loschmidt's number (the number of molecules in one cubic centimeter
of an ideal gas at standard temperature and pressure) = 2.7 × 10^19
so one is talking about 2700 N2 sized molecules per cc
vs. ~0.1 hydrogen atom per cubic centimeter in interstellar space.
The more massive Dark Tower is
about 40 times bigger (linearly)
than our Bok globule but equally opaque
so maybe just 2700/40 ~ 65 N2 sized molecules per cc here
vs. ~0.1 hydrogen atom per cubic centimeter in interstellar space.