In this section we will derive Boyle’s law for a self-gravitating cloud of arbitrary shape subject to a uniform external pressure Pb. In particular, we will obtain an ex-pression for the derivative
∂pb/∂V at constant temperature and fixed shape, for a cloud of given mass. A similar calculation had been performed by Bonnor (1956; see also Ebert 1955) in the case of a spherical cloud. Here we imagine that the cloud is embedded in an external medium in an arbitrary dynamical state. Our main assumption is that such an arbitrary state enforces a non-trivial geometry for the cloud, while the cloud has had time to settle into a hydrostatic equilibrium and is thus described by Eq.
It sounds like he’s starting with the conclusion and filling in the variables necessary to get there.
Self-gravitating cloud with uniform external pressure? From where?
How did that happen in an early universe? The first stars had to form fairly quickly, relatively speaking.
There have been 5 tests of some of the Dead Sea Scrolls using the new improved carbon 14 method and the scrolls tested turned out to be between 125 and 150 BC. See “Radiocarbon Dating of Scrolls and Linen Fragments from the Judean Desert” in Radiocarbon, vol. 37, no1, 1995, 14. The test included Isaiah 53 with its predictions of the messiah’s death.
The sun is gas held together by gravity. Gas does not enjoy exception to gravity, nor for that matter, from math.
And the math does not say gas clouds over a certain size / density can collapse - it says that they must collapse. The math does not say that gas clouds might collapse, it says they will collapse. There is no “if” to it - gravity indeed will win given time. Do not think so? Fate tends to be harsh on those who temp gravity.
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Klax
(The only thing that matters is faith expressed in love.)
406
Sorry, but with the size of space, if it were possible, we would see it happening everywhere. It’s not.
Go back to my post with the picture of our atmosphere on earth. How is it that with an iron core, our planet is still only dense enough to hold onto gases about 500km out? That alone should tell you how feeble gravity is as a collector. To draw in enough mass for a star, gases must draw together from well over a light year in area. That is beyond wishful thinking and well into the range of fantasy.
No problem! You will be happy to know that having an iron core is not that significant. Without a solid core, the Sun has a mass of 333,000 Earths. In turn, the Eagle Nebula, which has all those young stars, has about 12,000 solar masses available. So set your mind at ease, there is plenty of mass available in nebulas for gravity to do its work.
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Klax
(The only thing that matters is faith expressed in love.)
416
As the first Christians did, it is easy to make this, the Fourth Servant Song of the school of Isaiah, work in Greek. It works less well in the hands of Christians today, especially those trying to ‘save’ Hebrew reading Jews. The whole poem raises more theological questions than it answers if it is prophetic in the sense of foretelling.
The question posed was whether we can know when the scroll of Isaiah was written. We can. It also accurately predicts several striking things that were fulfilled by the manner of Christ’s death and so can properly be taken as confirming evidence by Christians. Whether it also raises theological questions was not the point. That can be said of almost any doctrine based on any scripture.
