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- Thread starter StephenPrivitera
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Nereid

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The easy answer is "until the core is hot and dense enough". Are you looking for something specific, e.g. how hot? how dense? or perhaps "it first begins to burn its deuterium, and destroy what little lithium it has, when [answer goes here]"How much must it collape before nuclear fusion begins?

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For example, in a spiral galaxy, the dominant motion of the stars in the disk is circular rotation in the plane of the disk. The variation in the orbital velocities with radius V(r) is called the rotation curve.

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Suppose you have a finite collection of point particles interacting gravitationally via good old Newtonian mechanics. And suppose that:

1. The time averages of the total kinetic energy and the total potential energy are well-defined.

2. The positions and velocities of the particles are bounded for all time.

Then we have:

<T> = -<V>/2

where <T> is the time average of the total kinetic energy, and <V> is the time average of the total potential energy.

I always found this to be a bit magical. It seems surprising at first that such a simple law could hold so generally. But in fact, it's just a special case of something called the "virial theorem", which also applies to forces other than gravity, and impacts everything from astronomy to the theory of gases.

For example, out in space, very often a bunch of particles will collapse to form a gravitationally bound system. If the system is roughly in equilibrium so the time averages of kinetic and potential energy are close to their current values, the virial theorem implies that T = -(1/2) V. we know that <T> = -<V>/2. This is a terrific thing, because it lets you find the masses of bound systems. In fact, it's really the reason we think that dark matter exists.

To be specific, suppose you measure the speeds of a bunch of visible objects in your system, and infer T. Then the virial theorem tells you V. If you find out that the potential well is deeper than what you'd get by adding up the contributions from the masses of everything you see, you know there's dark matter. People do this for spiral galaxies, elliptical galaxies, and galaxy clusters, getting strong evidence for dark matter in all cases, I guess.

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Yes, I suppose this is exactly what I'm looking for. What measurements imply that nuclear fusion is occuring? Mass? density? Temperature?Originally posted by Nereid

or perhaps "it first begins to burn its deuterium, and destroy what little lithium it has, when [answer goes here]"

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Originally posted by Jeebus

For example, out in space, very often a bunch of particles will collapse to form a gravitationally bound system. If the system is roughly in equilibrium so the time averages of kinetic and potential energy are close to their current values, the virial theorem implies that T = -(1/2) V. we know that <T> = -<V>/2.

Does this mean that a protostar which has the initial property T < V/2 will collapse until it reaches equilibrium at T = V/2? Suppose we know the average temperature, mass and density of a protostar. Can we predict what size star will result from the collapse by finding when T = V/2?

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Labguy

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Temperature, and the EM spectra (same measurement). Sub-stellar masses radiate heavily in IR and radio, but you won't get x-ray, gamma ray or much UV unless the core temperatures reach ~11 million K to start fusion.Originally posted by StephenPrivitera

Yes, I suppose this is exactly what I'm looking for. What measurements imply that nuclear fusion is occuring? Mass? density? Temperature?

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