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Gravity in the Sun in .NET Maker USS Code 128 in .NET Gravity in the Sun

8. Gravity in the Sun generate, create uss code 128 none on .net projects Use Mobile Phone to Scan 1D and 2D Barcodes Investigation 8.4. How the gas in the Sun behaves As mentioned in the text , we do not have direct measurements of temperature inside the Sun. We instead assume that the physics inside the Sun can be summarized by a relatively simple equation of state: a relation between pressure, temperature, and density. We shall use what physicists call a power-law relationship between density and pressure, that is a relationship where one variable is proportional to the other raised to a constant power (exponent).

The usual way physicists write this is: p = C .. It follows that the temp Visual Studio .NET ANSI/AIM Code 128 erature can be expressed in terms of the pressure by the power-law given in Equation 8.15, T =Ap , with the constants =11 1 = , n+1 and A = mp 1/ C , k (8.

14). (8.11). Astrophysicists call thi barcode standards 128 for .NET s a polytropic equation of state, which is another word for power-law , but they adopt a somewhat strange way of writing the exponent. They use a polytropic index n in place of the polytropic exponent , de ned by n= 1 , -1 or =1+ 1 .

n (8.12). A star with a polytropic equation of state is called a polytrope. Given the ideal gas law (Equation 7.12 on page 81) for a gas with mean molecular weight , we can solve it for the pressure to obtain p= k T .

mp (8.13). where C is the proportio VS .NET Code 128 Code Set C nality constant in Equation 8.11.

The constant C can be determined if the pressure and temperature are given in one place, say at the center of the Sun. Assuming the Sun to be a polytrope is in fact not as arbitrary as it might seem. In regions that are dominated by convection of heat from the interior of the Sun, and in regions where most of the pressure is provided by the radiation making its way outwards through the Sun, the equation of state does indeed follow such power-laws.

The physics hidden behind this statement is a little beyond our scope here. We shall simply adopt the polytropic equation of state and look at the models it produces..

the Sun equally in all d irections. The acceleration due to gravity inside the Sun is not hard to compute, however. Recall that in 4 we saw that inside a spherical shell, the force of gravity due to the shell is zero, whereas outside it the force is the same as if all the mass were concentrated at the central point.

If we consider a point inside the Sun, then if we draw a sphere about the Sun s center through the point in question, the sphere divides the Sun into an inside and an outside . The material outside the sphere does not contribute to the gravity, while that inside acts from the center. The acceleration due to gravity at the point is, therefore, just the acceleration due to that part of the mass of the Sun that is within the radius in question.

This means that the computer has to keep track of how the mass of the Sun is increasing as we go out in radius, but computers are good at doing such things. The other part of the program that needs to be modi ed is the computation of the temperature. This is not quite as easy to handle as gravity, because it requires a discussion of gases that goes beyond our treatment in 7.

This is the subject of the next section.. Figure 8.3. Comparing ou Code-128 for .

NET r solar model with the Standard Solar Model. Our computer model assumes that the relation between pressure p and density is p 1.357 everywhere, and then adjusts the constant of proportionality and the central pressure to set the model s total mass and radius to those of the Sun.

Of course, this relation is only an approximation to the real physics inside the Sun, so our model cannot describe all the details of the Standard Model. In particular, it overestimates the temperature everywhere..

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