# Estimating Central pressure in Star

1. Sep 20, 2009

### godzilla5002

I have a question in an assignment that says "Estimate the central pressure of 0.5, 1.0, and50 solar mass stars. Compare these pressures to the central pressure of the sun"

I can estimate for the sun using the Hydrostatic equilibrium equation:

dP/dr = -GM(r)p(r)/R^2

since I know Mass of sun is 1 solar mass and I know the radius. However, when I want to calclulate the central pressure of the other solar mass stars.. I don't know the radius.. So is there a way for coming up with that? The assignment doesn't give me any more information. Should I assume the same radius as the sun?

2. Sep 20, 2009

Here's my guess:

Use the scaling relation between stellar mass and radius:
$$R \propto M^{\frac{n-1}{n+3}}$$
Where n is the exponent describing how the nuclear energy output scales with the core temperature: $F \propto T^n$.

(n=16 for CNO-cycle hydrogen burning. n=4 approximates hydrogen burning by p-p chain.)

3. Sep 20, 2009

### Sorry!

maybe they just want you to use the same radius as our sun and compare the results.