# Opacity and density of the sun

• user12323567
In summary, according to one model of the sun, the central mass density is 1.53x10^5kg.m^-3 and the mean opacity at the center is 0.217m^2kg^-1. Using dimensional analysis, the mean free path of a photon at the center of the sun is calculated to be 3.01x10^-5m^-1 when all opacity is due to absorption. For coherent scattering, the average time for a photon to escape from the surface is calculated using a random walk model and the speed of the photon.
user12323567
Thread moved from the technical forums, so no Homework Template is shown.
Summary:: Given statement: according to one model of the sun, the central mass density is 1.53x10^5kg.m^-3 and the mean opacity at the center is 0.217m^2kg^-1

Given statement: according to one model of the sun, the central mass density is 1.53x10^5kg.m^-3 and the mean opacity at the center is 0.217m^2kg^-1

(a) Assume that all the opacity is due to absorption. Calculate the mean free path of a photon in meters at the center of the sun. Hint: Use dimensional analysis
* my answer : free-mean path = 1/k(kappa)p(rho) = 1/(1.53x10^5)(0.217x10^2)=3.01x10^-5m^-1 and I am not sure if I am correct please assist

(b)Now, instead, assume that all the opacity is due to coherent scattering. Calculating the average time it would take for a photon emitted at the center of the sun to escape from the surface if the diffusion length remained constant for the photon's journey to the surface and had a value equal to the mean free path calculated in part(a). (Ignore the fact that identifiable photons are constantly destroyed and created through absorption, scattering and emission)

Last edited:
For part (a) I think your answer is correct. For part (b), are you familiar with a random walk? Using this, you should be able to calculate how many steps of a random walk it would take to move from the center to the edge of the sun. You know the speed of the photon, so how long will this take?

## 1. What is the opacity of the sun?

The opacity of the sun refers to how much light is absorbed or scattered by the sun's atmosphere. It is measured by the amount of energy that passes through a certain area of the sun's atmosphere in a given time.

## 2. How does the opacity of the sun affect its temperature?

The opacity of the sun plays a crucial role in determining its temperature. Higher opacity means more energy is absorbed and scattered, resulting in a cooler temperature. On the other hand, lower opacity allows more energy to pass through, leading to a higher temperature.

## 3. What is the density of the sun?

The density of the sun refers to the amount of mass per unit volume. It is estimated to be around 1.41 g/cm³, which is about 25% of the density of the Earth.

## 4. How does the density of the sun affect its gravitational pull?

The density of the sun is directly related to its mass, which in turn determines its gravitational pull. The higher the density, the greater the mass and gravitational pull. This is why the sun has a strong gravitational force that keeps the planets in orbit around it.

## 5. How do scientists measure the opacity and density of the sun?

Scientists use a variety of instruments and techniques to measure the opacity and density of the sun. These include spectroscopy, which analyzes the absorption and emission of light, and helioseismology, which studies the vibrations of the sun's surface to determine its internal structure and density.

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