# Calculate Star Mass from Radius: An Integration Approach

• Unto
In summary, the conversation discusses finding the mass of a star within a radius and the method of integration used. The total mass of the star is calculated by substituting the total radius, R, into the equation and cancelling out the subjective r1. It is also mentioned that the total mass of anything can be calculated as M=pV, where p is the average density and V is the volume.
Unto
Sorry no one was answering my question, and I just wanted to get this done:

## Homework Statement

...Hence show that the mass of the star is M = $$4\pi$$$$p_{c}$$$$\left(R^{3}/3 )$$

## Homework Equations

M(r) = $$4 \pi$$$$p_{c}$$$$\left(r^{3}/3 - r^{4}/4R)$$
This is the mass within a radius

## The Attempt at a Solution

I already found the mass within a radius via intergration (look at relevant equations), and I know that I have to build up an 'infinite' number of radial masses to get the whole mass of the star. But do I use integration on this equation or something else? What do I do?

Oohh for f_cks sake... I realized

Total radius of the star is 'R'. Just substitute that in for $$r$$ and cancel, since r1 is subjective and doesn't factor for the whole star.

WHHHYYYYYY!??

The total mass of anything is just M=pV where p is the average density and V is the volume. Here V=4/3*pi*R^3. That's that...

## What is the purpose of calculating star mass from radius?

The purpose of calculating star mass from radius is to determine the total amount of matter contained within a star. This information is essential for understanding the internal structure and dynamics of stars, as well as their evolution and eventual fate.

## What is the integration approach for calculating star mass from radius?

The integration approach for calculating star mass from radius involves using the formula for the volume of a sphere (4/3 * pi * r^3) and integrating it over the entire radius of the star. This allows us to find the total volume of the star and then multiply it by the average density to get the total mass.

## Why is the integration approach more accurate than other methods?

The integration approach is more accurate than other methods because it takes into account the varying density and volume throughout the star's radius. Other methods, such as using the average density or assuming a uniform density, may not accurately reflect the true mass of the star.

## What data is needed to calculate star mass from radius using the integration approach?

To calculate star mass from radius using the integration approach, we need to know the radius of the star and its average density. This data can be obtained through observations or theoretical models.

## Are there any limitations to using the integration approach for calculating star mass from radius?

Yes, there are limitations to using the integration approach for calculating star mass from radius. This method assumes that the star is spherically symmetric and has a smooth density profile, which may not always be the case. Additionally, it may not be applicable to highly irregular or non-spherical stars.

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