Relative population density of stars and galaxies

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Homework Help Overview

The problem involves calculating the average population density of stars and galaxies based on given distances from the Sun. The original poster provides specific numbers of stars and galaxies within defined volumes, prompting a discussion on the appropriate volume calculations for these celestial objects.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the shape of the volume element, with some suggesting it is spherical. Questions arise regarding the volume calculations for the defined distances and whether the original poster's approach is correct.

Discussion Status

There is an ongoing exploration of the volume calculations necessary for determining population density. Some participants have provided clarifications regarding the nature of the volumes being considered, emphasizing the importance of understanding the context of the calculations.

Contextual Notes

Participants note that the original poster's calculations may be based on an assumption of spherical volumes, which is being examined for accuracy. There is also a recognition that the terminology used in the problem may lead to confusion regarding the volumes involved.

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Homework Statement



The number of stars around the Sun, within a distance of 17 ly, is 75. The number of galaxies in the local group, within a distance of 4.0 x106 ly from the Sun, is 26.

Calculate the average popluation density, per ly3, of stars and galaxies.

Homework Equations

The Attempt at a Solution


Stars: 75/173
Galaxies: 26/(4.0 x106)3

But the answers I obtain from my attempt is incorrect :s
Help please!
 
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What is the shape of the volume element?
 
voko said:
What is the shape of the volume element?

The question assumes that the Sun is a sphere. So I suppose the volume element is sphere.
 
What's the volume of the sphere?
 
voko said:
What's the volume of the sphere?
I think my brain went dead, because I got it after saying that we assume the Sun as the volume of a sphere.

So basically ly is the radius and we divide 75 by the volume of the star and galaxy to get the two answers :smile:

Am I right?! Please approve! :approve:
 
Pedantry: it is not the volume of the star, and not the volume of the galaxy. It is the volumes of two balls of the specified radii.

:)
 
voko said:
Pedantry: it is not the volume of the star, and not the volume of the galaxy. It is the volumes of two balls of the specified radii.

:)

Hah, I would say not pedantry at all! It's kind of a crucial detail that you're dividing the number of objects by the volume of the region. I hope the OP gets this now.
 

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