Relative population density of stars and galaxies

[thornluke]

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!

 

[voko]

What is the shape of the volume element?

 

[thornluke]

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.

 

[voko]

What's the volume of the sphere?

 

[thornluke]

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

Am I right?! Please approve!

 

[voko]

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.

:)

 

[cepheid]

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.