EST Density of our galaxy Estimate the average density of...

EST Density of our galaxy Estimate the average density of particles in our galaxy, assuming that the most abundant element is atomic hydrogen. There are about $10^{9}$ stars in the galaxy and the size of the galaxy is about $10^{5}$ light-years. A light-year is the distance light travels in 1 year moving at a speed of $3 \times 10^{8} \mathrm{m} / \mathrm{s}$ . What do you need to assume about the stars in order to answer this question?

Key Concepts

Uniform Distribution

A key assumption is that the stars are uniformly distributed throughout the galaxy. This lets you use the overall size of the galaxy to define a volume in which the stars, and by extension the atomic hydrogen (as the dominant particle species), are evenly spread. Without this assumption, the density calculation would be complicated by regions of over- or under-density and would require a more detailed spatial distribution model.

Point-Particle Approximation

Another important assumption is that each star can be treated as a point particle with a typical and roughly equal mass, neglecting the details of their individual sizes and mass differences. This simplification allows you to use the number of stars as a representative measure when estimating total matter content or when comparing the stellar component to the interstellar medium.

Transcript

00:02 Okay, so we would like to set up this problem here with a few assumptions.

00:10 Assumptions are, okay, let's see.

00:13 We assume first that the milky way is our galaxy, the milky way is a circular disk of some thickness zee.

00:30 And then we assume that it's made up of hydrogen only.

00:38 That's a false assumption, but that's, you know, hydrogen is the most abundant element in the universe, so that's fine.

00:48 And then, of course, we can assume sun equals an average star.

00:54 So what that means is that the mass of stars when we're calculating will be the mass of the sun.

00:58 Okay, average star.

01:00 All right, so i'm gonna, we want to calculate the density of the galaxy.

01:06 So density is mass over volume.

01:10 And so the volume part is pretty simple.

01:14 It's piar squared for the area of the circle times the height z.

01:18 This is like pyrued, basically radius, length cube dimensions here.

01:24 M is a bit trickier.

01:26 So you have small, mass of a molecule, mass of molecules times n p, number of particles, times n s, number of stars.

01:40 Okay, and mass of the molecule, if you'll recall, is the molar mass over avogadro's number.

01:46 So this is m over n a times number of particles, times number of stars over piar squared z.

01:56 Number of stars is given.

01:58 Molar mass is hydrogen h2's molar mass, hydrogen's molecular mass of our 2 grams.

02:05 R and z we will calculate in a bit, or volume will calculate in a bit.

02:10 Np, number of particles, number of particles in the sun.

02:17 So this will be the mass of the sun over, mass of the sun over again assuming all made up of hydrogen over mass of hydrogen atom and so this is two times 10 of the 30 kilograms over mass of hydrogen atom this will be molar mass of hydrogen per n a just as just as over here so this will be 10 to the minus kilograms per mole times apocadro's number of 6 times 10 of the 23 per mole.

03:05 And so, oops, and so you get about 10 to the 56 particles.

03:14 This is an approximate order of magnitude calculations.

03:18 Everything will pretty much be in terms of order of magnitude.

03:22 So this is 10 to the 56 approximately.

03:26 Uh, uh, uh, uh, not kilograms.

03:30 That should be number of, that should be 10 of the 56.

03:34 Uh, particles...

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