Astronomy · Unit 5: Galaxies & Cosmology ·  Problem 5.3.1

The Galaxy That Doesn't Add Up

How far away is it — and why is it spinning faster than its stars can explain?  ·  3 in-class days

Pulls TogetherThe Whole Unit
Unit 5: Galaxies & Cosmology

A radio astronomy team has spent a week observing a spiral galaxy with a large dish telescope, tuned to the 21-centimeter signal of cold hydrogen gas. Hydrogen is a perfect tracer: it extends far beyond the galaxy's visible stars, so it reveals motion out where there's almost nothing to see.

From the shift of the hydrogen and starlight across the galaxy, the team built two things: the galaxy's overall redshift, and its rotation curve — how fast gas orbits at each distance from the center. The first was routine. The second wasn't. Past the edge of the bright disk, the gas should be slowing down. It isn't.

The team lead has asked you, their newest analyst, to write it up: how far away is this galaxy, how fast is it receding, and what does the rotation curve mean? She's clear about one thing — she wants the numbers and the argument, and she wants you to deal with the obvious objections before the reviewers do.

Your Investigation Questions
Q1How far away is this galaxy, and how fast is it moving away from us?
Q2How fast should its outer gas be orbiting if its visible matter were all there is — and how fast is it really orbiting?
Q3How much mass is missing, and what's the best explanation for it?

This isthe assignment — your own galaxy's redshift and rotation curve are generated for you on the problem page. Everything in this unit was building toward being able to make, and defend, this exact argument.

🧭 Plot Summary

No new content here — this problem puts two halves of the unit together. First, you'll use your galaxy's spectrum to find its redshift, recession velocity, and distance with Hubble's law. Then you'll analyze its rotation curve: calculate how fast the outer gas shouldbe moving if the visible matter were all there is, compare it to what's measured, and work out how much mass is missing. Finally, you'll argue for the best explanation, using your numbers plus independent evidence, and take on at least one alternative explanation directly.

Resource Map — where each piece comes from

Stuck on one step? Jump straight to the lesson that covers it.

5.1.1Mapping the Milky Way

Disks, halos, and how 21-cm radio measures gas in a spinning galaxy

5.1.2The Hubble Tuning Fork

Recognizing the kind of galaxy you're analyzing

5.1.3Galaxy Field Guide

Classifying real galaxies by what's visible

5.2.1Redshift and Hubble's Law

z = Δλ ÷ λ₀, v = c × z, and d = v ÷ H₀ — the whole distance calculation

5.2.2Dark Matter and Dark Energy

Rotation curves, the expected-speed rule, the mass ratio, and the other evidence

5.2.3Timeline of Everything

Where dark matter fits in the universe's history

✅ Self-Check Before You Roll On

Check off each item as you get there. These aren't grades — they're your own signal.