Lesson 1 of 6 · Galaxy rotation and missing mass
Galaxy rotation and missing mass
10 minute lesson · 3 checks along the way
Your goal for this lessonTrace how motion, ordinary-matter inventories, and stated gravity assumptions lead to an inferred mass distribution.
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Measure motion before inferring mass
A galaxy photograph tells us where detected light appears, but it does not directly measure orbital speed. Astronomers compare spectral lines across a rotating galaxy: gas approaching us shifts differently from gas receding from us. Converting those line-of-sight velocities into rotation speeds requires the galaxy’s orientation. A nearly face-on disk makes that correction particularly uncertain, because little of its rotation points toward or away from us.
A plots inferred orbital speed against distance from the center. Many disk galaxies maintain substantial speeds well beyond their brightest central regions. This does not mean every galaxy has an exactly flat curve at every radius. Distance estimates, irregular gas motions, instrument resolution, and all affect the measurement. The useful question is whether a specified distribution of ordinary matter predicts the observed motion under a specified law of gravity.
Inventory the matter that emits light
Stars supply only part of that inventory. Astronomers also measure gas, including neutral hydrogen observed at radio wavelengths. Stellar brightness must be converted into stellar mass using a , which depends on the stellar population. Dust and young bright stars can complicate optical estimates. Infrared observations from the Spitzer Space Telescope help trace the stellar component, but infrared brightness still is not a direct weighing scale.
The SPARC research compilation combines 3.6-micrometer photometry with rotation curves for 175 disk galaxies. Its mass models explicitly include assumptions about stellar mass-to-light ratios. Comparing many systems tests whether one explanation works across different galaxy properties. Changing a mass-to-light assumption can alter the inferred ordinary-matter contribution; it does not give permission to choose an arbitrary mass independently at every radius without checking other evidence.
Check 1 of 3
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Work through a decision
Work through an enclosed-mass model
Use an invented spherical mass distribution with circular Newtonian orbits. In this model, is M(<r) = v²r/G, where v is orbital speed, r is radius, and G is the gravitational constant. Suppose speeds are 100 kilometers per second at both 5 and 10 kiloparsecs. The speed factors cancel in the ratio, leaving M(10)/M(5) = 10/5 = 2. The larger orbit requires twice the enclosed mass in this model.
Now compare a different hypothesis: the same fixed central mass dominates at both radii. Its predicted speed varies as 1/√r, so the outer speed would be 100/√2, about 71 kilometers per second. Distinguishing these predictions requires motion measurements, not judging which outer region looks darker. A real galaxy’s flattened disk requires a more appropriate gravitational calculation; this spherical exercise demonstrates the reasoning without pretending to fit an actual galaxy.
One speed pattern, two mass hypotheses
Both curves are instructional predictions over the displayed radial range. The flat-speed model has twice the enclosed mass at twice the radius; the fixed-central-mass curve falls as 1/√r. Real galaxy disks need a different geometry.
Open full-size diagram in a new tab: One speed pattern, two mass hypothesesCheck 2 of 3
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Separate a successful model from a particle identity
Adding an extended can account for rotation that the measured stars and gas do not explain under ordinary gravitational modeling. Here, “dark” describes matter inferred through gravity without enough accompanying detected electromagnetic emission. It is not simply the black background between stars. Nor does a rotation curve alone tell us the mass, interaction strength, or identity of an individual dark-matter particle.
A stronger investigation joins galaxy motions with , galaxy clusters, and cosmological structure. Alternative gravity models must confront that combined evidence too. Preserve three steps in any claim: what was measured, which assumptions converted the measurement into a mass estimate, and which candidate explanations remain. Agreement across independent methods is more informative than treating one attractive galaxy image as a complete proof.
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Put it together
Your lesson progress
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Go to the source
Explore the evidence behind this lesson. These optional readings and videos open in a new tab.
- Read: SPARC: the original galaxy mass-model sampleOriginal research abstract; 175 disk galaxies and explicit stellar mass-to-light assumptions.
- Read: Particle Data Group: dark matterTechnical review of gravitational evidence and particle searches.
- Read: ESA: the dark UniverseMission context for the wider set of gravitational evidence.