# Galaxies, dynamics and dark-matter evidence

> Galaxies contain stars, gas, dust and other gravitating components. Their morphology does not alone determine all their dynamical properties.

Course: [Astrophysics, cosmology and inference](https://studybrix.com/en/courses/astrophysics-and-cosmology/index.md)
Level: advanced
Prerequisites: Gravity, circular motion and observational uncertainty.

## Notes

### Structure

Galaxies contain stars, gas, dust and other gravitating components. Their morphology does not alone determine all their dynamical properties.

### Dynamics

In a simplified spherical model, circular speed obeys v²=GM(<r)/r. Inferring enclosed mass therefore uses a geometric and dynamical model.

### Evidence

Rotation curves, gravitational lensing and other observations constrain mass distributions. The evidence for unseen gravitating components is not a direct photograph of dark matter.

### Uncertainty

Inclination, distance, noncircular motion and mass-to-light estimates affect interpretation. Multiple independent probes help test explanations.

## Practice questions

### 1. In units G=1, circular speed is 4 at radius 3 in a spherical model. Find enclosed mass.

Answer: 48

Explanation: M=v²r/G=16×3.

### 2. A flat rotation curve in the stated spherical model implies enclosed mass changes how with radius?

A. It must fall as radius cubed
B. Approximately proportionally to radius
C. It must be zero
D. It must be constant

Answer: Approximately proportionally to radius

Explanation: With constant v, M(<r)=v²r/G grows linearly.

### 3. Which is an additional gravitational probe of mass distribution?

A. Gravitational lensing
B. Only a galaxy's name
C. Only visible colour without a model
D. A telescope's price

Answer: Gravitational lensing

Explanation: Lensing responds to gravitational effects on light propagation.

### 4. Why is converting luminosity directly into total mass model-dependent?

Sample answer / marking guidance: Stellar populations have different mass-to-light ratios, and gas or nonluminous components can contribute. Luminosity alone does not uniquely fix mass.

Explanation: Credit population models and unseen components.

### 5. At fixed circular speed in the spherical model, radius doubles. Find the inferred enclosed-mass factor.

Answer: 2

Explanation: M scales with r when v is fixed.

### 6. Explain why combining lensing and dynamics can be more informative than either alone.

Sample answer / marking guidance: The methods constrain gravitational effects through different data and assumptions. Agreement can strengthen or challenge a mass model while revealing systematics.

Explanation: Credit complementary constraints, not a guarantee of unique truth.

### 7. Does a rotation-curve inference directly identify the microscopic nature of dark matter?

A. Only at large radius
B. Yes, it measures a chemical formula
C. Yes, it names the particle
D. No

Answer: No

Explanation: Dynamical evidence constrains gravity and mass distribution, not automatically particle identity.

### 8. Name two observational uncertainties relevant to a rotation curve.

Sample answer / marking guidance: Disk inclination and distance, velocity measurement noise, noncircular motion or spatial resolution are relevant examples.

Explanation: Credit two concrete uncertainties.

## Further reading

- https://science.nasa.gov/universe/galaxies/

Original AI-assisted educational draft; not independently teacher-reviewed. References support further study, not copied exercises, affiliation or curriculum accreditation.