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Astronomy & space · lesson 1 of 4

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.

Advanced university8 practice questionsNotes + worked examples
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Learn the ideas

Prerequisites: Gravity, circular motion and observational uncertainty.

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.

Worked examples

Example 1

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

M=v²r/G=16×3.

48

Example 2

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

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

Approximately proportionally to radius

Check your understanding

8 questions

Decimals or fractions are accepted for numeric answers. Proofs and written responses use sample answers and require human marking. This is practice, not a protected examination.

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

Show answer and explanation

48

M=v²r/G=16×3.

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

Show answer and explanation

Approximately proportionally to radius

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

3 Which is an additional gravitational probe of mass distribution?

Show answer and explanation

Gravitational lensing

Lensing responds to gravitational effects on light propagation.

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

Sample answer and marking guidance

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

Credit population models and unseen components.

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

Show answer and explanation

2

M scales with r when v is fixed.

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

Sample answer and marking guidance

The methods constrain gravitational effects through different data and assumptions. Agreement can strengthen or challenge a mass model while revealing systematics.

Credit complementary constraints, not a guarantee of unique truth.

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

Show answer and explanation

No

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

8 Name two observational uncertainties relevant to a rotation curve.

Sample answer and marking guidance

Disk inclination and distance, velocity measurement noise, noncircular motion or spatial resolution are relevant examples.

Credit two concrete uncertainties.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.