Stars & the Universe — Problem set, Grade 9

Use stellar models, diagrams, and spectra to explain energy, elements, and cosmic history.

Review the key ideas

Stars, Fusion & Element Formation

Fusion powers stars; stellar history helps explain both energy reaching Earth and the origin of many elements.

Star Properties & H–R Diagrams

Temperature and luminosity together reveal more than brightness alone; read diagram axes and distance effects carefully.

Spectra & Evidence for an Expanding Universe

Spectral patterns reveal composition and shifts; multiple independent observations support cosmic expansion from an early hot, dense state.

Problem 1

A student says that atoms in a rocky planet could never have been part of a star. Respond using element formation.
Answer and explanation

Many heavier elements were produced by stellar or related astrophysical processes and dispersed into material from which later stars and planets formed.

Problem 2

Chapter review: Model star B has four times A’s available fuel but eighty times its fuel-use rate. Estimate its lifetime relative to A and explain why this is a ratio model rather than a complete stellar-evolution forecast.
Answer and explanation

The ratio is 4/80 = 0.05, so B’s lifetime scale is one twentieth of A’s. Actual evolution also depends on initial mass, composition, core structure and changing conditions; these supplied ratios are not a universal stellar formula.

The ratio is 4/80 = 0.05, so B’s lifetime scale is one twentieth of A’s. Actual evolution also depends on initial mass, composition, core structure and changing conditions; these supplied ratios are not a universal stellar formula.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 3

An H–R graph uses temperature decreasing left to right and logarithmic luminosity. Identify two mistakes a reader could make.
Answer and explanation

They might reverse hot/cool positions or treat equal vertical spacing as equal additive changes rather than equal factors.

Problem 4

Chapter review: Two ideal stars have equal surface temperature; star B has radius twice A’s. Find B/A luminosity. At the same observer distance and unobscured path, compare received brightness. Name one condition that would break the simple comparison.
Answer and explanation

Luminosity factor is 2² = 4 and received brightness is also four at equal distance/path conditions. Different temperatures, extinction or emission/measurement conditions would require additional factors.

Luminosity factor is 2² = 4 and received brightness is also four at equal distance/path conditions. Different temperatures, extinction or emission/measurement conditions would require additional factors.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 5

A galaxy has several spectral lines shifted by the same fractional amount. Why does that help distinguish a shift from an entirely different composition?
Answer and explanation

The relative pattern matches known lines when shifted together, supporting the same elements observed at changed wavelengths.

Problem 6

Chapter review: A 500 nm laboratory line is observed at 575 nm, and a 600 nm line at 690 nm. Calculate z for each. Explain what the agreement supports and what it does not uniquely establish.
Answer and explanation

Both give z = 0.15: 75/500 and 90/600. Agreement supports a common fractional shift of that identified pattern, while the physical cause, distance and full cosmological interpretation need context, calibration and additional evidence.

Compute (575−500)/500 = 0.15.

Compute (690−600)/600 = 0.15.

Interpret the common fractional shift without assigning a unique cause from arithmetic alone.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.
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