Topic 5.5: Fusion and Stars Questions

State one assumption made when estimating a star's main-sequence lifetime from t = E ÷ L.

State what is meant by nuclear fusion.

State the difference between the luminosity of a star and its apparent brightness.

A main-sequence star has a mass roughly equal to that of the Sun.

State the type of object this star leaves behind at the very end of its life.

An astronomer measures the parallax angle of the star Velora to be 0.025 arc-seconds, observed from opposite ends of Earth's orbit around the Sun.

What is the distance to Velora?

A red giant's black-body spectrum peaks at a wavelength of λₘₐₓ = 700 nm.

Calculate the surface temperature of the star.

(Wien's constant = 2.9 × 10⁻³ m K.)

When light nuclei fuse, the heavier product nucleus has slightly less mass than the nuclei that formed it.

Identify the source of the energy released by the reaction.

Two main-sequence stars are observed.

Star P glows blue-white and Star Q glows orange-red.

State, with reference to Wien's displacement law, which star has the higher surface temperature.

A main-sequence star has a mass of about twelve solar masses.

Identify the correct order of stages it passes through from the main sequence to the end of its life.

A star has a measured parallax angle of 0.040 arc-seconds.

Calculate the distance to the star, in parsecs.

A bright star is plotted in the top-right region of a Hertzsprung-Russell diagram, where the surface temperature is low but the luminosity is very high.

State the type of this star.

A particular star is observed from two different planets.

The star appears much fainter when seen from the more distant planet, even though it is the same star.

Explain this observation in terms of luminosity and apparent brightness.

Two stars, Vela-A and Vela-B, are treated as ideal black bodies. Vela-B has a luminosity that is 4 times the luminosity of Vela-A and a surface temperature that is twice that of Vela-A. Vela-A has radius R.

What is the radius of Vela-B?

A star has a luminosity of 4.0 × 10²⁸ W and is at a distance of 5.0 × 10¹⁸ m from Earth.

Calculate the apparent brightness of the star as observed from Earth.

A cool, swollen star has a radius 100 times the Sun's radius and a surface temperature of 2900 K (the Sun's surface temperature is 5800 K).

Calculate the luminosity of this star as a multiple of the Sun's luminosity.

Use L = σAT⁴ with A = 4πr², so L ∝ r²T⁴.

Star M has a black-body peak at λₘₐₓ = 450 nm and Star N has a peak at λₘₐₓ = 650 nm.

The two stars have equal radii.

Deduce which star is hotter and which is more luminous, justifying each conclusion.

A red supergiant is plotted on an H-R diagram with luminosity 14400 Lₛᵤₙ and surface temperature 3625 K.

The Sun's surface temperature is 5800 K.

Determine the radius of the supergiant as a multiple of the Sun's radius.

Use Rₛₜₐᵣ/Rₛᵤₙ = (Tₛᵤₙ/Tₛₜₐᵣ)² × √(Lₛₜₐᵣ/Lₛᵤₙ).

A white dwarf is plotted at the bottom-left of an H-R diagram.

Its luminosity is 0.0064 Lₛᵤₙ and its surface temperature is 14500 K, hotter than the Sun (5800 K).

Determine its radius as a fraction of the Sun's radius.

Use Rₛₜₐᵣ/Rₛᵤₙ = (Tₛᵤₙ/Tₛₜₐᵣ)² × √(Lₛₜₐᵣ/Lₛᵤₙ).

Star A and Star B both lie at known distances from Earth.

Star B has 8 times the luminosity of Star A and twice its surface temperature.

Two stars, Vega-9 and Vega-9b, have the same surface temperature. Vega-9 has radius 6.0 × 10⁸ m. Vega-9b lies three times as far from Earth as Vega-9, yet its apparent brightness measured at Earth is 4.0 times that of Vega-9.

What is the radius of Vega-9b?