Topic 5.5: Fusion and Stars Questions

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

Calculate the distance to the star, in parsecs.

State what is meant by nuclear fusion.

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.

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.

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 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.

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

A red giant's black-body spectrum peaks at a wavelength of λ_{max} = 700 nm.

Calculate the surface temperature of the star.

(Wien's constant = 2.9 × 10⁻³ m K.)

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

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 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.

Over its main-sequence life a star radiates a total energy of about E = 2.5 × 10⁴⁴ J.

Estimate the total mass the star loses by radiating this energy.

(c = 3.00 × 10⁸ m s⁻¹.)

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?

Star M has a black-body peak at λ_{max} = 450 nm and Star N has a peak at λ_{max} = 650 nm.

The two stars have equal radii.

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

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.

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?

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.

On an H-R diagram, Star J is plotted at the top-right (low surface temperature, very high luminosity) and Star K is plotted on the lower-left part of the main-sequence band (high surface temperature, moderate luminosity).

A detector on a probe measures the apparent brightness of a distant star to be 2.0 × 10⁻⁹ W m⁻².

The star is known to be 3.0 × 10¹⁷ m from the probe.

Calculate the luminosity of the star.