Option D: Astrophysics (Core topics)

Outline how Hubble’s law is related to $z$.

Outline how Hubble’s law is related to $z$.

Outline how Hubble’s law is related to $z$.

The light from a distant galaxy shows that $z=0.11$.

Calculate the ratio $\frac{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{when} \mathrm{the} \mathrm{light} \mathrm{was} \mathrm{emitted}}{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{at} \mathrm{present}}$.

The light from a distant galaxy shows that $z=0.11$.

Calculate the ratio $\frac{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{when} \mathrm{the} \mathrm{light} \mathrm{was} \mathrm{emitted}}{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{at} \mathrm{present}}$.

The light from a distant galaxy shows that $z=0.11$.

Calculate the ratio $\frac{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{when} \mathrm{the} \mathrm{light} \mathrm{was} \mathrm{emitted}}{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{at} \mathrm{present}}$.

Two of the brightest objects in the night sky seen from Earth are the planet Venus and the star Sirius. Explain why the equation $b\propto \frac{A{T}^4}{d^2}$ is applicable to Sirius but not to Venus.

Two of the brightest objects in the night sky seen from Earth are the planet Venus and the star Sirius. Explain why the equation $b\propto \frac{A{T}^4}{d^2}$ is applicable to Sirius but not to Venus.

Two of the brightest objects in the night sky seen from Earth are the planet Venus and the star Sirius. Explain why the equation $b\propto \frac{A{T}^4}{d^2}$ is applicable to Sirius but not to Venus.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the parallax angle in the table.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the parallax angle in the table.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the parallax angle in the table.

Outline how Hubble’s law is related to $z$.

Outline how Hubble’s law is related to $z$.

Outline how Hubble’s law is related to $z$.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the luminosity in the table, given that $L_{\odot }=3.83\times {10}^{26} \mathrm{W}$.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the luminosity in the table, given that $L_{\odot }=3.83\times {10}^{26} \mathrm{W}$.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the luminosity in the table, given that $L_{\odot }=3.83\times {10}^{26} \mathrm{W}$.

Estimate, in $\mathrm{pc}$, the distance to Eta Aquilae A using the parallax angle in the table.

Estimate, in $\mathrm{pc}$, the distance to Eta Aquilae A using the parallax angle in the table.

Estimate, in $\mathrm{pc}$, the distance to Eta Aquilae A using the parallax angle in the table.

Determine the velocity of the galaxy relative to Earth.

Determine the velocity of the galaxy relative to Earth.

Determine the velocity of the galaxy relative to Earth.

Determine the radius of Sirius B in terms of the radius of the Sun.

Determine the radius of Sirius B in terms of the radius of the Sun.

Determine the radius of Sirius B in terms of the radius of the Sun.

plot the position, using the letter P, of the main sequence star P you calculated in (b).

plot the position, using the letter P, of the main sequence star P you calculated in (b).

plot the position, using the letter P, of the main sequence star P you calculated in (b).

plot the position, using the letter G, of Gacrux.

plot the position, using the letter G, of Gacrux.

plot the position, using the letter G, of Gacrux.

The luminosity of the Sun L${}_{\odot }$ is 3.85 × 10²⁶ W. Determine the luminosity of Gacrux relative to the Sun.

The luminosity of the Sun L${}_{\odot }$ is 3.85 × 10²⁶ W. Determine the luminosity of Gacrux relative to the Sun.

The luminosity of the Sun L${}_{\odot }$ is 3.85 × 10²⁶ W. Determine the luminosity of Gacrux relative to the Sun.

The distance to Gacrux can be determined using stellar parallax. Outline why this method is not suitable for all stars.

The distance to Gacrux can be determined using stellar parallax. Outline why this method is not suitable for all stars.

The distance to Gacrux can be determined using stellar parallax. Outline why this method is not suitable for all stars.

Estimate, using the data, the age of the universe. Give your answer in seconds.

Estimate, using the data, the age of the universe. Give your answer in seconds.

Estimate, using the data, the age of the universe. Give your answer in seconds.

Main sequence stars are in equilibrium under the action of forces. Outline how this equilibrium is achieved.

Main sequence stars are in equilibrium under the action of forces. Outline how this equilibrium is achieved.

Main sequence stars are in equilibrium under the action of forces. Outline how this equilibrium is achieved.

Discuss, with reference to its change in mass, the evolution of star P from the main sequence until its final stable phase.

Discuss, with reference to its change in mass, the evolution of star P from the main sequence until its final stable phase.

Discuss, with reference to its change in mass, the evolution of star P from the main sequence until its final stable phase.

draw the main sequence.

draw the main sequence.

draw the main sequence.

Identify the assumption that you made in your answer to (a).

Identify the assumption that you made in your answer to (a).

Identify the assumption that you made in your answer to (a).

On the graph, one galaxy is labelled A. Determine the size of the universe, relative to its present size, when light from the galaxy labelled A was emitted.

On the graph, one galaxy is labelled A. Determine the size of the universe, relative to its present size, when light from the galaxy labelled A was emitted.

On the graph, one galaxy is labelled A. Determine the size of the universe, relative to its present size, when light from the galaxy labelled A was emitted.

Distinguish between a planet and a comet. 

Distinguish between a planet and a comet. 

Distinguish between a planet and a comet. 

Suggest, using the graphs, why star X is most likely to be a main sequence star.

Suggest, using the graphs, why star X is most likely to be a main sequence star.

Suggest, using the graphs, why star X is most likely to be a main sequence star.

Show that the temperature of star X is approximately 10 000 K.

Show that the temperature of star X is approximately 10 000 K.

Show that the temperature of star X is approximately 10 000 K.

Write down the luminosity of star X (L_X) in terms of the luminosity of the Sun (L_s).

Write down the luminosity of star X (L_X) in terms of the luminosity of the Sun (L_s).

Write down the luminosity of star X (L_X) in terms of the luminosity of the Sun (L_s).

Determine the radius of star X (R_X) in terms of the radius of the Sun (R_s).

Determine the radius of star X (R_X) in terms of the radius of the Sun (R_s).

Determine the radius of star X (R_X) in terms of the radius of the Sun (R_s).

Estimate the mass of star X (M_X) in terms of the mass of the Sun (M_s).

Estimate the mass of star X (M_X) in terms of the mass of the Sun (M_s).

Estimate the mass of star X (M_X) in terms of the mass of the Sun (M_s).

Star X is likely to evolve into a stable white dwarf star.

Outline why the radius of a white dwarf star reaches a stable value.

Star X is likely to evolve into a stable white dwarf star.

Outline why the radius of a white dwarf star reaches a stable value.

Star X is likely to evolve into a stable white dwarf star.

Outline why the radius of a white dwarf star reaches a stable value.

Explain how international collaboration has helped to refine this value.

Explain how international collaboration has helped to refine this value.

Explain how international collaboration has helped to refine this value.

Estimate, in Mpc, the distance between the galaxy and the Earth.

Estimate, in Mpc, the distance between the galaxy and the Earth.

Estimate, in Mpc, the distance between the galaxy and the Earth.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 $M_{\odot }$.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 $M_{\odot }$.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 $M_{\odot }$.

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

Use the graph to determine the age of the universe in s.

Use the graph to determine the age of the universe in s.

Use the graph to determine the age of the universe in s.

Outline how Hubble measured the recessional velocities of galaxies.

Outline how Hubble measured the recessional velocities of galaxies.

Outline how Hubble measured the recessional velocities of galaxies.

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = $L_{\odot }$

Mass                          = $M_{\odot }$

Radius                       = $R_{\odot }$

Epsilon Indi has a radius of 0.73 $R_{\odot }$. Show that the luminosity of Epsilon Indi is 0.2 $L_{\odot }$.

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = $L_{\odot }$

Mass                          = $M_{\odot }$

Radius                       = $R_{\odot }$

Epsilon Indi has a radius of 0.73 $R_{\odot }$. Show that the luminosity of Epsilon Indi is 0.2 $L_{\odot }$.

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = $L_{\odot }$

Mass                          = $M_{\odot }$

Radius                       = $R_{\odot }$

Epsilon Indi has a radius of 0.73 $R_{\odot }$. Show that the luminosity of Epsilon Indi is 0.2 $L_{\odot }$.

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

Using the graph, determine in s, the age of the universe.

Using the graph, determine in s, the age of the universe.

Using the graph, determine in s, the age of the universe.

Outline how Hubble measured the recessional velocities of galaxies.

Outline how Hubble measured the recessional velocities of galaxies.

Outline how Hubble measured the recessional velocities of galaxies.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 $M_{\odot }$.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 $M_{\odot }$.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 $M_{\odot }$.

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = $L_{\odot }$

Mass                          = $M_{\odot }$

Radius                       = $R_{\odot }$

Epsilon Indi has a radius of 0.73 $R_{\odot }$. Show that the luminosity of Epsilon Indi is 0.2 $L_{\odot }$.

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = $L_{\odot }$

Mass                          = $M_{\odot }$

Radius                       = $R_{\odot }$

Epsilon Indi has a radius of 0.73 $R_{\odot }$. Show that the luminosity of Epsilon Indi is 0.2 $L_{\odot }$.

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = $L_{\odot }$

Mass                          = $M_{\odot }$

Radius                       = $R_{\odot }$

Epsilon Indi has a radius of 0.73 $R_{\odot }$. Show that the luminosity of Epsilon Indi is 0.2 $L_{\odot }$.

The Sun will spend about nine billion years on the main sequence. Calculate how long Epsilon Indi will spend on the main sequence.

The Sun will spend about nine billion years on the main sequence. Calculate how long Epsilon Indi will spend on the main sequence.

The Sun will spend about nine billion years on the main sequence. Calculate how long Epsilon Indi will spend on the main sequence.

A line in the hydrogen spectrum when measured on Earth has a wavelength of 486 nm. Calculate, in nm, the wavelength of the same hydrogen line when observed in the galaxy’s emission spectrum.

A line in the hydrogen spectrum when measured on Earth has a wavelength of 486 nm. Calculate, in nm, the wavelength of the same hydrogen line when observed in the galaxy’s emission spectrum.

A line in the hydrogen spectrum when measured on Earth has a wavelength of 486 nm. Calculate, in nm, the wavelength of the same hydrogen line when observed in the galaxy’s emission spectrum.

Determine the peak apparent brightness of δ-Cephei as observed from Earth.

Determine the peak apparent brightness of δ-Cephei as observed from Earth.

Determine the peak apparent brightness of δ-Cephei as observed from Earth.

Calculate the peak surface temperature of δ-Cephei.

Calculate the peak surface temperature of δ-Cephei.

Calculate the peak surface temperature of δ-Cephei.

Outline why the Sun will maintain a constant radius after it becomes a white dwarf.

Outline why the Sun will maintain a constant radius after it becomes a white dwarf.

Outline why the Sun will maintain a constant radius after it becomes a white dwarf.

During its evolution, the Sun is likely to be a red giant of surface temperature 3000 K and luminosity 10⁴ L_☉. Later it is likely to be a white dwarf of surface temperature 10 000 K and luminosity 10-4 L_☉. Calculate the $\frac{\text{radius of the Sun as a white dwarf}}{\text{radius of the Sun as a red giant}}$.

During its evolution, the Sun is likely to be a red giant of surface temperature 3000 K and luminosity 10⁴ L_☉. Later it is likely to be a white dwarf of surface temperature 10 000 K and luminosity 10-4 L_☉. Calculate the $\frac{\text{radius of the Sun as a white dwarf}}{\text{radius of the Sun as a red giant}}$.

During its evolution, the Sun is likely to be a red giant of surface temperature 3000 K and luminosity 10⁴ L_☉. Later it is likely to be a white dwarf of surface temperature 10 000 K and luminosity 10-4 L_☉. Calculate the $\frac{\text{radius of the Sun as a white dwarf}}{\text{radius of the Sun as a red giant}}$.

The peak spectral line of Sirius B has a measured wavelength of 115 nm. Show that the surface temperature of Sirius B is about 25 000 K.

The peak spectral line of Sirius B has a measured wavelength of 115 nm. Show that the surface temperature of Sirius B is about 25 000 K.

The peak spectral line of Sirius B has a measured wavelength of 115 nm. Show that the surface temperature of Sirius B is about 25 000 K.

The surface temperature of Eta Cassiopeiae B is 4100 K. Determine the ratio $\frac{\mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{A}}{\mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{B}}$.

The surface temperature of Eta Cassiopeiae B is 4100 K. Determine the ratio $\frac{\mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{A}}{\mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{B}}$.

The surface temperature of Eta Cassiopeiae B is 4100 K. Determine the ratio $\frac{\mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{A}}{\mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{B}}$.

Calculate the ratio $\frac{\mathrm{mass} \mathrm{of} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{A}}{\mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{Sun}}$.

Calculate the ratio $\frac{\mathrm{mass} \mathrm{of} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{A}}{\mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{Sun}}$.

Calculate the ratio $\frac{\mathrm{mass} \mathrm{of} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{A}}{\mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{Sun}}$.

The peak wavelength of radiation from Eta Cassiopeiae A is 490 nm. Show that the surface temperature of Eta Cassiopeiae A is about 6000 K.

The peak wavelength of radiation from Eta Cassiopeiae A is 490 nm. Show that the surface temperature of Eta Cassiopeiae A is about 6000 K.

The peak wavelength of radiation from Eta Cassiopeiae A is 490 nm. Show that the surface temperature of Eta Cassiopeiae A is about 6000 K.

Estimate the age of the universe in seconds using the Hubble constant H₀ = 70 km s^–1Mpc^–1.

Estimate the age of the universe in seconds using the Hubble constant H₀ = 70 km s^–1Mpc^–1.

Estimate the age of the universe in seconds using the Hubble constant H₀ = 70 km s^–1Mpc^–1.

Deduce the final evolutionary state of Eta Cassiopeiae A.

Deduce the final evolutionary state of Eta Cassiopeiae A.

Deduce the final evolutionary state of Eta Cassiopeiae A.

The distance of the Eta Cassiopeiae system from the Earth is 1.8 × 10¹⁷m. Calculate, in terms of $L_{\odot }$, the luminosity of Eta Cassiopeiae A.

The distance of the Eta Cassiopeiae system from the Earth is 1.8 × 10¹⁷m. Calculate, in terms of $L_{\odot }$, the luminosity of Eta Cassiopeiae A.

The distance of the Eta Cassiopeiae system from the Earth is 1.8 × 10¹⁷m. Calculate, in terms of $L_{\odot }$, the luminosity of Eta Cassiopeiae A.

Outline why the estimate made in (b)(i) is unlikely to be the actual age of the universe.

Outline why the estimate made in (b)(i) is unlikely to be the actual age of the universe.

Outline why the estimate made in (b)(i) is unlikely to be the actual age of the universe.

Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.

Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.

Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.

Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.

Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.

Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.

The mass of Sirius B is about the same mass as the Sun. The luminosity of Sirius B is 2.5 % of the luminosity of the Sun. Show, with a calculation, that Sirius B is not a main sequence star.

The mass of Sirius B is about the same mass as the Sun. The luminosity of Sirius B is 2.5 % of the luminosity of the Sun. Show, with a calculation, that Sirius B is not a main sequence star.

The mass of Sirius B is about the same mass as the Sun. The luminosity of Sirius B is 2.5 % of the luminosity of the Sun. Show, with a calculation, that Sirius B is not a main sequence star.

Distinguish between the solar system and a galaxy.

Distinguish between the solar system and a galaxy.

Distinguish between the solar system and a galaxy.

A main sequence star P, is 1.3 times the mass of the Sun. Calculate the luminosity of P relative to the Sun.

A main sequence star P, is 1.3 times the mass of the Sun. Calculate the luminosity of P relative to the Sun.

A main sequence star P, is 1.3 times the mass of the Sun. Calculate the luminosity of P relative to the Sun.

The astronomical unit ($\mathrm{AU}$) and light year ($\mathrm{ly}$) are convenient measures of distance in astrophysics. Define each unit.

$\mathrm{AU}$:

$\mathrm{ly}$:

The astronomical unit ($\mathrm{AU}$) and light year ($\mathrm{ly}$) are convenient measures of distance in astrophysics. Define each unit.

$\mathrm{AU}$:

$\mathrm{ly}$:

The astronomical unit ($\mathrm{AU}$) and light year ($\mathrm{ly}$) are convenient measures of distance in astrophysics. Define each unit.

$\mathrm{AU}$:

$\mathrm{ly}$:

Show that the apparent brightness $b\propto \frac{A{T}^4}{d^2}$, where $d$ is the distance of the object from Earth, $T$ is the surface temperature of the object and $A$ is the surface area of the object.

Show that the apparent brightness $b\propto \frac{A{T}^4}{d^2}$, where $d$ is the distance of the object from Earth, $T$ is the surface temperature of the object and $A$ is the surface area of the object.

Show that the apparent brightness $b\propto \frac{A{T}^4}{d^2}$, where $d$ is the distance of the object from Earth, $T$ is the surface temperature of the object and $A$ is the surface area of the object.

Show by calculation that Eta Aquilae A is not on the main sequence.

Show by calculation that Eta Aquilae A is not on the main sequence.

Show by calculation that Eta Aquilae A is not on the main sequence.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the luminosity in the table, given that $L_{\odot }=3.83\times {10}^{26} \mathrm{W}$.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the luminosity in the table, given that $L_{\odot }=3.83\times {10}^{26} \mathrm{W}$.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the luminosity in the table, given that $L_{\odot }=3.83\times {10}^{26} \mathrm{W}$.

The light from a distant galaxy shows that $z=0.11$.

Calculate the ratio $\frac{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{when} \mathrm{the} \mathrm{light} \mathrm{was} \mathrm{emitted}}{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{at} \mathrm{present}}$.

The light from a distant galaxy shows that $z=0.11$.

Calculate the ratio $\frac{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{when} \mathrm{the} \mathrm{light} \mathrm{was} \mathrm{emitted}}{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{at} \mathrm{present}}$.

The light from a distant galaxy shows that $z=0.11$.

Calculate the ratio $\frac{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{when} \mathrm{the} \mathrm{light} \mathrm{was} \mathrm{emitted}}{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{at} \mathrm{present}}$.

Show by calculation that Eta Aquilae A is not on the main sequence.

Show by calculation that Eta Aquilae A is not on the main sequence.

Show by calculation that Eta Aquilae A is not on the main sequence.