Astronomy and Cosmology

State what is meant by the luminosity of a star.

Explain how standard candles are used to determine the distance to a galaxy.

The Sun rotates with a period of $2.07 \times 10^{6}\ \text{s}$.

Show that the radius of the Sun is $6.93 \times 10^{8}\ \text{m}$.

State and explain how the expected wavelength of the light observed from Z compares with the emitted wavelength.

The luminosity of the Sun is $3.8 \times 10^{26}\ \text{W}$.

Use the information in (b)(i) to calculate the surface temperature of the Sun.

temperature = ______ $\text{K}$

State Hubble’s law.

Explain why the observed wavelength and the emitted wavelength have different values.

Calculate the speed of the star relative to the Earth.

speed = ______ $\text{m s}^{-1}$

The wavelength of maximum intensity of emission is used to determine a value for the surface temperature of the star.

Explain how the temperature determined using the observed wavelength compares with the true value of temperature determined using the emitted wavelength.

A value for the Hubble constant is $2.3 \times 10^{-18}\ \text{s}^{-1}$.

Use your answer in (b)(ii) to determine the distance of the star in (b) from the Earth.

distance = ______ $\text{m}$

State Hubble’s law.

Explain why the observed wavelength and the emitted wavelength have different values.

Calculate the speed of the star relative to the Earth.

speed = ______ $\text{m s}^{-1}$

The wavelength of maximum intensity of emission is used to determine a value for the surface temperature of the star.

Explain how the temperature determined using the observed wavelength compares with the true value of temperature determined using the emitted wavelength.

A value for the Hubble constant is $2.3 \times 10^{-18}\ \text{s}^{-1}$.

Use your answer in (b)(ii) to determine the distance of the star in (b) from the Earth.

distance = ______ $\text{m}$

State Wien’s displacement law.

Fig. 9.1 shows the variation with $d^{-2}$ of the radiant flux intensity $F$ observed from a star X, where $d$ is the distance of the observer from the star. Fig. 9.2 shows the variation with wavelength $\lambda$ of the rates of emission $P$ of radiation by star X and the Sun.

The surface temperature of the Sun is $5770\ \text{K}$.

State three conclusions about star X that can be drawn from this data. The conclusions may be qualitative or quantitative. Use the space for any working.

1 ______

2 ______

3 ______

Star X is in a galaxy that is moving away from the Earth.

Suggest, with a reason, how the line for star X in Fig. 9.2 would appear differently if it had been obtained from data measured on the Earth.

State Wien’s displacement law.

Fig. 9.1 shows the variation with $d^{-2}$ of the radiant flux intensity $F$ observed from a star X, where $d$ is the distance of the observer from the star. Fig. 9.2 shows the variation with wavelength $\lambda$ of the rates of emission $P$ of radiation by star X and the Sun.

The surface temperature of the Sun is $5770\ \text{K}$.

State three conclusions about star X that can be drawn from this data. The conclusions may be qualitative or quantitative. Use the space for any working.

1 ______

2 ______

3 ______

Star X is in a galaxy that is moving away from the Earth.

Suggest, with a reason, how the line for star X in Fig. 9.2 would appear differently if it had been obtained from data measured on the Earth.

State what is meant by redshift.

Explain how observations of redshift lead to the idea that the universe is expanding.

Explain how Hubble’s law leads to the Big Bang theory of the origin of the universe.

Calculate the radius of the Sun.

radius = ______ $\text{m}$

The Earth is a distance of $1.50 \times 10^{11} \text{ m}$ from the Sun.

Calculate the radiant flux intensity $F$ of the radiation from the Sun at a distance of $1.50 \times 10^{11} \text{ m}$. Give a unit with your answer.

$F$ = ______ unit ______

The variation with wavelength of the intensity of radiation emitted from the Sun is shown in Fig. 10.1.

Another star has the same radius as the Sun but has a lower surface temperature.

On Fig. 10.1, sketch a line to show the variation with wavelength of the intensity of the radiation emitted for this star.

The visible emission spectrum for the Sun is shown in Fig. 10.2.

The lines are at wavelengths of $397 \text{ nm}$, $410 \text{ nm}$, $434 \text{ nm}$, $486 \text{ nm}$ and $656 \text{ nm}$. The compositions of the Sun and a star in the Corona Borealis galaxy are similar.

On Fig. 10.3, sketch the emission spectrum for the star in the Corona Borealis galaxy as observed from the Earth. No calculations are required.

The galaxy in Corona Borealis is moving away from the Earth at a speed of $21400 \text{ km s}^{-1}$.

Use information from (b)(i) to calculate, in nm, the observed wavelength of the lowest visible energy emission for the star in the Corona Borealis galaxy.

wavelength = ______ $\text{nm}$

The wavelength in (b)(ii) is used to calculate a value for the surface temperature of the star in the Corona Borealis galaxy. The calculation does not give an accurate value.

State and explain whether this value of temperature is too high or too low.

State what is meant by the luminosity of a star.

Explain how a standard candle in a distant galaxy can be used to determine the distance of the galaxy from an observer.

Calculate the luminosity of the Sun. Give a unit with your answer.

luminosity = ______ unit ______

Another star emits radiation that has a peak intensity at a wavelength of $624\ \text{nm}$.

Determine the surface temperature of this star.

surface temperature = ______ $\text{K}$

State what is meant by the luminosity of a star.

Explain how a standard candle in a distant galaxy can be used to determine the distance of the galaxy from an observer.

Calculate the luminosity of the Sun. Give a unit with your answer.

luminosity = ______ unit ______

Another star emits radiation that has a peak intensity at a wavelength of $624\ \text{nm}$.

Determine the surface temperature of this star.

surface temperature = ______ $\text{K}$

Explain how redshift leads to the idea that the Universe is expanding.

the distance $d$ of the galaxy from the Earth

$d$ = ______ $\text{m}$

the speed $v$ of the galaxy relative to the Earth.

$v$ = ______ $\text{m s}^{-1}$

On Fig. 10.1, sketch the variation of $v$ with $d$.

State the name of the quantity represented by the gradient of the line in Fig. 10.1.

gradient = ______