Option D: Astrophysics (Additional higher level option topics)

Identify two possible causes of the anisotropies in (a).

Identify two possible causes of the anisotropies in (a).

Identify two possible causes of the anisotropies in (a).

The Sun is a second generation star. Outline, with reference to the Jeans criterion (M_J), how the Sun is likely to have been formed.

The Sun is a second generation star. Outline, with reference to the Jeans criterion (M_J), how the Sun is likely to have been formed.

The Sun is a second generation star. Outline, with reference to the Jeans criterion (M_J), how the Sun is likely to have been formed.

Show that the critical density of the universe is

$$\frac{3H^2}{8\pi G}$$

where H is the Hubble parameter and G is the gravitational constant.

Show that the critical density of the universe is

$$\frac{3H^2}{8\pi G}$$

where H is the Hubble parameter and G is the gravitational constant.

Show that the critical density of the universe is

$$\frac{3H^2}{8\pi G}$$

where H is the Hubble parameter and G is the gravitational constant.

Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.

Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.

Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.

The mass of visible matter in the galaxy is M.

Show that for stars where r > R₀ the velocity of orbit is v = $\sqrt{\frac{GM}{r}}$.

The mass of visible matter in the galaxy is M.

Show that for stars where r > R₀ the velocity of orbit is v = $\sqrt{\frac{GM}{r}}$.

The mass of visible matter in the galaxy is M.

Show that for stars where r > R₀ the velocity of orbit is v = $\sqrt{\frac{GM}{r}}$.

Describe the formation of a type Ia supernova.

Describe the formation of a type Ia supernova.

Describe the formation of a type Ia supernova.

Explain, using the equation in (a) and the graphs, why the presence of visible matter alone cannot account for the velocity of stars when r > R₀.

Explain, using the equation in (a) and the graphs, why the presence of visible matter alone cannot account for the velocity of stars when r > R₀.

Explain, using the equation in (a) and the graphs, why the presence of visible matter alone cannot account for the velocity of stars when r > R₀.

Show that the distance to the supernova is approximately 3.1 × 10¹⁸ m.

Show that the distance to the supernova is approximately 3.1 × 10¹⁸ m.

Show that the distance to the supernova is approximately 3.1 × 10¹⁸ m.

Draw on the axes the observed variation with r of the orbital speed v of stars in a galaxy.

Draw on the axes the observed variation with r of the orbital speed v of stars in a galaxy.

Draw on the axes the observed variation with r of the orbital speed v of stars in a galaxy.

State one assumption made in your calculation.

State one assumption made in your calculation.

State one assumption made in your calculation.

Outline, with reference to the Jeans criterion, why a cold dense gas cloud is more likely to form new stars than a hot diffuse gas cloud.

Outline, with reference to the Jeans criterion, why a cold dense gas cloud is more likely to form new stars than a hot diffuse gas cloud.

Outline, with reference to the Jeans criterion, why a cold dense gas cloud is more likely to form new stars than a hot diffuse gas cloud.

Explain how neutron capture can produce elements with an atomic number greater than iron.

Explain how neutron capture can produce elements with an atomic number greater than iron.

Explain how neutron capture can produce elements with an atomic number greater than iron.

Explain the evidence that indicates the location of dark matter in galaxies.

Explain the evidence that indicates the location of dark matter in galaxies.

Explain the evidence that indicates the location of dark matter in galaxies.

Outline why a hypothesis of dark energy has been developed.

Outline why a hypothesis of dark energy has been developed.

Outline why a hypothesis of dark energy has been developed.

The present temperature of the cosmic microwave background (CMB) radiation is 3 K. Estimate the size of the universe relative to the present size of the universe when the temperature of the CMB was 300 K.

The present temperature of the cosmic microwave background (CMB) radiation is 3 K. Estimate the size of the universe relative to the present size of the universe when the temperature of the CMB was 300 K.

The present temperature of the cosmic microwave background (CMB) radiation is 3 K. Estimate the size of the universe relative to the present size of the universe when the temperature of the CMB was 300 K.

Show that the temperature of the universe is inversely proportional to the cosmic scale factor.

Show that the temperature of the universe is inversely proportional to the cosmic scale factor.

Show that the temperature of the universe is inversely proportional to the cosmic scale factor.

Compare and contrast, the variation with time of the temperature of the cosmic background (CMB) radiation, for the two models from the present time onward.

Compare and contrast, the variation with time of the temperature of the cosmic background (CMB) radiation, for the two models from the present time onward.

Compare and contrast, the variation with time of the temperature of the cosmic background (CMB) radiation, for the two models from the present time onward.

Describe the mechanism of formation of type II supernovae.

Describe the mechanism of formation of type II supernovae.

Describe the mechanism of formation of type II supernovae.

At critical density there is zero total energy. Show that the critical density of the universe is: ${\text{r}}_c=\frac{3H_0^2}{8\pi G}$.

At critical density there is zero total energy. Show that the critical density of the universe is: ${\text{r}}_c=\frac{3H_0^2}{8\pi G}$.

At critical density there is zero total energy. Show that the critical density of the universe is: ${\text{r}}_c=\frac{3H_0^2}{8\pi G}$.

Justify that the total energy of this particle is $E=\frac{1}{2}m{v}^2-\frac{4}{3}\pi G\text{r}{r}^{2}m$.

Justify that the total energy of this particle is $E=\frac{1}{2}m{v}^2-\frac{4}{3}\pi G\text{r}{r}^{2}m$.

Justify that the total energy of this particle is $E=\frac{1}{2}m{v}^2-\frac{4}{3}\pi G\text{r}{r}^{2}m$.

Proxima Centauri is a main sequence star with a mass of 0.12 solar masses.

Estimate $\frac{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Proxima} \mathrm{Centauri}}{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Sun}}$.

Proxima Centauri is a main sequence star with a mass of 0.12 solar masses.

Estimate $\frac{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Proxima} \mathrm{Centauri}}{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Sun}}$.

Proxima Centauri is a main sequence star with a mass of 0.12 solar masses.

Estimate $\frac{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Proxima} \mathrm{Centauri}}{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Sun}}$.

Calculate the density of matter in the universe, using the Hubble constant 70 km s^–1Mpc^–1.

Calculate the density of matter in the universe, using the Hubble constant 70 km s^–1Mpc^–1.

Calculate the density of matter in the universe, using the Hubble constant 70 km s^–1Mpc^–1.

Discuss one process by which elements heavier than iron are formed in stars.

Discuss one process by which elements heavier than iron are formed in stars.

Discuss one process by which elements heavier than iron are formed in stars.