Astrophysics (A-level only)

An astronomical telescope in normal adjustment has objective focal length $1.20\,\text{m}$ and eyepiece focal length $30.0\,\text{mm}$. Calculate the magnitude of its angular magnification.

A distant crater subtends $2.0\times10^{-4}\,\text{rad}$ at the unaided eye. It is viewed through a normal-adjustment telescope with $f_o=1.500\,\text{m}$ and $f_e=25.0\,\text{mm}$. Determine the angle subtended at the eye and the lens separation.

A telescope is to make an object that subtends $1.50\times10^{-4}\,\text{rad}$ appear to subtend at least $4.80\times10^{-3}\,\text{rad}$. The objective focal length is $0.960\,\text{m}$. Determine the greatest acceptable eyepiece focal length and the corresponding maximum telescope length in normal adjustment.

State one aberration that a reflecting telescope avoids because its primary element is a mirror rather than a lens.

Describe the path of initially parallel rays through a Cassegrain reflecting telescope up to the eyepiece.

A research group must choose between a large refracting telescope and a Cassegrain reflector of the same aperture. Discuss why the reflector is usually preferred, including aberrations and construction.

State why most X-ray telescopes used for astronomy are placed on satellites.

An optical telescope of diameter $0.200\,\text{m}$ observes at $550\,\text{nm}$. Estimate the diameter of a radio dish observing at $0.210\,\text{m}$ that would have the same Rayleigh angular resolution.

Discuss suitable observing locations for radio, infrared, ultraviolet and X-ray astronomy, and explain why a radio dish generally has a much larger diameter than an optical telescope.

A telescope aperture is increased from $0.30\,\text{m}$ to $0.60\,\text{m}$. Determine the factor by which its collecting power increases.

Calculate the Rayleigh minimum angular resolution of a $2.50\,\text{m}$ telescope at wavelength $500\,\text{nm}$. State the effect of increasing the diameter.

Two telescopes have diameters $4.00\,\text{m}$ and $10.0\,\text{m}$ and observe at $600\,\text{nm}$. A pair of faint stars is separated by $8.0\times10^{-8}\,\text{rad}$. Determine which telescope can resolve the pair, compare their collecting powers, and explain one advantage of recording with a CCD rather than the eye.

Two stars have apparent magnitudes $+1.0$ and $+4.0$. State which appears brighter.

Star P has apparent magnitude $2.00$ and star Q has apparent magnitude $5.00$. Calculate the ratio $I_P/I_Q$.

Interstellar dust reduces the received intensity from a star by a factor of $20.0$. Before the dimming, its apparent magnitude was $2.00$. Determine its new apparent magnitude and whether it should remain visible to the unaided eye under dark conditions.

A star is exactly $10\,\text{pc}$ from Earth and has apparent magnitude $4.3$. State its absolute magnitude.

A star has apparent magnitude $8.4$ and absolute magnitude $3.4$. Calculate its distance from Earth in parsecs.

A supergiant has apparent magnitude $12.0$ and absolute magnitude $-1.0$. Determine its distance in parsecs and in light years. Use $1\,\text{pc}=3.26\,\text{ly}$.

The black-body spectrum of a star peaks at $580\,\text{nm}$. Estimate its surface temperature using Wien's law.

Star B has twice the radius of star A but $0.800$ times its surface temperature. Using Stefan's law, calculate $P_B/P_A$.

A star $50.0\,\text{pc}$ away produces an intensity of $3.20\times10^{-10}\,\text{W m}^{-2}$ at Earth and has peak wavelength $480\,\text{nm}$. Assuming isotropic emission and black-body behaviour, determine its surface temperature and radius. Use $1\,\text{pc}=3.086\times10^{16}\,\text{m}$ and $\sigma=5.67\times10^{-8}\,\text{W m}^{-2}\text{K}^{-4}$.

Three stars have spectral classes B, G and M. State which has the highest surface temperature.

A star's continuous spectrum peaks at $410\,\text{nm}$. Estimate its temperature and hence identify its most likely spectral class. Use Wien's constant $2.9\times10^{-3}\,\text{m K}$.

Explain why hydrogen Balmer absorption lines can be weak in both a very hot class O star and a cool class M star but strongest in a class A star.

State the region of an HR diagram occupied by the Sun and give its approximate spectral class.

A star has surface temperature $12000\,\text{K}$ and absolute magnitude $+12$. Deduce its region on an HR diagram and justify your answer.

Describe the path of a star with a mass similar to the Sun on an HR diagram from formation until its white-dwarf stage. Refer to changes in temperature and absolute magnitude where appropriate.

A newly identified black hole has mass $5.20\times10^{30}\,\text{kg}$. Determine its event-horizon radius using $G=6.67\times10^{-11}\,\text{N m}^2\text{kg}^{-2}$ and $c=3.00\times10^8\,\text{m s}^{-1}$.

A type Ia supernova has absolute magnitude $-19.5$ and peak apparent magnitude $18.5$. Use the distance modulus to estimate its distance in parsecs.

The collapse of a supergiant produces a gamma-ray burst of energy $4.0\times10^{44}\,\text{J}$ and leaves a compact object of mass $6.0\times10^{30}\,\text{kg}$. Calculate the object's Schwarzschild radius and the time for the Sun, at constant power $3.8\times10^{26}\,\text{W}$, to emit the burst energy. Give the time in years and use $G=6.67\times10^{-11}\,\text{N m}^2\text{kg}^{-2}$, $c=3.00\times10^8\,\text{m s}^{-1}$ and $1\,\text{year}=3.156\times10^7\,\text{s}$.

A spectral line of laboratory wavelength $500.00\,\text{nm}$ is observed at $500.40\,\text{nm}$. Calculate the redshift $z$.

Radiation emitted at $1.42000\,\text{GHz}$ is received from a gas cloud at $1.41900\,\text{GHz}$. Determine the cloud's radial speed and state whether it is approaching or receding. Use $c=3.00\times10^8\,\text{m s}^{-1}$.

In an equal-mass binary system viewed in the plane of its circular orbit, a line of rest wavelength $656.300\,\text{nm}$ alternates between $656.000\,\text{nm}$ and $656.600\,\text{nm}$ for one star. The orbital period is $8.00\,\text{days}$. Estimate the speed of that star, its orbital radius about the centre of mass, and the separation of the stars. Use $c=3.00\times10^8\,\text{m s}^{-1}$.

Use $H=70\,\text{km s}^{-1}\text{Mpc}^{-1}$ to calculate the recession speed of a galaxy $120\,\text{Mpc}$ away.

Estimate the age of the Universe for $H=68.0\,\text{km s}^{-1}\text{Mpc}^{-1}$. Assume $H$ is constant and use $1\,\text{Mpc}=3.086\times10^{22}\,\text{m}$ and $1\,\text{year}=3.156\times10^7\,\text{s}$.

A galaxy's hydrogen line has laboratory wavelength $486.10\,\text{nm}$ and is observed at $493.40\,\text{nm}$. Use the non-relativistic Doppler approximation and $H=70.0\,\text{km s}^{-1}\text{Mpc}^{-1}$ to estimate the galaxy's distance. Check whether $v\ll c$, taking $c=3.00\times10^5\,\text{km s}^{-1}$.

State the central engine believed to power a quasar.

A quasar at distance $900\,\text{Mpc}$ produces a flux of $2.5\times10^{-15}\,\text{W m}^{-2}$ at Earth. Estimate its power output assuming isotropic emission. Use $1\,\text{Mpc}=3.086\times10^{22}\,\text{m}$.

A low-redshift quasar has $z=0.0200$ and measured flux $1.60\times10^{-13}\,\text{W m}^{-2}$. Estimate its distance, power output and power in units of the Sun's luminosity. Use $c=3.00\times10^5\,\text{km s}^{-1}$, $H=70.0\,\text{km s}^{-1}\text{Mpc}^{-1}$, $1\,\text{Mpc}=3.086\times10^{22}\,\text{m}$ and $L_{\odot}=3.83\times10^{26}\,\text{W}$. Assume isotropic emission.

A star's brightness shows equal, regularly repeated dips. Name the exoplanet-detection method indicated by this observation.

During a transit, a star's detected intensity falls by $0.810\%$. Estimate the radius of the planet if the star's radius is $6.90\times10^8\,\text{m}$.

A star has radius $8.0\times10^8\,\text{m}$. Every $5.2\,\text{days}$ its intensity falls by $0.160\%$, while a $600.0\,\text{nm}$ absorption line shifts with the same period by up to $0.014\,\text{nm}$ to either side of its mean. Calculate the planet's radius and the star's maximum radial speed, then explain why the combined observations are stronger evidence for an exoplanet than either observation alone. Use $c=3.00\times10^8\,\text{m s}^{-1}$.