Astrophysics

What astrophysics covers

One of the five AQA option units, and you sit only one option, so confirm it is yours. It runs from telescopes and the limits on what they resolve, through what starlight reveals about a star's temperature, brightness and distance, to red shift and the expanding universe. Lenses from Waves and the inverse-square law are both assumed.

The main ideas

• The refractor in normal adjustment, angular magnification, the Cassegrain reflector, and the aberrations that separate the two designs.
• Telescopes at other wavelengths and why they are sited where they are, the Rayleigh criterion, and collecting power through the square of the diameter.
• Apparent magnitude, the parsec, light year and astronomical unit, parallax, and absolute magnitude as a comparison at a fixed distance.
• Black-body curves with Wien's and Stefan's laws, and the spectral classes O to M with their temperatures, colours and absorption lines.
• The Hertzsprung-Russell diagram, the life of a Sun-like and of a massive star, type Ia supernovae as standard candles, neutron stars and black holes.
• The Doppler effect in starlight, spectroscopic binaries, Hubble's law and the age of the universe, and the evidence for the Big Bang.
• Quasars, and the two indirect methods that detect exoplanets.

Key equations

M = f_of_e$M = \frac{f_o}{f_e}$M = f_o/f_e

angular magnification in normal adjustment

θ ≈ λD$\theta \approx \frac{\lambda}{D}$θ ≈ λ/D

the Rayleigh criterion, in radians

p = 1d$p = \frac{1}{d}$p = 1/d

parallax in arcseconds against distance in parsecs

m - M = 5 logd10$m - M = 5\,\text{log}\frac{d}{10}$m - M = 5 log (d/10)

apparent against absolute magnitude

λ_max T = 2.9 × 10^-3 m K     P = σAT⁴$\lambda_{max} T = 2.9 \times 10^{-3}\,\text{m K} \qquad P = \sigma AT^{4}$λ_max T = 2.9 × 10^(-3) m K P = σAT^4

Wien's and Stefan's laws, for temperature and power

z = Δλλ = vc     v = Hd$z = \frac{\Delta\lambda}{\lambda} = \frac{v}{c} \qquad v = Hd$z = Δλ/λ = (v/c) v = Hd

red shift, recession speed and Hubble's law

Every equation the astrophysics notes display is collected, with its conditions, on the astrophysics equations page.

Common errors

• The magnitude scale runs backwards and is logarithmic. A larger number is a fainter object, one step is a factor of 2.51, and five steps is a factor of 100.
• Parallax works only with the angle in seconds of arc and the distance in parsecs, and the Rayleigh criterion only in radians. The units are part of the physics in both.
• The Big Bang was not an explosion at a point in space. Every observer sees the same recession, which is what the cosmological principle states.
• The approximation z = v/c is reliable only at low speeds, and quasar questions push it far enough that the answer has to be given as an estimate.

Suggested order

The four telescope lessons first, as one block, then the magnitude scale and stellar distances, since distance is needed for everything after it. Black-body radiation and spectral classes next, which the HR diagram depends on, then stellar evolution. Doppler and Hubble, then quasars and exoplanets, close the unit.