Telescopes
Astronomical Distances
Distances in astronomy are vast and require special units:
- Astronomical Unit (AU): the mean Earth–Sun distance. 1 AU ≈ 1.50 × 1011 m
- Light-year (ly): the distance light travels in one year. 1 ly ≈ 9.46 × 1015 m
- Parsec (pc): the distance at which 1 AU subtends 1 arcsecond. 1 pc = 3.26 ly ≈ 3.09 × 1016 m
Stellar Parallax
The apparent shift in position of a nearby star against distant background stars as the Earth orbits the Sun. The parallax angle p (in arcseconds) gives the distance d (in parsecs):
Worked Example
A star has a parallax angle of 0.05 arcseconds. Find its distance.
d = 1/p = 1/0.05 = 20 pc
In light-years: 20 × 3.26 = 65.2 ly
Types of Telescope
Refracting telescopes use lenses to form images. Reflecting telescopes use curved mirrors. Reflecting telescopes are preferred for large apertures because mirrors are lighter, easier to support, and do not suffer from chromatic aberration.
Radio telescopes, infrared telescopes, and space-based telescopes observe different parts of the electromagnetic spectrum, each revealing different features of the universe.
Key Facts
- Parallax only works for relatively nearby stars (within a few hundred parsecs)
- Larger telescopes have better resolving power (ability to distinguish close objects)
- Space telescopes avoid atmospheric absorption and turbulence
Classification of Stars
Luminosity & Stefan's Law
Luminosity L is the total power output of a star (in watts). Using the Stefan–Boltzmann law:
where σ = 5.67 × 10−8 W m−2 K−4 is the Stefan–Boltzmann constant, r is the stellar radius, and T is the surface temperature.
Wien's Displacement Law
The peak wavelength of a star's spectrum is inversely proportional to its temperature:
Hotter stars peak at shorter (bluer) wavelengths; cooler stars peak at longer (redder) wavelengths.
Worked Example
A star has surface temperature 5800 K. Find its peak wavelength.
λmax = 2.898 × 10−3 / 5800 = 5.0 × 10−7 m = 500 nm
This is visible yellow-green light (like our Sun).
Apparent & Absolute Magnitude
Apparent magnitude (m): how bright a star appears from Earth. Lower = brighter.
Absolute magnitude (M): the apparent magnitude a star would have at a standard distance of 10 parsecs.
Worked Example
A star has m = +6.0 and M = +1.0. Find its distance.
Step 1: m − M = 5 log(d/10) ⇒ 5 = 5 log(d/10)
Step 2: log(d/10) = 1 ⇒ d/10 = 10
Step 3: d = 100 pc
Spectral Classes
Stars are classified by surface temperature: O, B, A, F, G, K, M (hottest to coolest).
Mnemonic: "Oh Be A Fine Girl/Guy, Kiss Me"
The Sun is a class G star with surface temperature ≈ 5800 K.
Exam Tip
Stefan's law has T4, so small changes in temperature produce huge changes in luminosity. If a star's temperature doubles, its luminosity increases by a factor of 16.
Stellar Evolution
Hertzsprung–Russell Diagram
The HR diagram plots stellar luminosity (or absolute magnitude) against surface temperature (or spectral class). Stars cluster in distinct regions.
Hertzsprung–Russell diagram showing the main sequence, red giants, supergiants, and white dwarfs
Life Cycle of Stars
A star's fate depends on its mass:
Low/medium mass stars (like the Sun):
Nebula → Protostar → Main sequence (fusing H → He) → Red giant (core contracts, outer layers expand) → Planetary nebula → White dwarf
High mass stars (> 8 solar masses):
Nebula → Protostar → Main sequence → Red supergiant (fuses heavier elements up to Fe) → Supernova → Neutron star or Black hole
Stellar evolution flowchart — a star's fate depends on its initial mass
Key Facts
- Stars spend most of their lives on the main sequence, fusing hydrogen to helium
- More massive stars burn faster and have shorter lifetimes
- The Chandrasekhar limit (≈ 1.4 M☉) is the maximum mass for a white dwarf
- A black hole forms when the remnant core exceeds about 3 solar masses
Exam Tip
Learn the two evolutionary paths thoroughly. A common 6-mark question asks you to describe the full life cycle of either a Sun-like star or a massive star.
Cosmology
Doppler Effect & Redshift
When a light source moves away from an observer, the observed wavelengths are shifted towards the red end of the spectrum (redshift):
where z is the redshift, v is the recession velocity, and c is the speed of light.
Worked Example
A hydrogen line is observed at 486.9 nm instead of its rest wavelength of 486.1 nm. Find the recession velocity.
Step 1: Δλ = 486.9 − 486.1 = 0.8 nm
Step 2: v = c × Δλ / λ = 3.0 × 108 × 0.8 / 486.1
Step 3: v = 4.9 × 105 m s−1
Hubble's Law
The recession velocity of a galaxy is proportional to its distance from us:
where H0 is the Hubble constant (≈ 70 km s−1 Mpc−1).
This implies the universe is expanding. An estimate of the age of the universe:
Worked Example
A galaxy has a recession velocity of 2.1 × 104 km s−1. Find its distance using H0 = 70 km s−1 Mpc−1.
d = v / H0 = 21 000 / 70 = 300 Mpc
Big Bang Evidence
Two key pieces of evidence support the Big Bang theory:
- Hubble's law (expansion): Galaxies are moving apart; more distant galaxies recede faster. Extrapolating backwards implies everything was once together.
- Cosmic Microwave Background (CMB): Uniform microwave radiation at ≈ 2.7 K detected from all directions. This is the cooled remnant of the hot, dense early universe, exactly as predicted by the Big Bang model.
Key Facts
- Redshift of distant galaxies shows the universe is expanding
- The CMB was discovered in 1965 by Penzias and Wilson
- The universe is approximately 13.8 billion years old
- Type Ia supernovae are used as standard candles for measuring large distances
Exam Tip
When asked to explain evidence for the Big Bang, always give both pieces of evidence (Hubble's law AND the CMB) and explain how each supports the theory.
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