Astrophysics option (one possible Unit 2 AoS 2 option): the structure of the solar system, stellar life cycles, the colour-magnitude diagram, distance measurement (parallax, standard candles), and cosmological structure (galaxies, the expanding universe, Big Bang model)

What this dot point is asking

VCE Physics Unit 2 AoS 2 is an option topic chosen by the school from a list (sound, astrophysics, sport science, light, biomechanics, motion in two dimensions). This page covers the astrophysics option as one example.

The solar system

Structure. Sun at centre. Eight planets: terrestrial (Mercury, Venus, Earth, Mars) and gas giants (Jupiter, Saturn, Uranus, Neptune). Dwarf planets (Pluto, Eris, Ceres). Asteroid belt between Mars and Jupiter. Kuiper Belt beyond Neptune.

Distance scales.

• Earth-Sun: 1 astronomical unit (AU) = $1.5 \times 10^{11}$ m.
• Earth-Moon: $3.84 \times 10^8$ m.
• Sun-Neptune: about 30 AU.

Origin. Formed about 4.6 billion years ago from a collapsing molecular cloud (the solar nebula).

Stars and stellar evolution

Stars

Self-gravitating spheres of plasma producing energy by nuclear fusion. Hydrogen fuses to helium in the core (for sun-like stars).

Classification

Spectral types O, B, A, F, G, K, M (hottest to coolest). Sun is G-type. Brown dwarfs are sub-stellar.

Main sequence

Stars spend most of their lives fusing hydrogen. Position on the Hertzsprung-Russell (HR) diagram depends on mass; massive stars are hotter and more luminous but shorter-lived.

Life cycle of a sun-like star

1. Protostar (collapsing nebula).
2. Main sequence (hydrogen fusion, several billion years).
3. Red giant (hydrogen exhausted in core; helium burning).
4. Planetary nebula and white dwarf.

Life cycle of a massive star.

1. Protostar.
2. Main sequence (much shorter, millions of years).
3. Red supergiant.
4. Supernova explosion.
5. Neutron star (if remnant mass 1.4 to 3 solar masses) or black hole (above about 3 solar masses).

Supernovae. Released energy comparable to a galaxy's luminosity for weeks. Produce elements heavier than iron (which cannot form by fusion in normal stellar burning).

The Hertzsprung-Russell (HR) diagram

A plot of luminosity (vertical) vs surface temperature (horizontal, reversed). Stars cluster into specific regions:

• Main sequence. A diagonal band from hot bright (top left) to cool dim (bottom right).
• Red giants. Upper right (cool but bright).
• White dwarfs. Lower left (hot but dim).

A star's position on the HR diagram reveals its evolutionary state.

Distance measurement

The "cosmic distance ladder" uses different techniques at different scales.

Parallax. As Earth orbits the sun, nearby stars appear to shift against the background. The apparent angular shift (parallax angle $p$) gives the distance:

Works for stars within about 1,000 parsecs (with Gaia satellite up to about 10,000 pc).

1 parsec = 3.26 light-years = $3.086 \times 10^{16}$ m.

Standard candles. Objects with known intrinsic brightness. Compare to apparent brightness to determine distance.

• Cepheid variables: brightness varies periodically; the period-luminosity relation gives intrinsic brightness.
• Type Ia supernovae: very consistent peak luminosity; standard candles for cosmological distances.

Redshift. Light from distant galaxies is shifted to longer wavelengths (the Hubble flow). The redshift gives recession velocity; Hubble's law $v = H_0 d$ gives distance.

Galaxies and structure

Milky Way

Spiral galaxy, around 100,000 light-years across. About 200 billion stars. Sun is in the Orion Spur, about 26,000 light-years from the galactic centre. Galactic centre contains a supermassive black hole (Sagittarius A*, about 4 million solar masses).

Local Group

Cluster of 50+ galaxies including Milky Way, Andromeda, and many dwarfs. About 10 million light-years across.

Observable universe

About 93 billion light-years in diameter (due to expansion). 100 billion to 2 trillion galaxies. Filamentary large-scale structure with voids between.

The expanding universe and Big Bang

Hubble's discovery (1929)

Distant galaxies are receding from us, with velocity proportional to distance. The universe is expanding.

Hubble's law

$v = H_0 d$, where $H_0$ is Hubble's constant (about 70 km/s/Mpc).

Big Bang model

Extrapolating expansion backward, the universe was very dense and hot about 13.8 billion years ago. Evidence:

1. Hubble redshift (universe expanding).
2. Cosmic microwave background (CMB): faint radiation from the early universe, observed at temperature 2.7 K.
3. Abundance of light elements (hydrogen, helium, lithium) matching Big Bang nucleosynthesis predictions.

Dark matter. Galaxies rotate as if there is more mass than visible. Dark matter constitutes about 27 percent of the universe's mass-energy.

Dark energy. The expansion is accelerating (discovered 1998 via Type Ia supernovae). Dark energy is the hypothesised driver (about 68 percent of mass-energy).

Examples in context

Example 1. Mt Stromlo observatory parallax of Proxima Centauri. Mt Stromlo near Canberra measures stellar parallax to nearby stars. Proxima Centauri has parallax $p = 0.7687$ arcseconds, giving distance $d = 1/p = 1.301$ pc or $4.244$ light-years. The technique works only for stars within about $100$ pc because parallax angles become smaller than telescope resolution. For more distant stars, astronomers use Cepheid variable standard candles, whose pulsation period correlates with luminosity. A Cepheid with period $10$ days has absolute magnitude $M \approx -4$; measuring its apparent magnitude $m$ gives distance via $m - M = 5 \log(d/10)$ pc.

Example 2. SKA Murchison detection of neutral hydrogen at high redshift. The Square Kilometre Array (SKA) under construction at Murchison in Western Australia detects neutral hydrogen at the $21$ cm spin-flip transition. Hubble's law $v = H_0 d$ with $H_0 = 70$ km s$^{-1}$ Mpc$^{-1}$ relates recession velocity to distance. A galaxy at redshift $z = 0.1$ has recession velocity $v \approx 30\,000$ km s$^{-1}$, giving $d \approx 430$ Mpc. SKA-Low will observe the cosmic-dawn era at $z > 6$, when neutral hydrogen filled the universe before star formation, helping resolve when reionisation completed and how the first generation of stars formed.

Try this

Q1. Define stellar parallax and state the conversion between parallax angle and distance in parsecs. [2 marks]

• Cue. Apparent shift of a nearby star against distant background due to Earth's orbital motion; $d$ (pc) = $1/p$ (arcseconds).

Q2. A Cepheid variable in the Andromeda Galaxy has period $20$ days and absolute magnitude $M = -5$. Observed apparent magnitude is $m = 19$. Calculate the distance in megaparsecs. [4 marks]

• Cue. $m - M = 24 = 5 \log(d/10)$, so $\log(d/10) = 4.8$, $d = 10^{5.8}$ pc = $6.3 \times 10^5$ pc = $0.63$ Mpc.

Q3. Refer to SKA observations of distant hydrogen. (a) State Hubble's law. (b) Calculate the recession velocity of a galaxy at $d = 200$ Mpc with $H_0 = 70$ km s$^{-1}$ Mpc$^{-1}$. (c) Explain how cosmological redshift is distinct from a classical Doppler shift. [2+2+2 marks]

• Cue. (a) $v = H_0 d$. (b) $14\,000$ km s$^{-1}$. (c) Cosmological redshift is stretching of wavelengths by expansion of space, not relative motion through space.