Astronomy And Cosmology (Copy)

A2 Level Physics – Section 25: Astronomy and Cosmology (Detailed Notes)

25.1 Standard Candles

1. Luminosity (L)

• Luminosity: the total energy per second (power) radiated by a star in all directions
  • Unit: watts (W)
  • Intrinsic property of a star (does not depend on distance)

2. Inverse Square Law for Radiant Flux

• Radiant flux intensity (F): energy received per unit area per unit time
  F = L / (4πd²)
  • F = flux (W/m²)
  • L = luminosity (W)
  • d = distance to star (m)
• Intensity decreases with square of distance

3. Standard Candle

• A standard candle is an astronomical object of known luminosity
• Comparing measured flux with known luminosity allows calculation of distance

4. Determining Distance to Galaxies

• Use the inverse square law:
  • Measure F on Earth
  • Use known L of standard candle
  • Rearranged:
    d = √(L / 4πF)
• Examples of standard candles:
  • Cepheid variable stars
  • Type Ia supernovae

25.2 Stellar Radii

1. Wien’s Displacement Law

• λ_max ∝ 1 / T, or
  λ_max·T = constant
• λ_max = peak wavelength of emitted radiation (m)
• T = surface temperature of star (K)
• Constant = 2.90 × 10⁻³ m·K

Used to estimate temperature of a star from its spectrum

2. Stefan–Boltzmann Law

• L = 4π·σ·r²·T⁴
  • L = luminosity (W)
  • σ = Stefan–Boltzmann constant = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴
  • r = radius of star (m)
  • T = surface temperature (K)
• Total energy radiated is proportional to surface area × T⁴

3. Estimating Stellar Radius

• Use Wien’s law to find T
• Use L (from flux and distance) and T in Stefan–Boltzmann law to find r

Rearranged:
r = √(L / (4πσT⁴))

25.3 Hubble’s Law and Big Bang Theory

1. Spectral Redshift

• Light from distant galaxies shows redshift:
  • Wavelengths are longer than in lab measurements
  • Absorption/emission lines shifted toward red end of spectrum
  • Indicates that the source is moving away

2. Redshift Equation

• z = ∆λ / λ = ∆f / f = v / c
  • ∆λ = change in wavelength
  • λ = rest wavelength
  • v = recessional velocity
  • c = speed of light

Used for low redshifts (non-relativistic speeds)

3. Expanding Universe

• Redshift observed in almost all galaxies → galaxies are moving away
• Greater redshift = greater velocity → space is expanding

4. Hubble’s Law

• v = H₀·d
  • v = recessional velocity (m/s)
  • d = distance to galaxy (m)
  • H₀ = Hubble constant ≈ 70 km/s/Mpc = 2.3 × 10⁻¹⁸ s⁻¹
• Linear relationship: more distant galaxies recede faster

5. Big Bang Theory

• If the universe is expanding now, it must have been denser and hotter in the past
• Extrapolation backward → all matter originated from a single point: the Big Bang
• Hubble time:
  t ≈ 1 / H₀ → estimate of universe’s age