Astronomy and cosmology

Learning objectives

• Use luminosity, flux and inverse-square spreading.
• Connect blackbody spectra with stellar temperature and radius.
• Interpret redshift and the Hubble relationship within their range.

The big idea

Luminosity is total radiated power; observed flux is power per unit detector area. Distance changes flux without necessarily changing luminosity. A blackbody approximation connects stellar spectra and power to surface temperature and radius.

At sufficiently low cosmological redshift, recession speed is approximately proportional to distance. Cosmic microwave background radiation is further evidence for cosmic evolution. An age estimated from an expansion rate depends on assumptions about expansion history.

1. Separate source power from received flux

Luminosity is a star’s total radiated power; flux is received power per unit area. For an isotropic source without intervening absorption, F = L/(4πd²). Moving a detector twice as far away reduces flux to one quarter while luminosity is unchanged. A faint star can therefore be intrinsically faint, very distant or affected by absorption; brightness alone does not uniquely establish its distance.

2. A spectrum constrains temperature and radius

A blackbody approximation gives λmax T = b and L = 4πR²σT⁴ for a spherical star. Hotter surfaces have shorter peak wavelengths. If temperature and luminosity are known, the second relation can estimate radius. The peak depends on which spectral representation is plotted, so the familiar wavelength-form Wien constant must match the graph used. Real stellar atmospheres introduce lines and deviations from a perfect blackbody.

3. Redshift and the Hubble relationship

Compare an identified spectral line with its reference wavelength: z = (λobserved − λemitted)/λemitted. At sufficiently low cosmological redshift, recession speed can be approximated by cz and related to distance through v ≈ H₀d. This local approximation must not be applied blindly at large redshift. Calibration and the methods used to infer distance matter when interpreting a graph of recession speed against distance.

4. Evidence and model-dependent inference

The cosmic microwave background has a nearly thermal spectrum and arrives from essentially every direction. It is evidence for a hot early Universe that became transparent and whose radiation subsequently stretched during expansion. An estimate of expansion age from 1/H₀ assumes an oversimplified expansion history. Gravitationally bound systems such as the Solar System do not simply expand according to the same large-scale distance law; distinguish local dynamics from cosmological expansion.

A method you can reuse

1. Decide whether a quantity belongs to the source or to the detector.
2. Use distance units consistent with luminosity, flux or Hubble constant.
3. Choose the correct blackbody spectral representation.
4. Identify spectral lines before calculating redshift.
5. State the low-redshift or expansion-history assumptions behind any speed or age estimate.

Equations and relationships

Investigate and explain

Find peak wavelength at two blackbody temperatures and compare λmax T, keeping plotting conventions consistent.

Use the spectrum model for temperature and orbital models for bound motion. None directly simulates cosmic expansion, stellar evolution or the microwave background, so connect those topics to observations and explicit models.

Open the interactive investigation

Check your understanding