Spectra and Astronomical Distances

Continuous spectrum — emitted by a hot dense body, such as a star's interior: all wavelengths present, with intensity set by temperature.

Emission line spectrum — produced by a hot, low-density gas. Electrons drop between discrete energy levels, emitting photons of precise energies, so the spectrum is a set of bright lines at specific wavelengths.

Absorption line spectrum — produced when light with a continuous spectrum passes through a cooler gas. Electrons absorb photons of exactly the energies matching their level differences, leaving dark lines at those wavelengths.

Why the lines identify elements — every element has a unique set of energy levels, so it produces a unique pattern of lines. The pattern is a fingerprint that does not change with distance.

Example: this is how the composition of stars is known. A star's light carries an absorption spectrum imprinted by its own cooler outer layers, and matching those dark lines against laboratory spectra identifies the elements present. Helium was discovered in the Sun's spectrum in 1868, before it was ever isolated on Earth — named after Helios for that reason.

Photon energy and level spacing —

hf = ΔE

so a larger gap between energy levels produces a higher-frequency, shorter-wavelength photon.

Astronomical distance units

Astronomical unit (AU) — the mean Earth–Sun distance, about 1.50 × 10¹¹ m. Convenient within the solar system.

Light year (ly) — the distance light travels in one year, about 9.46 × 10¹⁵ m. It is a distance, not a time, despite the name.

Parsec (pc) — the distance at which one AU subtends an angle of one arcsecond, about 3.09 × 10¹⁶ m, or 3.26 light years.

Stellar parallax — a nearby star appears to shift slightly against distant background stars as the Earth moves around its orbit. Measuring that shift gives the distance:

d (parsec) = 1 ÷ p (arcseconds)

where p is the parallax angle. The parsec is defined to make this relationship as simple as it is.

Why parallax has a limited range — the angles are minute even for the nearest stars, and shrink with distance, so beyond a few thousand parsecs the shift is too small to measure and other methods are needed.