Physics Fundamentals Applied to Astronomy
Core concepts
Be solid on mechanics, thermodynamics, radiation, and atomic physics as applied to astrophysics: blackbody radiation and the Planck, Stefan-Boltzmann, and Wien laws; the Doppler effect; atomic energy levels and spectral lines; the ideal gas law; and conservation laws. Understand radiative transfer basics, optical depth, and the difference between emission and absorption.
Traps
Do not mix Wien's displacement law (peak wavelength inversely proportional to temperature) with the Stefan-Boltzmann law (flux proportional to T^4). Remember that Doppler shift depends on line-of-sight velocity only. Watch for unit errors between wavelength and frequency forms of Planck's law.
Worked example
A star's spectrum peaks at 500 nm. Wien: λ_max T ≈ 2.9×10^-3 m·K, so T ≈ 2.9×10^-3 / 5×10^-7 ≈ 5,800 K. Stefan-Boltzmann then gives flux per unit area σT^4 ≈ 6.4×10^7 W/m^2. Rule of thumb: peak wavelength in nanometers times temperature in kelvin is roughly 2.9×10^6.
Rule of thumb
A factor-of-two temperature change shifts the peak wavelength by a factor of two and the flux by a factor of sixteen.