Astronomy and cosmology

The luminosity (L) of a star is the total radiant power it emits into space. Think of it as the star's intrinsic brightness, measured in Watts (W). It's a fundamental property of the star itself. However, what we observe from Earth is not its luminosity, but its radiant flux intensity (F). Radiant flux intensity is the radiant power received per unit area at a certain distance from the star, measured in Watts per square metre (W m^-2). As light spreads out from a star, its intensity decreases with distance. This relationship follows an inverse square law: the radiant flux intensity is inversely proportional to the square of the distance(d) from the star. This means that if you double the distance, the intensity becomes one-quarter. The formula connecting these quantities is F = L / (4πd^2), where 4πd^2 represents the surface area of a sphere at distance d from the star. Objects with a known luminosity are incredibly useful in astronomy and are called standard candles. By measuring their radiant flux intensity and knowing their luminosity, astronomers can calculate their distance from Earth using the inverse square law, allowing us to map out the vastness of the universe.

The properties of stars, such as their surface temperature and radius, are closely linked to their emitted radiation. Two key laws help us understand these relationships: Wien's Displacement Law and the Stefan-Boltzmann Law. Wien's Displacement Law describes the relationship between a star's surface temperature (T) and the peak wavelength (λ_max) of its emitted radiation. Hotter stars emit more radiation at shorter wavelengths, appearing bluer, while cooler stars emit more at longer wavelengths, appearing redder. The law states that λ_max T = constant (approximately 2.898 x 10^-3 m K). This means if you know the peak wavelength of a star's spectrum, you can estimate its surface temperature. The Stefan-Boltzmann Law relates a star's total luminosity (L) to its surface temperature (T) and radius (r). It states that L = 4πσr^2T^4, where σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W m^-2 K^-4). This law tells us that a larger or hotter star will be more luminous. By combining these two laws, astronomers can estimate the radius of a star if its luminosity and surface temperature are known.

Observations of distant galaxies reveal a phenomenon called redshift. This means that the spectral lines (specific wavelengths of light emitted or absorbed by elements) from these galaxies are shifted towards the red end of the electromagnetic spectrum, indicating an increase in their observed wavelength (Δλ). This redshift is analogous to the Doppler effect for sound waves: just as a receding ambulance siren sounds lower in pitch, light from a receding source has its wavelength stretched. The Doppler redshift equation quantifies this: Δλ/λ ≈ Δf/f ≈ v/c, where λ is the original wavelength, Δλ is the change in wavelength, f is the original frequency, Δf is the change in frequency, v is the recession speed of the source, and c is the speed of light in a vacuum. The observation that almost all distant galaxies show redshift implies that they are moving away from us. Furthermore, the amount of redshift is proportional to the distance of the galaxy. This leads to Hubble's Law, which states that the recession speed(v) of a galaxy is directly proportional to its distance(d) from us: v = H_0d, where H_0 is the Hubble constant. This law is fundamental evidence for the Big Bang theory, which posits that the universe originated from an extremely hot, dense state and has been expanding ever since. The redshift of galaxies is not them moving through space, but rather the expansion of space itself, stretching the wavelengths of light as it travels.