Unit 21: Space and Environment — Short Questions

Luminosity (L) is the total amount of electromagnetic energy emitted by a star per unit time. It is an intrinsic property of the star (independent of the observer's distance), measured in watts, and is a measure of the star's true brightness. It depends on the star's radius and surface temperature, as expressed by L = 4πr²σT⁴.

Radiant flux intensity from a star at distance r is F = L/(4πr²). As luminosity L stays constant, F falls off with the square of the distance — doubling the distance reduces the flux to one-quarter, and tripling it reduces the flux to one-ninth. Its significance is that it links a star's true (intrinsic) brightness to its apparent brightness as measured from Earth, which lets astronomers calculate distances (e.g. using standard candles) or compare the true luminosities of stars at different distances.

A standard candle is an astronomical object with a known, predictable intrinsic luminosity, such as a Cepheid variable star or a Type Ia supernova. Astronomers measure the apparent flux F of the standard candle received at Earth and, since its true luminosity L is already known, use the inverse-square law F = L/(4πr²) to solve for the distance r to the galaxy containing it.

Stefan-Boltzmann's law states that the total output power (luminosity) of a star is proportional to the product of its surface area and the fourth power of its absolute surface temperature: L = 4πr²σT⁴. It relates the luminosity L (in watts), the star's radius r, its surface temperature T (in kelvin), and the Stefan-Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.

First, the star's surface temperature T is found from its peak emission wavelength λmax using Wien's law, T = b/λmax (b = 2.9 × 10⁻³ m K). Then, with the star's luminosity L known (e.g. from its measured flux and distance), the Stefan-Boltzmann law L = 4πr²σT⁴ is rearranged to give the radius: r = √(L/4πσT⁴).

Hubble's law states that the recession velocity v of a galaxy is directly proportional to its distance d from Earth, v = H₀d, where H₀ is Hubble's constant. Since all galaxies are receding and farther galaxies recede faster, running time backward implies the universe was once far smaller, denser, and hotter, converging to a single point. This supports the Big Bang theory, which holds that the universe began about 13.8 billion years ago from such an initial hot, dense state and has been expanding ever since.

The five components are the atmosphere (air), the hydrosphere (water), the cryosphere (ice and permafrost), the lithosphere (Earth's upper rocky layer), and the biosphere (living things).

A star's total power (luminosity) is an intrinsic property and does not depend on distance, so it alone does not tell us how bright the star actually looks from Earth. Radiant flux intensity, F = L/(4πr²), accounts for the distance r by applying the inverse-square law, giving the energy actually received per unit area at Earth. This makes flux intensity the quantity that matches real observations, allowing fair comparison of how stars appear even though they lie at very different distances.

Standard candles, such as Cepheid variable stars and Type Ia supernovae, have predictable, well-established intrinsic luminosities. By measuring the flux F received at Earth from a standard candle inside a distant galaxy and substituting its known luminosity L into F = L/(4πr²), astronomers can solve for the distance r. The known luminosity is critical because the inverse-square law has two unknowns (L and r) when only F is measured directly; without independently knowing L, the observed flux alone cannot distinguish a faint nearby object from a luminous distant one, so the calculated distance would be unreliable.

As light from a distant galaxy travels through the universe, the expansion of space stretches the light waves, increasing their wavelength — this is called redshift. The shift to longer wavelengths compared to known laboratory values shows that the galaxy (and the space between it and Earth) is moving away from us; the larger the redshift, the greater the distance and recession speed of the galaxy.

If the universe were not expanding, the spectral lines from distant galaxies would appear at their normal, known laboratory wavelengths, with no systematic redshift correlated with distance. There would be no overall stretching of wavelengths; any shifts observed would only be small, random Doppler shifts from individual galaxies' local motions, not the consistent one-directional redshift (increasing with distance) that is actually observed and that supports an expanding universe.

Earth's climate is driven by the balance between solar energy absorbed and energy radiated back to space (Earth's energy budget); when this balance is steady, Earth's temperature remains constant. However, the Sun heats Earth's surface unevenly: the equator receives direct, intense sunlight causing warm air to rise and form low-pressure zones, while the poles receive weaker, slanted sunlight causing cold air to sink and form high-pressure zones. This equator-to-pole energy imbalance drives global atmospheric circulation, producing wind belts — trade winds near the equator, westerlies in mid-latitudes, and polar easterlies near the poles — which, together with ocean currents, redistribute heat from the equator toward the poles.

Earth's energy budget stays balanced when the incoming solar energy absorbed equals the outgoing infrared energy radiated back to space. Human activities such as burning fossil fuels and deforestation increase the concentration of greenhouse gases in the atmosphere. These gases trap outgoing infrared radiation and prevent it from escaping into space, so less energy leaves than enters. This disrupts the natural balance of the energy budget, causing Earth to retain more heat and warm up — the phenomenon known as global warming.