ASP Astrophysics Fundamentals 1 — Questions and Answers
Question 1: What is Wien's displacement law?
- It describes how stars move through the galaxy
- It states that the peak wavelength of blackbody radiation is inversely proportional to temperature (Correct answer)
- It defines the relationship between stellar mass and luminosity
- It describes how gas clouds collapse under gravity
Correct answer: It states that the peak wavelength of blackbody radiation is inversely proportional to temperature
Wien's displacement law states that the peak wavelength (λmax) of blackbody radiation is inversely proportional to the absolute temperature: λmax × T = 2.898 × 10⁻³ m·K, explaining why hotter objects appear bluer.
Question 2: What is the Stefan-Boltzmann law?
- A law relating orbital period to orbital distance
- A law stating that a blackbody radiates power proportional to the fourth power of its temperature (Correct answer)
- A law describing the relationship between magnetic field strength and stellar rotation
- A law governing the rate of nuclear fusion in stellar cores
Correct answer: A law stating that a blackbody radiates power proportional to the fourth power of its temperature
The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a blackbody is proportional to the fourth power of its temperature (E = σT⁴), explaining why small temperature increases cause huge luminosity increases.
Question 3: What is Kepler's third law of planetary motion?
- Planets move in elliptical orbits with the Sun at one focus
- A planet moves faster when closer to the Sun
- The square of a planet's orbital period is proportional to the cube of its semi-major axis (Correct answer)
- Each planet orbits the Sun at a constant average speed
Correct answer: The square of a planet's orbital period is proportional to the cube of its semi-major axis
Kepler's third law states that P² ∝ a³, where P is the orbital period and a is the semi-major axis, meaning planets farther from the Sun take disproportionately longer to complete an orbit.
Question 4: What is the Doppler effect and how is it used in astronomy?
- The bending of light by gravity; used to measure black hole masses
- The change in observed frequency of waves from a moving source; used to measure radial velocities of celestial objects (Correct answer)
- The focusing of light by a gravitational lens; used to find exoplanets
- The reddening of light by dust; used to map interstellar medium
Correct answer: The change in observed frequency of waves from a moving source; used to measure radial velocities of celestial objects
The Doppler effect is the change in observed frequency or wavelength of waves emitted by a moving source; in astronomy, spectral line shifts reveal radial velocities of stars, galaxies, and gas clouds.
Question 5: What is the inverse square law of light?
- Light speed decreases with the square of distance traveled
- The apparent brightness of a source decreases with the square of the distance from the observer (Correct answer)
- A star's luminosity is inversely proportional to its mass squared
- The wavelength of light is inversely proportional to photon energy squared
Correct answer: The apparent brightness of a source decreases with the square of the distance from the observer
The inverse square law states that the apparent brightness (flux) of a light source decreases proportional to the square of the distance (F = L/4πd²), because light spreads over an ever-growing spherical surface.
Question 6: What is the virial theorem in astrophysics?
- A theorem relating the kinetic energy of a gas to its expansion rate
- A theorem stating that the average kinetic energy of a gravitationally bound system equals half the magnitude of its average gravitational potential energy (Correct answer)
- A theorem describing the orbital resonances of moons
- A theorem governing the rotation curves of spiral galaxies
Correct answer: A theorem stating that the average kinetic energy of a gravitationally bound system equals half the magnitude of its average gravitational potential energy
The virial theorem states that for a gravitationally bound system in equilibrium, the total kinetic energy equals −½ the total gravitational potential energy, used to estimate masses of clusters from velocity dispersions.
ASP Astrophysics Fundamentals 1
What is Wien's displacement law?