Questions: Stellar Properties: Luminosity, Temperature, and Size
3 questions to test your understanding
Score: 0 / 3
Question 1 Multiple Choice
Star A and Star B have identical luminosities. Star A is twice as far from Earth as Star B. How does Star A's apparent brightness compare to Star B's?
AHalf as bright
BOne-quarter as bright
CTwice as bright
DThe same brightness
Brightness follows the inverse-square law: apparent brightness ∝ 1/d². Doubling the distance reduces brightness by a factor of 2² = 4. So Star A appears one-quarter as bright as Star B despite having the same intrinsic luminosity. This is why apparent magnitude (how bright a star looks) and absolute magnitude (intrinsic brightness) require distance information to relate to each other.
Question 2 True / False
For stars, a red color indicates a higher surface temperature than a blue color.
TTrue
FFalse
Answer: False
This is the opposite of everyday intuition (red = hot on a stovetop) but correct for stars. Wien's displacement law states that peak emission wavelength is inversely proportional to temperature: hotter stars peak at shorter (bluer) wavelengths, cooler stars at longer (redder) wavelengths. Betelgeuse (red supergiant) has a surface temperature of ~3,500 K; Rigel (blue supergiant) is ~11,000 K.
Question 3 Short Answer
Why can't astronomers directly measure the physical radius of most stars using a telescope, and how is it determined instead?
Think about your answer, then reveal below.
Model answer: Stars are too distant to resolve as disks even with large telescopes — they appear as point sources. Radii are calculated indirectly from the Stefan-Boltzmann law: once luminosity (from apparent magnitude + distance) and surface temperature (from spectral peak or color) are known, radius follows from L = 4πR²σT⁴.
Only a handful of very large, nearby stars (like Betelgeuse) have been directly imaged as disks by interferometric telescopes. For the vast majority, stellar radius is a derived quantity. This illustrates a core theme in observational astronomy: most physical parameters cannot be measured directly and must be inferred from the electromagnetic signal.