Practise calculating luminosity and radiant flux, applying the inverse-square relationship and using standard-candle observations to determine astronomical distance.
State what is meant by the luminosity of a star.
total power
power radiated (by the star)
Explain how a standard candle in a distant galaxy can be used to determine the distance of the galaxy from an observer.
standard candle has known luminosity
radiant flux intensity measured by observer
(distance calculated using) F=L/4πd2
The Sun has a radius of 6.96×108 m and a surface temperature of 5780 K . Light from the Sun is observed to have a peak intensity at a wavelength of 501 nm .
Calculate the luminosity of the Sun. Give a unit with your answer.
unit
luminosity =4πσr2T4=4π×5.67×10−8×(6.96×108)2×57804=3.85×1026 W
A star of luminosity 3.8×1031 W is a distance of 1.8×1024 m from the Earth.
Calculate the radiant flux intensity at the Earth of the radiation emitted by the star.
radiant flux intensity = Wm−2
F=L/(4πd2)=(3.8×1031)/[4π×(1.8×1024)2]=9.3×10−19 W m−2
A cosmology student observes the electromagnetic radiation received from a star in a galaxy. The student uses Wien's law to estimate the surface temperature of the star, a standard candle to estimate the distance to the galaxy, and the Stefan-Boltzmann law to estimate the radius of the star.
The student observes that the radiation from the star is redshifted.
State what is meant by a standard candle.
(astronomical) object of known luminosity
State what is meant by the luminosity of a star.
total power
power radiated (by the star)
Explain how a standard candle in a distant galaxy can be used to determine the distance of the galaxy from an observer.
standard candle has known luminosity
radiant flux intensity measured by observer
(distance calculated using) F=L/4πd2