Light, Thermal Radiation, & the Doppler Shift
Dec. 2015
Light and Thermal Radiation
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All bodies shine with electromagnetic radiation (light) because of their temperature
c: Speed of light = wavelength x frequency,c=3 x 105 km s-1 = 3 x 108 m sec-1
Gamma rays – X-rays – ultraviolet – visible – infrared – microwave – radio
Short wavelength, high energy, high frequency (gamma rays, x rays, ultraviolet)
Long wavelength, low energy, low frequency (infrared, microwave, radio)
Hot bodies radiate mostly in short wavelength light; cool bodies radiate at long
wavelengths
The Planck function/black body function describes how much radiation a body emits
as a function of temperature
Wien's law for black body radiation relates the peak wavelength in cm with the
temperature in Kelvin:
max T = 0.29 cm K
Stefan-Boltzman Equation gives the total luminosity of a star as a function of temperature
and radius:
L  4R 2T 4
 is the Stefan Boltzman constant:  = 5.67 x 10-5 erg s-1 cm-2 K-4
The Doppler Shift
If a source of radiation (light!) is moving toward or away from the observer, the
wavelength of the light emitted is shifted to shorter or longer wavelength. The shift is to
shorter wavelength of the source and observer are moving closer together (“blue shift”),
and the shift is to longer wavelength if the source and observer are moving further apart
(“red shift”). The amount of the shift depends on velocity:
Δλ/λ=v/c
(Positive for motion away from the observer, i.e. positive is increasing separation)
Δ λ = observed wavelength – rest frame wavelength
Redshift: The “redshift” of a source (z) is defined as Δλ/λ=v/c
1 + z = λobsv/λemit
Problems to Work:
1. The full amplitude of the radial velocity variations for the star 51 Peg is about 100
meters per second. What is the displacement of its spectral lines in Angstroms from
one side of its orbit to the other at a wavelength of 6000 Angstroms?
2. The temperature of 51 Peg is about 5570 degrees at its photosphere. At what
wavelength does 51 Peg emit the most energy?
3. The temperature of Kepler 186 is about 3790 K. At what wavelength does Kepler186 emit the most energy?
4. WASP-18 has a temperature of 6370 K and a radius of 1.2 solar radii. How does the
total luminosity of WASP-18 compare in brightness to the Sun? What is the
difference in absolute magnitude between this star and the Sun? (The Sun has a
surface temperature of 5,780 K.)
5. The two stars in the 55 Cnc system have temperatures of 5370 and 3200 K, and radii
of 1.15 and 0.3 solar radii. What is the ratio of their luminosities?
6. A star has a temperature of 6000K and a diameter of 1.2 solar radii. Its planet has a
temperature of 600 K and a diameter of 0.1 solar radii.
a. What is the ratio of their total luminosities?
b. If the planet transits in front of the star, how much does the brightness of the
star drop?