Download Radiation from Proxima Centauri

Radiation from Proxima Centauri.
The closest star to the Solar System is known as Proxima Centauri. Its distance has been accurately
measured as 4.243 light years [4.01  1016 m].
The strength of the radiation at different wavelengths has been studied by satellites orbiting the Earth and
the spectrum has the following appearance:
Intensity of radiation
wavelength
1.
Careful analysis of the spectrum shows that the surface temperature of Proxima Centauri is
3042 K. Use this information to show that the peak wavelength is approximately 106 m and
label the peak wavelength of the spectrum with a more accurate figure.
2.
Sketch a graph on the same axes to show how the spectrum of a star with a slightly higher
temperature would appear.
3.
Using your figure for the peak wavelength, show that the energy of a typical photon from the
star is 2.09  1019 J.
4.
The total power received from Proxima Centauri per second per m2 by a satellite detector is
3.27  1011 W m2. Calculate the number of photons received per second.
5.
Using the given distance of Proxima Centauri, show that it gives out a total of 6.61  1023 W
of power.
6.
(a) Use your answer to Q5 to calculate a value for the radius of the star.
(b) Because this star is so close, it has been possible to determine its radius directly as
1.01  108 m. Comment on the significance of this type of measurement.
7.
Alpha Centauri, bright star, close to Proxima Centauri, has a radius 8.46 times as big and its
Kelvin temperature is 1.903 times as big as that of Proxima Centauri. What would you expect
its power output to be?
Some stellar data
L = luminosity of Sun = 3.9  1026 W
R = radius of Sun = 6.96  108 m
M = mass of Sun = 1.99  1030 kg
1 l-y = 1 light year = 9.46  1015 m.
Proxima Centauri
M = 0.123 ± 0.006 M
R = 0.145 ± 0.011 R
L = 0.0017 L
T = 3042 ± 117 K
d = 4.243 ± 0.002 l-y
Alpha Centauri
M = 1.100 M
R = 1.227 R
L = 1.519 L
T = 5790 K
d = 4.365 ± 0.007 l-y
Polaris -  Ursae Minoris
M = 6.0 ± 0.5 M
R = 30 R
L = 2200 L
T = 7200 K
d = 430 ± 30 l-y
Regulus -  Leonis
M = 3.15 M
R = 3.5 R
L = 150 L
T = 10300 - 15400 K [rapid rotation – brighter at poles!]
d = 77 ± 1 l-y
Spica -  Virginis
M = 11 M
R = 7.8 R
L = 13400 L
T = 22400 K
d = 260 ± 20 l-y