duke intro to astro, summer 2006                      homework 1                                    due: tuesday, july 11

1) For your star,

a) find the temperature (by using the spectral class given in Appendix 5 and decoding graph on page 424; note that each spectral class letter is divided into 10 parts; for example B0 is the hottest class of the B stars, followed by B1, B2, etc.; the next class after B9 is A0).

b) calculate the wavelength (in nm) at which the most flux is emitted.

c) what color (or part of the spectrum) is this max-flux wavelength in?

d) what color will it look to humans?

e) use the blackbody applet on the web page, to find out what % of light is emitted in the ultraviolet, what % in the visible, and what % in the infrared

f) find the luminosity relative to the luminosity of the sun (i.e., a ratio), by using the (for now, unexplained) formula

             L/L_sun  =  2.512^{(4.7 - M)}

    where M is the absolute visual magnitude.  You should be able to check your answer (approximately) by using Fig 19-14a, p. 428.

g) use your results from parts a, f above (and the known temperature of the sun) to find the radius of your star relative to the sun.
     Follow the same procedure that the book did in calculating the radius of Betelguese (or Sirius B) relative to the sun in Box 19-4, page 426.
    You should be able to check your answer ( approximately) by using Fig 19-14b, p. 428.
     You do not have to calculate the radius of your star in km, although you are welcome to.
   
h) calculate the flux measured at earth (assuming no light is absorbed in between) in watts/m².  You will need the distance to your starl
    it's in the Appendix 5 table, and you will also need to convert the distance value to units of meters.

    Once you have calculated you's r starflux, find the ratio of the flux of the sun (at earth; see ox 5-2) to the flux of your star at earth. 
    This number tells you how many times "brighter" the sun is than your star.
   

2)  The Pleiades (Fig 20-18) is a nearby star cluster that is also a reflection nebula.  Tiny particles of dust (not much bigger than the molecules in the earth's atmosphere) exist in the nebula surrounding the stars in the cluster.  

To get some practice drawing, draw a half-page diagram showing the custers stars, the nebula region, some sample dust grains in the nebula, and the earth. 

Draw the paths of some red photons and some blue photons leaving the star, in order to show why the nebula looks as it does.  Your diagram should be somewhat like that in Box 5-4.  Ignore the effects of scattering due to the earth's atmosphere (even though it still is happening).

How do the stars look to us (color-wise) compared to what they would have looked like had there been no dust surrounding these stars?

3) Review question #30 in chapter 7.  (Since we have now actually found a planet out at this distance, we will eventually be able to see if our predictions are correct.)

4) By now you aware that nearly 200 planets have been discovered around sun-like stars in our galaxy in the past 10 years.  The sun-like star
51 Pegasi was the first one found with an orbiting planet.  You can see the distance at which it orbits its parent star in Figure 8-13. 

Suppose that the planet around 51 Peg actually formed at the distance from its star it presently orbits at.  (This is not considered likely.)
What type of planet would it be?  what things would it be made of?  what would have been its size, mass, and density compared to either the terrestrial and jovian planets in our solar system?

You can answer this question qualitatively in a convincingly way, I think, but it would be better to actually calculate its temperature using the formula we came up with in class (and then talk about what things would have been able to condense and accrete).  You would have to assume an albedo (although the temperature you end up with doesn't depend heavily on the value you choose.)

If you have read the book, you'll know that your answer is very different than what is claimed for the composition of the planet.  Why?  What is the book hypothesizing about where/how this planet formed?

5) The table (or graph) on page 384 displays a model of the sun: in other words how temperature, density, pressure, etc. change from the center to the surface.
a) Calculate the wavelength that is most prevalent (i.e., the wavelength of maximum intensity) at the center of the sun.  What part of the spectrum is this wavelength in?

b) Suppose that you took a trip from the center of the sun to the surface.  How would the wavelength of max intensity change as you traveled?