Stellar Homework #4

Remember to show all your work and to put your final answer for each question in the form of a complete English sentence!

 

 

1.  Consider a Main Sequence star with a mass of 0.2 solar masses.

a) What is the approximate spectral class of the star? What kind of lines would you expect to find in its spectrum?

b) From the diagrams in the book, estimate the luminosity of the star, relative to the Sun.

HINT: The questions can be answered with help from Table 17-2 and Figure 17.22.

c) From the diagrams in the book, estimate the luminosity of the star, relative to the Sun. If the Sun has an absolute magnitude of 5, what is the absolute magnitude of this star?  If I say the star has an apparent magnitude of +5.3, is the star closer than 10 parsecs away or farther? Why do you say this?

HINT: In class, we worked out how to convert a difference in magnitudes between a star and the Sun into a luminosity ratio. Work the process backwards to answer this question.  To answer the second question, remember the definition of absolute magnitude and the "backward" nature of the magnitude system.

d) Why was I so picky about saying that the star is on the main sequence?

HINT: What does the Main Sequence represent? Why is it useful?

2.    Consider a binary system (two stars orbiting each other). In terms of color and spectral type, the two stars are identical so we can consider them to be equals. The pair is known to be 2 parsecs away.

a) If the two stars are seen to be 1 arcsecond apart, how far are they apart in AU? (HINT: what is the definition of a parsec?)

HINT: What is the technical definition of a parsec (NOT the purely mathematical one!)? It has to do with the apprarent size of 1 Astronomical Unit as seen from one parsec away.

b) If we know that the stars take 2 years to orbit each other, then what is the mass of one of these stars? Consider the distance you computed in part a) to be the semi-major axis of their mutual orbit.

HINT: This is a straightforward application of Newton's Version of Kepler's Third Law. Remember that the equation will only give you the SUM of the masses; you must use clues given in the problem to decide what the mass of ONE star will be!

3.    Estimate the lifetimes of the following stars:

a) A B-type star with a mass 15 times that of the Sun and a luminosity 4500 times that of the Sun.

b) A K-type star with half the Sun's mass and one-eighth the Sun's luminosity.

HINT: Both of these require use of the stellar lifetime formula given in class. Remember that we compare the lifetime of the star to the Sun's lifetime, 10,000,000,000 years. Remember what we said about the effect of mass on stellar lifetimes, to see if your answers make sense!

 
Updated 5/22/02
By James E. Heath
  
 
 
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