BUCKNELL UNIVERSITY

Astronomy 102 - Final Exam, Solution

Part I: answer all 16 questions (48 points total+2 points for name & seat#)

1. This course covered the following topics:

2. Light with 800 billionths of a meter distance between a crests of an electromagnetic wave is 3. After 10 billion years of fusing hydrogen into helium the sun may become
 
 
 

4. The constellation of Leo, the lion, (Zodiac sign for August) may rise at sunset on

5. Some stars seem to move uniformly around Polaris because 6. The temperature of the solar surface is roughly
7. Lines of increased brightness in the rainbow spectrum of an O2 star are probably due to
8. In the center of the sun energy from fusion of hydrogen into helium is released in the form of 9. We find the distance to the closest star
 
 
 

10. Neutron stars that rotate around their axis may be observed as

11. The galaxies that we see and our galaxy have a similar chemical composition . This may imply that 12. Edwin Hubble discovered the following 13. A blue photon is emitted from a galaxy 1000 Mpc away. If the Hubble constant is 75 km/s/Mpc we may see this photon now as 14. At t~1 seconds after the big bang the universe was made of mostly
15. The no boundary hypothesis asserts that
16. Using a CCD camera we used one of the following steps in finding the distance to stars Part II: answer all 5 questions (50 points)
  1. (10 points) For a few seconds "Gamma Ray Bursters" (GRBs) shine with luminosity 1017 (!!!) times greater than that of the Sun. If such a GRB were to appear in our sky as bright as the Sun, how far away from us must it be located?

    2.  
This problem is the same as the one in HW#4 prob. #1.
  Same brightness = The power of the sun / 4 p r*2 = The power of the GRB / 4 p r2

Where r* is the distance to the sun (1 A.U.) and r is the distance to the GRB.

Solving for r:

r=r* sqrt { Power of the GRB/ Power of the sun} = r* sqrt{1017} = 3.2 x 108 A.U.
 

2. Two stars that appear four second of arc from each other in the night sky have the following absorption lines: One of the stars has an absorption line at wave length 486.08 nm and the other star has an absorption line at wave length 486.12 nm. Both lines are due to the same atomic transition with rest frequency of 486.10 nm.

  1. (5 points) Assuming that both lines are from the same atomic transition, describe the motion of the stars (no numbers needed).

    2.  

     

    One is moving away from us while the other is moving towards us.
     
     
     

          b. (3 points) Calculate the speed of these stars.
      Using the Doppler formula (see exam beginning):
      {486.10nm – 486.08nm}/486.10nm = V / 3 x 108 m/s

    Solving for V:

    V=12,000 m/s.
  2. (2 points) If both stars are 10 pc from us, how far are they from each other?
Using trigonometry: The apex angle is 4", so half that angle is 2", We may therefore find half the distance between the stars:

X=10 pc x sin(2/3600)= 10-5 pc
 

And the distance between the stars is 2 x 10-5 pc.
 
 

3.  You observe an A2 star:

  1. (4 points) What is the color of this star? (Peak brightness: Red? Yellow? Green? Blue?)

    2. From the book: T=7500-10,000K. Within this range A2 is the third hottest out of 10 categories (A0,A1, etc.). So the temperature is in the range 9500 – 9250K (we may use the middle of that range, 9375K.). Using Wein’s law the color is
     WL=2.9 x 106K nm / 9375K = 310 nm.

    That’s in the ultra violet, which means that the star appears bluish.

    b. (3 points) What is it's surface temperature?
    From a: 9375K.
     

  2. (3 points) Given that the luminosity of the star is 8 x 1027 Watt and its mass is 7 x 1030 kg, what is its average density?

    3.  

     

    Density=Mass/Volume. To find the volume we have to find the radius of the star. That may be found from the area of the star, 4pr2 . We may find that because we know the power from the star, and

the power from each square meter = sigma T4. So the power from the whole surface is:
4pr2 sigma T4 = 8 x 1027 Watt. We find r, and substitute into
D=Mass/(4pr3/3)

We get : 950 Kg/m3 .
 

4. (10 points) Two stars have the same exact brightness. The peak of the black body spectrum of the first star is blue and that of the second star is red. From parallax measurements we know that both are at the same distance from earth. What types of stars might these be?
 

Since the stars have different colors and similar brightness they CAN’T be two main sequence stars. So they may be

A red giant and an O star

Or:

A white dwarf and an M star

Or:

(an interesting suggestion from one of your peers)

a red giant and a variable star.
 
 

5. (10 points) According to a certain theory of the "big-bang" the universe is slowing down its expansion, or at least NOT speeding up its expansion. Some measurements show that the age of globular clusters is 15 billion years. Assuming that the Hubble constant is 75 km/s/Mpc to a very high accuracy, can the theory be rejected? Explain your reasoning in one-two sentences.
 

Yes. The theory can be rejected.

If the Hubble constant is indeed accurately measured to be 75 Km/s/Mpc you would get a universe that is 13 billion years old. If we hypothesize that the universe is slowing down its expansion, this number is an OVERESTIMATE (lab#8), i.e. the universe is LESS than 13 billion years old. So this is INCONSISTANT with the measurement of the age of globular clusters, and the hypothesis can be rejected!  (As of yet the Hubble constant is NOT known to such a great accuracy, but several researchers are getting the errors to be fairly small.)