BUCKNELL UNIVERSITY

Astronomy 102

Second Hour Exam

1998 April 15

Here are some quantities and relationships that you might find useful:

• for a circle:
  • circumference = 2 x pi x radius
• for a sphere:
  • surface area = 4 x pi x radius²

• distances:
  • 1 parsec = 3.09 x 10¹⁶ m

• for a wave:
  • speed = wavelength x frequency

• for light waves:
  • energy = h x frequency = h x c/wavelength
  • the speed of light --- c = 3 x 10⁸ m/sec
  • Planck's constant --- h = 6.626 x 10^-34 J s

• mass-energy equivalence:
  • energy = mass x c²

• Doppler formula:

                     speed of emitter      change in frequency
                ---------------------- = ----------------------
  	            speed of wave         rest frequency
  

• flux = luminosity/(4 x pi x distance²)

• dynamical mass:
  • mass = speed² x orbital radius / G
  • G = 6.67 x 10^-11 m³/(s² kg)

• The observer's triangle relation:

  

• alpha/57.3^o = w/R (a in degrees)

Multiple Choice Questions:

1) How many neutrons are in one nucleus of ₈₃Bi²⁰⁹?

• a) 0
• b) 1
• c) 83
• d) 126
• e) 209

2) One of the primary differences between elliptical and spiral galaxies is that

• a) elliptical galaxies do not have black holes at their centers.
• b) spiral galaxies do not have globular clusters.
• c) elliptical galaxies don't have as much dust as spirals.
• d) spiral galaxies are smaller than ellipticals.
• e) elliptical galaxies are older than spirals.

3) The astronomer who determined that the Sun is not at the center of the Milky Way galaxy was

• a) Henry Norris Russell.
• b) Cecilia Payne.
• c) Edwin Hubble.
• d) Henrietta Leavitt.
• e) Harlow Shapley.

4) When we look up into the night sky and see that faint circular band of light we call the Milky Way, we can tell, just as Johann Lambert and Thomas Wright could, that

• a) we live inside a disk-shaped galaxy.
• b) we live inside a spiral galaxy.
• c) we are not located at the center of the galaxy.
• d) we cannot see all of our galaxy.
• e) all of the above.

5) Why can we see the center of our galaxy in infrared light, but not in visible light?

• a) The center of our galaxy doesn't emit visible light.
• b) Because infrared photons have a lower energy than visible photons, stars emit more infrared light than visible light.
• c) Because infrared photons have a longer wavelength than visible light, infrared light can travel through the obscuring dust between here and the galactic center.
• d) Because infrared photons have a higher frequency that optical photons, they travel faster through the interstellar medium.
• e) The black hole at the center of our galaxy absorbs all of the light emitted in the galactic center region.

6)When photons are emitted from a region of strong gravity such as the surface of a neutron star, their wavelengths change as they move outward because of

• a) the doppler effect.
• b) the Hubble law.
• c) neutron degeneracy.
• d) the gravitational redshift.
• e) electron degeneracy.

7)In the H-R Diagram below, draw the path a low mass star takes after it leaves the Main Sequence. Label your path with the various phases the star goes through (e.g., red giant, helium flash, planetary nebula ejection, supernova, white dwarf) as appropriate.

(4 points)

8)In the H-R Diagram below, draw the path a high mass star takes after it leaves the Main Sequence. Label your path with the various phases the star goes through (e.g., red giant, helium flash, planetary nebula ejection, supernova, white dwarf) as appropriate.

(4 points)

9) Plotted as x's on the H-R Diagram below are the surface temperatures and luminosities of all of the stars in a galactic open cluster, along with a line indicating the position of the Main Sequence. Look at the diagram, and with the help of the data in the table below it, estimate the age of the cluster.

(4 points)

Spectral Type	Effective Temperature (K)	Luminosity (solar lum.)	Main Sequence lifetime (years)
O	40000	200000	10 million
B	22000	10000	100 million
A	11000	100	1 billion
F	7500	8	5 billion
G	6000	2	10 billion
K	5000	0.2	30 billion
M	3500	0.1	200 billion

10) Below is a diagram showing a face-on view of the disk of the Milky Way galaxy. The center of the galaxy is indicated by the circle in the center , and four spiral arms extend outward from it. On this diagram,

• a) indicate the position of the Sun with a large "X" (2 points)
• b) indicate the positions where you would likely find O and B stars with "O"s (1 point)
• c) indicate the locations of globular clusters and show how they are distributed around the galaxy by placing at least 20 "+"s on this diagram. (1 point)

Problems:

(Show your work!! I will be very generous with partial credit!!!)

Problem 1) By measuring the period of its variation in flux, you determine that the luminosity of a Cepheid variable star the M99 galaxy is 50,000 L_o (1 L_o = 3.8 x 10²⁶ W) You measure its average flux to be 3.3 x 10^-16 W/m².

Part 1) Calculate the distance to the M99 galaxy.

(10 points)

Solution

Part 2) The M99 galaxy has an angular size of 0.9 degrees. Calculate its linear size.

(10 points)

Solution

Problem 2) During the course of its Main Sequence lifetime, a typical O star converts 1 M_o (= 2.0 x 10³⁰ kg) of hydrogen into helium in the following net reaction:

Part 1) Given that the mass of one helium atom (m_He = 6.63 x 10^-24 kg) is 99.3% of the mass of four hydrogen atoms (m_H =1.67 x 10^-24 kg), calculate how much energy is generated during the O star's Main Sequence lifetime.

(10 points)

Solution

Part 2) If the O star spends 10 million years (= 3.16 x 10¹⁴ seconds) on the Main Sequence, calculate its average luminosity during this time.

(10 points)

Solution

Problem 3) Radio wavelength observations of one of the clouds swirling around a black hole in the center of galaxy Lepus X-2 show that radiation from the hydrogen spin-flip transition (rest frequency = 1420.406 MHz) is detected at a frequency of 1421.229 MHz.

Part 1) Calculate the speed of this cloud and whether it's moving toward or away from us.

(10 points)

Solution

Part 2) If this gas cloud is located 0.1 pc from the black hole and it is orbiting it in a circle, calculate the mass of the black hole.

(10 points)

Solution