29:50 Modern Astronomy
Second Hour Exam ...First Problem Exam
October 18, 2002
Form A

Nota Bene: Be sure to check the set of equations and figures at the back of the exam. You will need them. There are 12 questions

Walk with Ursus!

1. The star Altair, easily visible in the evening sky, is at a distance of 5.1 parsecs. You transmit a radio signal there. Space aliens receive the signal and immediately transmit a reply. How long is the interval between your transmission and reception of the response?
   (a) 5.2 weeks
   (b) 33 years
   (c) 978 years
   (d) 3320 years
   (e) 15250 years
2. You like driving your car. You would drive it anywhere. Recently you have started hanging around with space aliens. The aliens fix up your car so you can drive out into outer space. The only problem is that you cannot drive any faster than you can on Interstate 80. You decide to drive to the Sun. How long does it take you to get there? You cannot ask your space alien buddies to come along and pick you up in their spaceship.
   (a) 8 minutes
   (b) 7543 years
   (c) 2100 years
   (d) 7.23 months
   (e) 150 years
3. Two bright stars presently in the evening sky are Capella and Formalhaut. Which is brighter? What is the amount by which the brighter one exceeds the dimmer one? For this last question I want the ratio of readings of a power meter, not the magnitude difference.
   (a) Formalhaut is brighter by a factor of 2.5
   (b) Formalhaut is brighter by a factor of 1.10
   (c) Capella is brighter by a factor of 2.5
   (d) Capella is brighter by a factor of 1.10
   (e) Capella is brighter by a factor of 16.43
4. A star has an absolute magnitude of 5.0. It is at a distance of 1000 parsecs. What is its apparent magnitude?
   (a) -5.0
   (b) 5.0
   (c) 4.85
   (d) 10.0
   (e) 15.0
5. Look at the attached Figure 1. What is the surface temperature of Star B? 1 micron meters.
   (a) 3000 K
   (b) 26380 K
   (c) 77 K
   (d) 15000 K
   (e) 7000 K
6. Look at Figure 1 again. Which of the following statements about stars A,B, and C is true?
   (a) A is hotter than B which is hotter than C.
   (b) C is hotter than B which is hotter than A
   (c) A is more luminous than B, but B is more luminous than C.
   (d) B is more luminous than A, which is more luminous than C.
   (e) Star A must be mainly hydrogen, B is composed of helium, and C is mainly oxygen.
7. Observations of a binary star system show a small star orbiting a brighter, more massive star. The radius of the smaller star's orbit is kilometers, and the speed at which it moves in its orbit is 21 km/sec. What is the mass of the more massive star?
   (a) kilograms
   (b) kilograms
   (c) kilograms
   (d) kilograms
   (e) kilograms
8. Figure out the Main Sequence lifetime of a star with a mass of 5 solar masses.
   (a) 10 billion years
   (b) 178 million years
   (c) 120 billion years
   (d) 4.5 million years
   (e) 850 million years
9. The distance of Jupiter from the Sun is 5.2 astronomical units. At what speed does it move in its orbit around the Sun?
   (a) 5.2 meters/sec
   (b) 30 kilometers/sec
   (c) 13 kilometers/sec
   (d) 49.3 meters/sec
   (e) 250 kilometers/sec
   
10. A new process called the ``X Process'' can convert matter to energy with 20 % efficiency. That is, when matter goes through the X process, 20 percent of the mass is converted to energy. You wake up Saturday morning and really need a boost. You take your serving of Count Chocula (30 grams) and run it through the X process, and channel the energy directly into your body. How much energy do you get? Note that one kilogram = 1000 grams.
    (a) Joules
    (b) Joules
    (c) Joules
    (d) Joules
    (e) Joules
11. Some of you have seen the Andromeda galaxy during our observing field trips. It is 700,000 parsecs away. Some of the brightest stars in our galaxy have absolute magnitudes of -5. What would be the apparent magnitude of those stars in Andromeda? Hint: For the purposes of this problem, you can make life easy for yourself and round off the distance to 1,000,000 ( ) parsecs and calculate the apparent magnitude. This approximate answer will be very close to the correct one given below, and much closer than any of the other possibilities.
    (a) -1.0
    (b) 4.85
    (c) 15
    (d) 19
    (e) 26
12. You have been abducted by space aliens! They take you to their base at Area 51 in Nevada to await transfer to the mother ship. While there, they force abductees to attend general education lectures on the astronomy of their home system, their literature and social interactions, alien culture and dance, etc. In these lectures, you learn that the home stellar system of the space aliens is Ursa Majoris, a spectral class A0V Main Sequence star. In the paleontology lectures you learn that complex life arose on their planet (the sixth from UMa) 500 million years ago, which was 1 billion ( ) years after the star and its planets formed.

    You start recalling what you learned in Modern Astronomy. You remember that a A0V star has a mass of about 2 solar masses. You suddenly realize something tremendously urgent that you have to tell the aliens before you get on the mother ship. What is it?
    (a) At this time after the star has formed it changes from the proton-proton cycle to the Triple Alpha process for its energy. As a result, the luminosity decreases by about a factor of 100, which will freeze the planet.
    (b) The main sequence lifetime of this star is equal to the time since it formed. It is about to change dramatically in brightness.
    (c) Spectral class A0V stars emit all of their radiation at ultraviolet wavelengths. It would be lethal for an earthling like you.
    (d) A star with a mass of 2 solar masses will not have enough material left to form Earth-like planets. You will not be able to live there.
    (e) This star must be so far away it is out of the Milky Way galaxy.

Table of Formulae and Data

Gravitational Force: ,
Circular Orbit equation: OR
Wien's Law: meters
Schwarzschild Radius:
Stefan-Boltzmann Law: watts/m ,
Speed of light: m/sec.
Gravitational constant:
surface area of sphere:
circumference of a circle:
Distance Modulus - Distance relation:
Mass-Luminosity relation:
mass of sun: kg
radius of sun: m
Absolute Magnitude of the Sun: +4.85
Luminosity of Sun: Watts
Energy-Mass equivalence:
1 nanometer = meters
1 parsec = meters
1 kilometer = meters.
1 mile = 1.61 kilometers.
1 astronomical unit = meters
1 year = seconds
1 day = seconds
Relationship between magnitude difference and brightness ratio

brightness ratio
1 magnitude difference = factor of 2.5 in brightness
2 magnitude difference = factor of 6.3 in brightness
3 magnitude difference = factor of 16 in brightness
4 magnitude difference = factor of 40 in brightness
5 magnitude difference = factor of 100 in brightness
7 magnitude difference = factor of 630 in brightness
10 magnitude difference = factor of 10000 in brightness
15 magnitude difference = factor of 1,000,000 ( ) in brightness
20 magnitude difference = factor of in brightness
25 magnitude difference = factor of in brightness

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