Rules: This examination is to be taken without help of books or papers or notes. It is to
be worked on individually; the Vanderbilt Honor Code applies. You may use calculators. Please write clearly.

The first 10 questions ask for very short answers, without explanations. Be very brief and to the point. Longer answers are expected for questions 11-17.  Each question has an assigned point value (in brackets), with the points totaling 100 for the exam.  While I don't expect you to write a book in a time-limited exam setting, I expect logically complete, though concise, answers.  Correct but incomplete answers, or incorrect answers with correct logical support will receive varying degrees of partial credit.

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v_esc= (2GM/R)^0.5
v_ave= (3kT/m)^0.5
M_*V_* = M_pV_p
G = 6.67 x 10^-11 N m² / kg²
k = 1.38 x 10^-16 gm cm² / sec² deg

1. [3 pts] What is a black hole?
   
   

An object from which the escape velocity is greater than the speed of light.
 
2. [3 pts] Where did comets form?
   
   

5-30 AU.  (not "at 5 AU" nor beyond 50 AU)
 
3. [3 pts] In one sentence or phrase of less than 20 words, describe generally all the planets discovered around other Sunlike stars.
   
   

Giant, or Jupiter-like, planets orbiting at very small distances (most well inside of 1 AU).
 
4. [3 pts] The escape velocity from Pluto is about 1 km/sec.  If Pluto were made of rock instead of ice, such that it's average density was four times greater than its current density, what would be the escape velocity for Pluto?
   
   

2 km/sec.  (V_esc is proportional to the square root of the mass; the mass is directly proportional to the density)
 
5. [3 pts] What is the "snow line"?
   
   

The distance from the Sun outside of which water freezes to ice, inside of which water remains a vapor.
 
6. [3 pts] List three general properties of the solar system that must be explained by any successful theory of solar system formation.
   
   

1. all planets orbit in same plane
2. all planets and moons revolve in same direction
3. almost all planets and moons rotate in same direction
4. most of mass is H and He
5. giant planets close to Sun, small planets close to Sun
(lots of other answers are reasonable, also)
 
7. [3 pts] The escape velocity (v_esc) from Mars is 5.0 km/sec.  If the average velocity (v_ave) of oxygen atoms high in the Martian atmosphere is only 1.5 m/sec, what will happen to this population of oxygen atoms over the next few hundred million years?
   
   

all will escape (since v_esc is less than 6 times greater than v_ave)
 
8. [3 pts] Which body is the most volcanically active object in the solar system?
   
   

Io
 
9. [3 pts] Which solar system body almost certainly has a warm, liquid ocean deep beneath its icy crust?
   
   

Europa
 
10. [3 pts] What are the two most important constituents of the atmospheres of the four giant planets? What third component is also a significant component of the atmospheres of Uranus and Neptune?
    
    

H and He. Methane (CH₄)
 
11. [10 pts]  How are the concepts of "radial velocity" and "the Doppler Shift" related?
    
    

Radial velocity is the motion of an object toward or away from us.  The Doppler shift is a measure in the change in wavelength or frequency of a wave (sound, light) because the object is moving toward (blue shifted) or away (red shifted) from us as it makes its sound.
 
12. [10 pts] How did the giant planets grow to be so big?
    
    

They had to accrete large (10 Earth mass-sized) solid cores of rock and iron quickly; this was possible because they formed beyond the snowline, where solids were available in abundance; then, they were able to gather a great deal of H and He gas from the gaseous nebula before the gases dispersed.
 
13. [10 pts] Explain how our "origin of planets"  theory succeeds or fails to explain the planets thus far discovered around other stars.
    
    

Our theory predicts the formation of giant planets outside the snow line.  All the planets discovered thus far are inside the snow line.  This would seem to be a contradiction. But planets forming outside the snow line will spiral inwards because of their interaction with the gaseous disk, so a newly modified version of our old theory does work.
 
14. [10 pts] Would you expect to find more impact craters on Io or Callisto? Why?
    
    

More on Callisto.  Io is so volcanically active, it erases or covers over all impact craters in a very short period of time. Also, the surface is likely to soft to hold the imprint of a crater for long.  Callisto, on the other hand is frozen solid with no heat sources.  Like the Moon, it should preserve a record of its cratering history for the full history of the solar system.
 
15. [10 pts] Describe, qualitatively, the method by which astronomers are now able to detect planets around other stars. Be sure to discuss what factor, or factors, fundamentally limit our ability to make these discoveries.
    
    

Radial velocity searches.  We measure the Doppler shift of light from stars due to their reflex motion as they respond to the gravitational tugs of a nearby planet.  Since the planets are much smaller than the stars, the stars don't move much, or very fast.  So we need instruments that can make very precise measurements of speeds of only a few m/sec.
 
16. [10 pts] Assume a planet orbits a nearby star that is identical to the Sun and that the planet orbits at 1 AU from that star.  Assume we have not yet discovered this planet.  What is the smallest such planet (in terms of mass) that you could hope to detect with the best telescopes and detectors available today?
    
    

Using the equation M_*V_* = M_pV_p, we are interested in knowing what planet can be found if the stellar velocity is about 10 m/sec (today's practical limit) and knowing that the planet orbits at a speed of 30 km/sec = 30,000 m/sec.
Thus, we find  M_p/M_* = V_* /V_p= 10/30,000 = 1/3000.  So the smallest planet we could possibly detect would be 3000 times smaller than the Sun, or 3 times smaller than Jupiter (i.e., the size of Saturn).
 
17. [10 pts] What is the Copernican Principle? Is it being tested by our discoveries of extrasolar planets or is it irrelevant to issues related to the existence of planets around other stars?


The Copernican Principle is the idea that we do not live in a special place in the Universe.  By implication, neither the Sun nor the Earth are special.  Thus, other planets should commonly have Earthlike planets.  So, clearly the search for extrasolar planets is a test of the Copernican principle. Thus far, we are not finding Earths around other stars, although our detection methods are not sensitive to them yet. On the other hand, the planets thus far discovered likely preclude the existence of Earthlike planets in those systems.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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