MCC PHS 142 M01  Astronomy Homework Ch.12-13      
Adj Prof Astronomy: Sam Wormley <sam.wormley@gmail.com>
Web: edu-observatory.org


Background Material

  Textbook - Read Chapters 12-13
  Textbook - http://highered.mcgraw-hill.com/sites/0073512184/student_view0/chapter12/
  Textbook - http://highered.mcgraw-hill.com/sites/0073512184/student_view0/chapter13/
      (take the Multiple Choice Quiz for for each chapter)

  Web - http://janus.astro.umd.edu/SolarSystems/ 
  Web - http://edu-observatory.org/swormley/eo/planets.html 
  Web - http://edu-observatory.org/swormley/eo/solar_system.html 
  Web - http://edu-observatory.org/swormley/eo/science.html 
  Web - http://antwrp.gsfc.nasa.gov/apod/archivepix.html 



      Jupiter, its closest Galilean satellite, Io, and Io's shadow
      on the "surface" of Jupiter.

The Laws of Nature: A Skeptic's Guide by Zoran Pazamet

   Awareness of the fundamental laws of nature is essential to any
   skeptical endeavor. These principles are presented so they can be
   understood, and explained to others, without assuming specialized
   prior knowledge.

   Anyone who has studied physics (the science of the laws of nature)
   knows how daunting the task is of learning the philosophical and
   mathematical formalisms needed to fully comprehend, express, and
   apply natural laws. Complicating this situation is the fact that
   some of these laws are still "under construction"-being debated by
   the scientific community. Moreover, today we have two fundamental
   approaches to studying the natural world (quantum theory and
   Einsteinian physics), built from completely different basic
   assumptions (Sachs 1988). Fortunately, in the macroscopic ("real")
   world, the subject of this article, physics has revealed to us
   definite rules by which nature always operates-rules for
   establishing what is physically possible and for eliminating the
   impossible. We have confidence in these laws because with all the
   observations and experiments that have been (and continue to be)
   performed, no exception to them has yet come to light; that is, they
   constitute the best explanation of the natural world available to us
   today. At this point, one could ask: Why do these laws exist in the
   first place? The answer to this question is beyond the reach of
   science; all we know is that we can identify natural laws, observe
   them in action, and use them to explain and predict natural
   phenomena. This is what Einstein meant with his famous statement,
   "To me, the most incomprehensible thing about the universe is that
   it is comprehensible" (my emphasis).

   Arguably the most fundamental of these laws is one due to Einstein
   himself, though it isn't a law about the behavior of nature but,
   rather, a law about natural laws themselves.

   Principle of Universality

   The Principle of Universality says that all laws of nature must work
   the same way everywhere. That is, the laws are objective; it doesn't
   matter who does the experiment or where, the same results should be
   produced under the same conditions. This is why knowledge of, say,
   biology, chemistry, and the forces of nature in our part of the
   universe allows us to outline the potentialities and limitations of
   life and space travel in other regions. Since the speed of light (c
   in the equation E=mc2) is the speed limit for travel and signal
   propagation here, it is also the (extensively verified) limit
   everywhere else; no matter how advanced spacefaring technology may
   be on other worlds, their inhabitants are still condemned to travel
   the vast reaches of interstellar space, for many thousands or
   millions of years, at speeds below c. (And as for "wormholes," those
   hypothetical shortcuts through space, they are pure theoretical
   abstractions possessing serious conceptual difficulties-including
   violation of several of the laws outlined below-as well as
   insurmountable practical ones.)

   Principle of Causality

   Causality states that causes must exist for all effects, and must
   come before the effects they produce. Parents must be born before
   their children; they cannot be born after them. In Einstein's
   physics causality holds in all domains of the natural world, but
   quantum theory allows for violation of microcausality at the
   (microscopic) quantum level. In our macroscopic world, however,
   causality holds absolutely. This is one important reason why time
   travel is impossible; to go backwards in time means reversing every
   cause-and-effect event in the entire universe between then and now.
   Apart from the obvious practical difficulties, this would entail
   violations of other fundamental natural laws-such as conservation
   (see below)-if the traveler's own birth (or other specific event)
   was not to be reversed! (True, solutions of certain equations for
   travel at speeds exceeding c do allow a reversal of the direction of
   time, but this is physically meaningless because the particles which
   could exist in such a world-named tachyons-would not be real; they
   have imaginary masses!) 

   It is also important to remember that the connection between a cause
   and its effect must be a legitimate consequence of natural laws.
   Pseudoscience frequently misapplies irrelevancies (such as simple
   coincidence) to imply such a connection, then brings in untestable
   (therefore scientifically meaningless) supernatural agents to
   connect cause and effect.

   I should also mention that a system that is too complex for us to
   model with cause-and-effect relations (for example, a roomful of air
   molecules) is usually studied using statistics and probability. This
   approach has been called the "mathematical theory of ignorance"
   (Kline 1964) because we use it where we can't follow (are ignorant
   of) the physical behavior of every specimen in the system. The
   statistical treatment bypasses the details of how the natural laws
   affect each individual particle, and instead gives us information
   about the state of the whole system; it's therefore descriptive
   rather than explanatory. However we investigate it, though, the
   behavior of every component of our system is still governed by the
   same natural laws as the rest of the universe.

   Law of Extrema

   Simply put, the Law of Extrema states that all natural processes act
   to extremize (maximize or minimize) a physical quantity. (In
   mathematics, an extremum-plural, extrema-is the maximum or minimum
   of a function.) An especially important instance of this (related to
   the Law of Entropy, below) is the principle that all systems, by
   themselves, tend toward a state of minimum energy. This explains
   many phenomena in nature including the deaths of all organisms as
   well as of stars, water running downhill by itself but not uphill,
   the temperature of a hot object decreasing to that of its
   surroundings, and all possible chemical reactions-from the formation
   of atoms into molecules and molecules into matter, to combustion of
   fuels, to metal rusting, to metabolism in living beings. This is why
   the dead do not spontaneously come back to life, and why one cannot
   make an engine that uses water (the "ashes" from combustion of
   hydrogen and oxygen) as fuel. A further example comes from
   Einstein's theory of general relativity, where all bodies influenced
   by gravity move along paths of maximum or minimum length, called
   geodesics. And all of geometrical optics (the study of light moving
   through macroscopic media) derives from Fermat's principle: Light
   follows the path for which time is a minimum. 

   Conservation of Matter and Energy

   In general, conservation means that in an isolated system a given
   physical quantity does not change with time. (If you do have outside
   interference, it can be included by extending the definition of the
   "system" and conservation will still hold.) An especially important
   and useful conservation law is that matter and/or energy are neither
   created nor destroyed over time; they merely change form, and their
   sum total always remains the same. For example, the chemical energy
   of a quantity of gasoline is changed into the same amount of kinetic
   energy in a moving car. Braking to a stop converts this kinetic
   energy into the same amount of heat energy in the brakes, and this
   increases the heat of the ambient air by, again, the same amount.
   You can of course add in external effects of air resistance,
   friction with the road, and so on; the grand total will still equal
   the initial energy released by the gasoline. And the total mass of
   air and gasoline ingested by the engine equals the total mass of the
   exhaust products. Consider now the erroneous belief that electric
   automobiles run on "free" energy. The vehicle's kinetic energy comes
   from electrical energy made elsewhere, predominantly from conversion
   of chemical energy in fossil fuels or thermal energy from a nuclear
   reactor. And these processes produce waste, so cars (and other
   devices) running on electrical energy usually aren't truly
   "pollution free," either!

   Many people claim that ghosts from time to time leave their
   nonphysical realm to appear here in ours. If they can interact with
   our material environment (by becoming visible to human eyes or
   cameras, causing objects to move, and so on), they must be at least
   partially composed of matter themselves (since it's observational
   fact that only matter produces the radiation, gravity, and
   mechanical forces that affect other matter). Therefore, by
   disappearing from their domain and appearing in ours, they violate
   conservation of matter (and energy) in both worlds! And in ours,
   this simply cannot occur.

   Law of Entropy

   The concept of entropy is still being actively debated by
   philosophers of science and is difficult to convey, so what follows
   is my own working definition. I find it useful to define an increase
   or decrease in entropy as a loss or gain in any one, two, or all
   three of these properties of a system: order, information, and
   available energy. The Law of Entropy then states that, in any
   real-world situation, entropy irreversibly increases for an isolated
   system.

   Consider an ordinary piece of photocopy paper. There is a certain
   amount of order to it (its geometric shape, uniform thickness, and
   so on). It also contains information, since all of its particles
   reside within its clearly defined form and have definite locations
   within it. It also has some available energy, since we can burn it
   to produce heat and light. Suppose we now do ignite this piece of
   paper and let it burn completely. Order has been lost because there
   is no longer a nice rectangular shape to the material, and the
   particles have dispersed. Information is lost because we no longer
   know where a given particle is; most have in fact broken up into
   smoke and ashes. And available energy is lost too, because the heat
   and light have dissipated into the environment and the burnt remains
   possess far less available energy than the paper did. In sum,
   entropy has increased. 

   But can we "recombine" the fire, smoke, and ashes by reversing every
   microscopic process involved in the combustion and reconstitute the
   paper? In theory, yes-but only through external efforts; one
   consequence of the Law of Entropy is that the paper (like any
   isolated system) will not spontaneously regenerate itself. In
   practice, of course, this would be an unfeasible task, so the
   burning of the paper remains an irreversible process. The same
   holds, for example, for the death of any living being.

   All living creatures take in energy from their surroundings to
   offset the natural tendency toward increasing entropy (and its
   ultimate consequences, death and total decomposition). But while
   this allows for small-scale, individual growth in size and
   complexity (increasing order, information, and available energy,
   meaning a local decrease in entropy), the entropy of the ambient as
   a whole increases. As the Sun emits energy into space, its entropy
   increases irreversibly. A plant uses a tiny fraction of this energy,
   and chemicals from its environment, to decrease its own entropy as
   it grows. Put the plant in an airtight, lightproof container,
   though, and this now-isolated system will quickly succumb to the Law
   of Entropy: It will die and decompose as it approaches its maximum
   entropy state.

   Another consequence of the Law of Entropy is that all real-world
   processes, biological or otherwise, must produce some waste in the
   form of cast-off energy (and, often, matter also). However small
   this waste may be, it is never zero-that is, no natural or man-made
   process can ever be 100 percent efficient. The human metabolism, for
   example, is only about 50 percent efficient; half of the energy we
   derive from food and oxygen intake becomes waste heat. Clearly, the
   Law of Entropy rules out practical perpetual-motion machines whose
   efficiency is by definition 100 percent, not to mention those
   miraculous "free-energy" machines that, on their own, produce more
   energy than they consume (thus exceeding 100 percent efficiency).

   We conclude by noting that the Law of Entropy can be stated in terms
   of the Law of Extremes: All natural processes act to maximize the
   entropy of a system. As we have seen, any such system can
   temporarily sustain itself from the energy cast off by another
   system as it progresses towards its own state of maximum entropy,
   but ultimately the entropy of the entire ambient must irreversibly
   increase. This offers another argument against time travel (as well
   as, for example, resurrection of the dead), since all of the myriad
   processes and events that elapse between any two dates (such as the
   beginning and end of the dying process) are, for all practical
   purposes, irreversible. (Some philosophers connect this with the
   concept of the arrow of time.) It indeed appears that the ancient
   Greek thinker Heraclitus was right: You can never step into the same
   river twice.

   References

       Kline, M. 1964, Mathematics in Western Culture, New York: Oxford
       University Press.  
       
       Sachs, M. 1988, Einstein versus Bohr: The continuing
       controversies in physics, La Salle, Ill.: Open Court. 

   About the Author

   Zoran Pazameta teaches astronomy and physics at Eastern Connecticut
   State University. His research interests include relativity,
   cosmology, and the philosophy of science. Address: Physical Sciences
   Department, Eastern Connecticut State University, Willimantic CT
   06226. E-mail: pazameta@ecsuc.ctstateu.edu. 


How do You Know What to Believe?

"In the macroscopic "real" world, the subject of the above article,
physics has revealed to us definite rules by which nature always
operates--rules for establishing what is physically possible and for
eliminating the impossible. We have confidence in these laws because
with all the observations and experiments that have been (and continue
to be) performed, no exception to them has yet come to light; that is,
they constitute the best explanation of the natural world available to
us today". 

The same is true for the two great pillars of 20th century physics, the
Quantum Mechanics dealing with the world of the atom, and General
Relativity dealing with the Universe as a whole. Was Einstein right?
Without a doubt! These theories have been tested for almost a century
and have never failed to be in agreement with observation and
experiment. 

What about Darwinian Evolution? Darwinian Evolution is very often
misquoted and misunderstood. Indeed Evolution correctly accounts for
much of the observation and experimental result in the biological
world. 

For life, there are limited resources. Species compete for those
resources. Random mutations occur (minor as they may be) in
reproduction of life forms from generation to generation. On the whole,
it is "the survival of the fittest" that produce the most offspring and
generations adapt to the changing environment. When resources are
plentiful, diversity tends to take place often accompanied by the
proliferation of new species. When resources are scarce, whole lines of
species die out, become extinct. This is the basic mechanism that
Darwin observed and understood. 

Was Darwin right? Without a doubt! Evolution is certainly tied to
astronomy. There is evolution of the Universe, evolution of the
galaxies and stars, evolution of the Earth, its atmosphere, its
contents, its geology, its life forms, and, of us. All of these are in
a continual state of change and on the grand scale it is all
intertwined. The iron in your blood was made in the cores of very
massive stars. The evolution of mammals and eventually us, came about
after the mass extinction 65 million years ago, thought to be brought
about by a cosmic impact on the Earth. 

Darwinian Evolution, like Special and General Relativity and the
Quantum Mechanics, although historically called theories, are all
elevated to scientific fact, supported by decades of observation and
experiment. I see no need of religious conflict. God seems to work with
all the mechanisms that humans are discovering. Science is not a set of
"facts", but a process in which we understand nature about us, how it
works, how it evolves... The mechanisms of how we know things are:
observation and experiment. Models and theories are tools to help us
understand. They are revised and corrected with new and changing
evidence... rarely are they over-thrown, but usually always refined as
we converge toward a better understanding of the Universe and our place
in it.

I bought an astronomy textbook some years ago, "The Physical Universe"
by Frank H. Shu. I liked this textbook because Dr. Shu describes all
the physical processes in the Universe as a battle between Gravity and
the 2nd Law of Thermodynamics, Entropy. Gravity is trying to collapse
stars, the thermonuclear fusion holds the star up against gravity. The
2nd Law says that systems tend toward decay and tearing down, yet on
the Earth, life tends evolve to form greater complexity. A
contradiction? No, the energy for building on the Earth comes from the
Sun. As long as the Sun provides the Earth with energy, Entropy is held
at bay. 

"We conclude by noting that the Law of Entropy can be stated in terms
of the Law of Extremes: All natural processes act to maximize the
entropy of a system. As we have seen, any such system can temporarily
sustain itself from the energy cast off by another system as it
progresses toward its own state of maximum entropy, but ultimately the
entropy of the entire ambient must irreversibly increase. This offers
another argument against time travel (as well as, for example,
resurrection of the dead), since all of the myriad processes and events
that elapse between any two dates (such as the beginning and end of the
dying process) are, for all practical purposes, irreversible. (Some
philosophers connect this with the concept of the arrow of time.) It
indeed appears that the ancient Greek thinker Heraclitus was right: You
can never step onto the same river twice". 


Homework Problems

Note the answers to the odd (Conceptual Questions, Problems and
Figure-Based Questions) are in the back of your textbook. It is
strongly suggested that you do some of those in every chapter so you
have immediate feedback as how well you are understanding the material.
There are online multiple choice quizzes for each chapter of your
textbook. Goto http://www.mhhe.com/fix then click on

  Your book
  Student Edition
  Choose a chapter
  Multiple Choice Quiz
  
You are expected to do all of your own homework. Statistical patterns
showing copying or collaboration will result in no credit for the
homework assignment for all participants involved. The Code of Academic
Conduct for Iowa Valley Community College District is found in the
Student Handbook.

Physical Science classes require the use of mathematics. If you don't
know algebra, you sould NOT be taking this class. If you need to review,
look at Introduction to Algebra 
  http://www.math.armstrong.edu/MathTutorial/
  
WolframAlpha is way faster than a scientific calculator.
  http://www.wolframalpha.com

There is little excuse for turning homework in late. You have a whole
week between classes to read the chapters and do the homework. Homework
one week late - half credit. Two or more weeks late - no credit. Do the
homework during the week, not in class! You got homework questions,
email me 24/7. sam.wormley@gmail.com  Even if you don't have a homework 
question, email me anyway!


Problem 1:
Use figure 13.5 to estimate the pressure at the depths in the
atmospheres of Uranus and Neptune where ammonia (NH3) clouds lie.
Hint: Regardless of the cloud labels in the diagram, ammonia clouds 
form at a temperature of 140 K.

Problem 2: 
Using your Planisphere (starwheel), in what constellation is the Sun
on your birthday?  Hint: The Sun transits at Noon on your Birthday.

Problem 3: 
Using your Planisphere (starwheel), how long is the day in hours and
minutes (sunrise to sunset) on your birthday?  Alternate resource:
  http://edu-observatory.org/mcc/syllabus/skycalendar.html
   
Problem 4: 
How many distinct "ringlets" can be identified in Figure 12.32
between 113,000 km and 113,200 km from Saturn? Takes a little work!

Problem 5: 
Describe what forms (physical states) hydrogen takes in Jupiter from
the surface to the center of the planet. 

Problem 6: 
How does the size and shape of Jupiter's magnetosphere compare to
the Earth's magnetosphere? Be specific.

Problem 7: 
What evidence do we have that Saturn's rings aren't solid disks?

Problem 8: 
What was the reason that, after the discovery of Uranus, astronomers
began to believe that there was a planet beyond Uranus?

Problem 9: 
Pluto has a temperature of about 50 K. Use Wien's law (Chapter 7)
to calculate the wavelength at which Pluto is brightest.

Problem 10: 
How were the ring systems of Uranus and Neptune detected before they
were actually seen in Voyager 2 images?