AT 8th Ed.
Ch. 2 Homework
Assigned:  R&D 1-11
           M-C 1-7
(Other answers are also shown for completeness.)

1. What contributions were made to astronomy by Chinese and Islamic
astronomers during the Dark Ages in Europe?
  The Chinese contributed a calendar and records of 
  celestial events like comets and novae which are still used today.
  The Islamic culture built on the Almagest by Ptolemy during
  the dark ages.  They gave most stars the names we use today.
  They established trigonometric and algebraic methods (to, e.g.,
  find the direction to Mecca from any place on Earth) important
  in astronomy.
2. Briefly describe the geocentric model of the universe.
  The geocentric model has the Earth at rest at the center 
  with the Sun and Moon orbitting it. The inferior planets moved on
  epicycles which were centered on a bar between the Earth and
  the Sun.  The superior planets were also modelled as moving on 
  epicycles which moved on deferents, but the deferents were
  beyond the Sun.  The stars were on the most distant "sphere".
3. The benefit of our current knowledge lets us see flaws in the
  Ptolemaic model of the universe.  What is its basic flaw?
  The basic flaw of the Ptolemaic model is that the Earth
  is fixed at the center.  It is also complex, but that is not so
  much a flaw as an undesireable quality in a theory.
4. What was the great contribution of Copernicus to our knowledge
  of the solar system?  How was his model still flawed?
  He did not contribute much knowledge in the sense of new
  discoveries (like Galileo could with the telescope), but he
  put together a heliocentric (sun-centered) model of the solar 
  system that was much more comprehensive than our records of 
  Aristarchus' model.  He explained how the Earth rotated to
  explain daily motions and the Earth orbited the Sun to
  explain annual motions of the Sun.  The planets no longer
  had to move in loops, but only appear to because of the 
  Earth's motion.  It was still flawed in that it insisted 
  on circular motions.
5. What is a theory?  Can a theory ever be proved to be true?
  A theory, in its weakest definition, is just a hypothesis. 
  For its stronger definition, it is a set of related ideas 
  which describe a large collection of observations.
  A theory cannot be proved to be true, only disproved.
6. What is the Copernican Principle?
  The Copernican Principle is, most generally, that we are
  not special.  Originally, this meant that the Earth is not
  at the center of the solar system.  Since then it has been
  extended to include our Galaxy, our local group of galaxies,
  our local supercluster, and the universe.  It is also cited
  when considering life in the universe - we may not be the 
  only place with life or even intelligent life.
7. What discoveries of Galileo helped confirm the views of
   Copernicus and how did they do so?
  Since a theory cannot be proved, only disproved, Galileo's
  observations confirmed the Copernican view by discrediting
  the Ptolemaic model.  A gibbous phase of Venus was not allowed
  in the Ptolemaic model (which always had Venus between Earth
  and then Sun) but was allowed by the Copernican model.  Thus,
  the discovery of a gibbous Venus disproved the Ptolemaic model
  while leaving the Copernican unscathed.  Galileo also made
  several discoveries which contradicted the philosophical
  underpinnings of the Ptolemaic model, which originated with
  Plato, Aristotle and the like.  These include: the moons orbitting 
  Jupiter (Earth was supposed to be the center of all motions),
  and sunspots on the Sun (the Sun was supposed to be perfect and
  unblemished).  In addition, experiments studying falling and
  rolling bodies on Earth disproved Aristotle's notions that
  heavier objects fall faster. 
8. Briefly describe Kepler's three laws of planetary motion.
  First Law: the orbits of planets are in the shape of an ellipse
  with the Sun at one focus.  Second Law: a line connecting the
  Sun and a planet sweeps out equal areas in equal time intervals.
  Third Law: the square of the orbital period is proportional
  to the cube of the semi-major axis.
9. How did Tycho contribute to Kepler's laws?
  Tycho made meticulous observations of the positions of
  planets over many years.  Kepler then analyzed this data
  and determined the true orbits of the planets around the Sun.

10.  When Venus is near inferior conjunction, it is possible to
   bounce radar waves off of it and measure the time for radar
   to make the trip to Venus and back to Earth.  The relative 
   size (0.7 AU) and shape of Venus's orbit were known, so the 
   distance to Venus during inferior conjunction (about 28 million 
   miles) could be used to calculate the distance to the Sun (the AU).  
   Specifically, if the distance from Earth to Venus is 28 million miles
   and this is 3/10 of 1 AU, then you can solve 
   1 AU * 0.3 = 28,000,000 to find  1 AU = 93,000,000.
11. What does it mean that Kepler's laws are empirical?
   Kepler's laws are empirical because they were based on
   analysis of observational data rather then deriving from 
   some theoretical premise.  They are descriptive laws
   which don't explain why the planets move as they do.
12. What are Newton's laws of motion and gravity?
   1st law:  every body continues in a state of rest or in 
   uniform motion in a straight line unless it experiences
   some net force.  2nd law: when a force F acts on a body
   of mass m it causes the body to accelerate at a rate a=F/m
   3rd law: for every force there is an equal but opposite
   force.
13.  Why do we say that a baseball falls toward Earth, and
   not Earth toward the baseball?
   The Earth moves in response to the baseball but its motion
   is not noticeable because it is so slight.  From Newton's
   3rd law, both the baseball and the Earth feel the same attractive
   force.  However, Newton's 2nd law states that an object's 
   acceleration is inversely proportional to its own mass (a=F/m), 
   thus, the smaller mass (baseball) will accelerate/move much 
   more than the larger mass (Earth).
14. In what sense is the Moon falling toward Earth?  How
    can we use this fact to measure Earth's mass?
   When the force of gravity pulls an object toward the Earth,
   the object is said to be "falling".  The Moon is being
   pulled continuously toward the Earth by gravity, sometimes
   it moves toward Earth and sometimes it moves away, but 
   continuously falling.  Whether it is moving toward or away
   from the Earth, it is ALWAYS ACCELERATING towards the Earth
   since it is moving in a curved orbit.  From the acceleration
   we can calculate the force of gravity and thus the mass of
   the Earth-moon system.  F_g = G(M*m/r^2). 
15. What is the meaning of the term escape speed?
   If body 1 orbits body 2 at the escape speed, its orbit
   will be open instead of closed.  That is body 1 will leave
   the vicinity of body 2 and never return (unless influenced
   by some 3rd body).

Important OLD EDITION QUESTION:
15. What were the modifications made by Newton to Kepler's laws?
    The two modification by Newton to Kepler's laws:
   1) For the first law, one focus of an elliptical orbit
      was located at the center-of-mass of the solar system
      rather than on the Sun itself.
   2) For the 3rd law, the mass of the system should be
      taken into account to make it more widely applicable ...
	 P^2 = R^3/M_tot

Mult Choice
1. a
2. d
3. b
4. c
5. c
6. a
7. c
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8. b
9. c
10. a