HRW PROBLEM SUPPLEMENT #1 - CHAPTER 6
  66.  The first known collision between space debris and a functioning
       satellite occurred in 1996.  At an altitude of 700 km, a year-old
       French spy satellite was hit by a piece of an Ariane rocket that
       had been in orbit for 10 years.  A stabilizing boom on the
       satellite was demolished, and the satellite was sent spinning out
       of control.  Just before the collision and in kilometers per hour,
       what was the speed of the rocket relative to the satellite if both
       were in circular orbits and the collision was (a) head on and
       (b) along perpendicular paths.

  74.  The gravitational force between two particles with masses m and M,
       initially at rest at great separation, pulls them together.  Show
       that at any instant the speed of either particle relative to the
       other is sqrt(2G(M+m)/d), where d is their separation at that
       instant.  (Hint: Use the law of conservation of energy and 
       conservation of linear momentum.)(M is not >> m in this problem.)

  88.  In a double-star system, two stars of mass 3.0 X 10^{30} kg each
       rotate about the system's center of mass at a radius of
       1.0 X 10^{11} m.  (a) What is their common angular speed? (b) If
       a meteoroid passes through the system's center of mass 
       perpendicular to their orbital plane, what minimum speed must
       it have at that point if it is to escape to "infinity" from the
       two-star system?

 90.   A 50 kg satellite circles plant Cruton every 6.0 h.  The
       magnitude of the gravitational force exerted on the satellite by 
       Cruton is 80 N.  (a) What is the radius of the orbit?  (b) What 
       is the kinetic energy of the satellite?  (c) What is the mass
       of Cruton?
  
       FISHBANE - CHAPTER 8
   6.  (The figure for this problem is Fig. 14-16 on page 309 of HRW.)
       Two objects, of masses m1 and m2 (m2 > m1), respectively, move
       in circular orbits that have the same center.  If the force that
       gives rise to this motion is a force of attraction between the
       two objects acting along a line joining them, using momentum
       conservation and Newton's second law, (a) show that they move
       with the same angular speed, and (b) calculate the ratio of
       the radii of the two circular orbits.

       FISHBANE - CHAPTER 12
  35.  A small package is fired off Earth's surface with a speed v at a
       45 degree angle with the local horizontal.  It reaches a maximum
       height h above the surface at h = 6370 km, a value equal to Earth's
       radius itself.  What is its speed when it reaches this height?
       Ignore any effects that might come from Earth's rotation or from
       air resistance.  (Hint: You will need to use two conservation
       equations and solve two equations in two unknowns.)

  55.  The Little Prince ( a character in a book by Antoine de Saint-
       Exupery) lives on the spherically symmetric asteroid B-612.  The
       density of B-612 is 5200 kg/cubic meter.  Assume that the asteroid
       does not rotate.  The Little Prince noticed that he felt lighter
       whenever he walked quickly around the asteroid.  In fact, he found
       that he became weightless and started to orbit the asteroid like a
       satellite whenever he speeded up to 2 m/s.  (a) Estimate the radius
       of the asteroid from these data.  (b) What is the escape speed for
       the asteroid?  (c) Suppose that B-612 does rotate about an axis
       such that the length of the day there is 12 h.  Can the Little
       Prince take advantage of this rotation when he wants to orbit the
       asteroid?  What is his minimum ground speed for orbit in this case?

       SERWAY - CHAPTER 12

  49.  (The picture for this problem is the same as for Fishbane CH 8,
       problem 6.  You may use your result for that problem in solving
       this one.)  Two stars of masses m1 and m2, separated by a distance
       of d, revolve in circular orbits about their center of mass.  Show
       that each star has a period given by

                  T^2 = (4pi^2)d^3/G(m1+m2)

       (Hint: Write Newton's 2nd Law for each star, and use r2+r1 = d)

       PROBLEM A3
   3.  You weigh 530 N at sidewalk level outside the Petronas Towers in
       Kuala Lumpur, Malaysia.  Supose that you ride from this level to
       the top of one of its 420 m towers.  Ignoring Earth's rotation,
       how much less would you weigh there (because you are slightly
       farther from the center of Earth)?