Sample Questions

1. a. Comet Hale-Bopp has a period of 4200 years. What is the semi-major axis of its orbit.
   
   b. At its closest approach to the sun on April 1 (perihelion passage) it will be traveling 45 km/ sec. By how much will the Doppler effect shift its light as seen by a stationary observer?
   c. The declination of Hale Bopp is approximately 40 degrees. Above what latitude is it a circumpolar object? Below what southern latitude is it invisible?

   Rayleigh scattering causes both reddening and blueing. Give two examples of each.

   a. Primordial fireball radiation has a temperature of approximately 3K. What is the wavelength of the maximum radiation (in either cm or Angstroms)?

   b. When it was produced that radiation had a temperature of approximately 6000K; what was its wavelength maximum?

   c. What is z for this radiation which is experiencing the largest of all relativistic Doppler effects that we have observed.

   a. Distinguish between inertial mass and gravitation mass.

   b. How does Newton's second law of motion define inertial mass?

   c. How does Newton's concept of gravitation define gravitational mass?

   a. Why did Newton argue that inertial mass must precisely equal gravitation mass?

   b. Why did Einstein argue that gravitational mass does not exist?

   a. A white dwarf may have a radius of 7000km compared to the 700,000 km of the sun. The escape velocity of the sun is approximately 600 km/sec. What is the escape velocity of such a white dwarf?

   b. A black hole has a radius which another 2500 times smaller. What is its escape velocity?

   a. What is the gravitational red shift of light from a black hole?

   b. What happens to time at the event horizon?

   When a circle is drawn on a sphere such that the circle covers the entire sphere what is the circumference of the circle.

   a. Triangles can tell us whether space is flat or curved. What is the sum of the interior angles of a triangle in flat space?

   b. When drawn on a sphere such that the triangle covers 1/8 the surface area of the sphere what is the sum of its interior angles?

   a. What is the radius of a black hole with a mass equal to that of the sun?

   b. What is its radius when it has a mass equal to that of small galaxy containing 100 billion stars?

   c. The mass of the earth is three millionths of the sun. What is the radius of a black hole with the mass of the earth?

   What are two situations in which time stops?

   Newton's first law of motion is that free particles move along a straight line at a constant speed. What is Einstein's modification of that law?

   How many high tides does one experience on the earth in one day?

   A planet is discovered to revolve around a nearby star. What is the mass of the star if the planet revolves around it with a period of 1 year and at a distance of 10 a.u.?

   Einstein argues that gravity is a fictitious force, like centrifugal "force". What observation can you make to verify the fictitiousness of centrifugal "forces"?

   What are the distance and period of an asteroid which has a 1:2 resonance with Jupiter?

   Why does one see more meteors just before dawn than just after dusk?

   a. What is the source of shower meteors?

   b. What is the source of most meteorites?

   How do the periods of comets in the Oort comet cloud differ from those of planets?

   a. Why may the Tunguska explosion have been caused by a comet rather than a meteorite?

   b. Where is the crater associated with the extinction event of 65 million years ago?

   c. Why is was liquid water (and therefore life) absent on the earth for some 800 million years after its formation?

   a. Why are the two brightest stars of Libra named Zubelgenubi and Zubeneschamali?

   b. Why is the second brightest star in Leo named Denebola?

   c. Why is Algol known as the Demon star?

   a. What are the three bright stars of the winter triangle?

   b. How do their temperatures compare to that of the sun?

   a. What constellation is closest to the pole of our galaxy?

   b. Why is that area of the sky known as the Realm of Galaxies?

   c. What constellation is the longest? what is the smallest?

   a. In what constellation is the sun currently at the time of vernal equinox?

   b. In what constellation was the sun at vernal equinox 2000 years ago?

   c. In what constellation will it be at VE in another 2000 years?

   Gravitational lensing causes the displacement of stars at a total eclipse which first verified Einsteins ideas of curved space and the doubling of the images of very distant galaxies.

   a. What kind of curvature of space produces the same effect as that of a double convex lens?

   b. What kind of curvature produces the same effect as that of a double concave lens?

   c. What kind of curvature produces the same effect as that of a concave mirror?

   For a double convex lens with a focal length of 10 inches, at what distance from the lens is an image of a star formed?

   What were three discoveries made by Galileo with his telescope that supported the heliocentric view?

   Venus has a much more circular orbit than Mars. Why is it fortunate that Kepler choose to investigate Mars first, rather than Venus?

   Would you choose a short or long focal length eye piece to observe Hale Bopp; the moon?