Astro 250: Astronomy Bizarre
Spring 2007

Assignment #2
Due: Wednesday, February 20, 2008

Name: ______________________________________

1. Some fun with the equivalence of Mass and Energy:
   1. How much mass does a 100-Watt bulb dissipate in the form of energy (heat and light) if it is left on for an entire year? First figure out how much energy is used (a Watt is a Joule/second). Keep the proper units by using the speed of light as 3x10^8> meters/second to calculate the mass dissipated in kilograms.

   2. Pedaling a bicycle at full throttle, you generate 1/2 horsepower (about 750 Watts) of useful power. The human body is about 25% efficient; that is, 25% of the food burned can be converted to useful work. How long a time will you have to ride your bicycle in order to lose 1 kilogram by conversion of mass to energy? Express your answer in years (31,600,000 s = 1 yr.).

      
      

2. Draw space-time diagrams with the space axis along the 'surface' of each of the following. For each diagram, sketch the future light cone.

    

   1. a white dwarf star

         
       
       
      

   2. a neutron star

         
       
       
      

   3. the photon sphere of a black hole.

       
       
       
      

   4. the event horizon of a black hole  
       
       
      

3. For each of the following objects, compute the radius, in centimeters, of the event horizon were they to become a black hole. Express your answer using scientific notation (i.e. a x 10^b). You will need to consult some reference material (or the WWW) to find the mass of the following objects. Be sure to state the mass that you are using. Remember that the mass of the Sun is 2x10³³ grams. What is the radius of the event horizon of a black hole with the mass of:

    

   1. The planet Jupiter

       
      

       

       

   2. The Earth's moon

       

       
      

       

       

   3. Michael Strahan (defensive end for the Super Bowl Champion New York Giants)