Homework 2

Due September 15th 2006


1) Consider three events in the laboratory reference frame A(ct,x)=(1m,2m); 
B(3m,4m) and C(4m,1m)
a) Indicate the type of each space time interval (AB), (CB) and (AC). For each 
specify if the two events can be in causal relation.
b) For each pair of events, specify, if possible, the velocity of the 
reference frame in which they appear simultaneous (same t'). Also indicate the 
distance separating the two events in that reference frame.  
c) For each pair of events, specify,  if possible, the velocity of the 
reference frame from which the two events will appear at the same location 
(same x'). Also indicate the time interval separating the two events in that 
reference frame. 


2) You are flying the Millenium Falcon. Your goal is to shoot the death star 
at the closest range possible. You fly-by the death star at speed 0.8c. Just 
at the time of your closest approach, when the death star is 90 degrees from 
your direction of motion, you shoot your laser gun (a beam of light) at the 
death star. You become a hero by destroying the death star only if you have 
properly calculated the angle at which you had to shoot the laser to hit the 
death star. What is the angle you must set between your direction of motion 
and the laser gun on board the Millenium Falcon? 

3) A ring of gas is orbiting a black-hole at speed 0.8c. We will neglect 
all general relativity related effects. At rest, the gas emits light with 
450nm wavelength. You are observing the ring edge on from a great distance. 
What are the wavelengths you will observe on the receding end, approaching end 
and from the center?