Suppose the us was expanding (stretching) at a constant rate, causing the distances between cities to increase. further assume that you live in denver and you gain information by observing the light emitted from street lamps in other cities. all lamps emit light of the same color in each city and the all lamps have the same brightness.
a) if you somehow measured the speed at which new york city (nyc) and los angeles (la) would appear to move away from you, which of these two cities would you measure a greater speed for? explain. hint: nyc is further away from denver than la.
b) if the expansion is fast enough you could notice that the light you observe from lamps located in nyc and in la have different colors as compared to the ones you observe in denver. explain how the observed color of the light from lamps in la and nyc would be different from the light you observe in denver.
c) which of the street lights would you observe to be brighter (more luminous), the ones form nyc or the ones from la? explain your answer.
d) how could you measure the distance to nyc and la based only on information gained from the light? hint: answer to question c)! state all assumptions you need to make for your method to work.
e) if you made a graph of the distance of each city from denver and the speed that each city move away from you, what graph would you get and what could you learn from the slope of the graph? note that there are two things you could gain from the slope - extra credit will be awarded if you state both with full explanations.