Question: I tried to use the hinted formula on Problem 8 and I ended up getting a number greater than C. Also, I assumed that since they said that they lost 1 second in a day, that I could use the seconds in a day for the delta t. Is that a correct assumption? And I also am not sure how to prove the hint. Could you give me a hint about the hint?

Answer: vsv. the hint. This is like error analysis or Taylor expansion. See the note on small numbers approximations on the web (from the class home page).

vsv. getting a speed greater than c. I suspect that you put the gamma on the wrong side or in the wrong place or had the sign of the second wrong. On earth we see the number of seconds in a day. In the space ship, they measure one second less. Since gamma>1, and t_earth>t_ship, t_earth=t_ship * gamma.

Question: When I did the taylor series expansion for the doppler shift gamma equation(while taking note that it was receding!), I come up with a corrected factor of 1- (v/c) rather than just -(v/c). Is there something that I am not doing?

Answer: You are calculating f_observed/f_source. Calculate instead (f_observed-f_source)/f_source = Delta(f)/f_source.