A broadcasting spaceship moving with speed v passes directly over an observer at altitude 500 km. Consider the motion to be along a straight line from left to right. (a) Find an expression for the angle θ=θ 0 (propagation direction measured in the stationary S frame) at which the Doppler shift is zero as a function of β=v/c. What are the values of θ 0 for β≪1,β→0, and β→1 ? (b) Tabulate the values of θ 0 and the arrival angle of the radiation from the vertical φ 0 =90 ∘ −θ 0 ) for β=0.01,0.1,0.5,0.9,0.99,0.999,0.9999. (c) Consider a low-Earth-orbiting satellite that passes overhead at 7.7 km/s. How far from the vertical is it when its Doppler shift is zero? Again, assume straight-line motion. (d) Find the actual angular position of the satellite (not the signal direction) relative to the vertical when the null signal is detected. Will the satellite have passed the zenith at this time?