An astronaut in a starship travels to α Centauri, a distance of approximately 4 ly as measured from Earth, at a speed of u/c=0.8.
(a) How long does the trip to α Centauri take, as measured by a clock on Earth?
(b) How long does the trip to α Centauri take, as measured by the starship pilot?
(c) What is the distance between Earth and α Centauri, as measured by the starship pilot?
(d) A radio signal is sent from Earth to the starship every 6 months, as measured by a clock on Earth. What is the time interval between reception of one of these signals and reception of the next signal aboard the starship?
(e) A radio signal is sent from the starship to Earth every 6 months, as measured by a clock aboard the starship. What is the time interval between reception of one of these signals and reception of the next signal on Earth?
(f) If the wavelength of the radio signal sent from Earth is λ=15 cm, to what wavelength must the starship's receiver be tuned?