Darin is traveling on a spaceship moving away from earth at a velocity of 30,000 km/sec. just when he reaches a distance of 100 aui (in earth coordinate system), katia on earth sends him a radio signal at frequency 2.5 ghz. immediately after receiving the signal darin’s radio transmits a response at the same frequency it was received.

(a) how long (in hours) after katia’s transmission does the return signal arrive?

(b) what frequency (in ghz) does darin measure for the incoming signal?

(c) what frequency (in ghz) does katia measure for the return signal?

(d) by what fractional amount does the exact relativistic kinetic energy of the spaceship differ from the newtonian value?

(e) repeat part (d) but this time obtain it by expanding the relativistic expression for kinetic energy to order β 4.

(f) for what value of β is the fractional error 10%?