A space probe travels past two space stations in a straight line at a constant speed of 0.700c. The space stations are called Red Station and Green Station, and they are not moving with respect to one another. The distance between the stations in the stations' frame is 5.00 light-seconds.

A light-second (symbol cs) is defined as the distance travelled by light in one second. Keep distances in light-seconds and speeds as multiples of c in your calculations. The probe emits a radio signal as it passes Red Station. The emission is timed at 0.000 s both by a clock in the probe and by a clock in Red Station. A third clock in Green Station times the arrival of the radio signal. Subsequently, it times when the probe passes Green Station.

(b) (i) Using the appropriate Lorentz transformations, transform all three events into the probe's frame. Hence determine their position and time coordinates in the probe's frame. (ii) What time is shown on the probe clock when the radio signal arrives at Green Station? (iii) State the velocity of Green Station in the probe's frame of reference. (iv) Using your answers from parts (i) and (iii), calculate the distance between the two stations in the probe's frame of reference.

(c)

(i) Other than comparing your results with the predictions of time dilation, explain two other checks that you have carried out on your answers in part (b).

Please complete part (c) (i) and provide two other checks one can perform on the answers found in part (b). One is length contraction and the another possible one is calculating c in the probe's frame. Please confirm and explain.