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A spaceship travels past the Earth and Moon in a straight line at a constant speed of 0.600 c. The spaceship passes the Earth first and then a short while later passes the Moon. The distance between Earth and Moon as measured in the Earth-Moon frame is 1.20 light-seconds. A light-second (symbol: Is) is defined as the distance travelled by light in one second. To simplify your working you should do all your calculations in seconds and light-seconds and express speeds as multiples of c; it is not necessary to convert distances and speeds into SI units.

Figure 1 shows the situation as the spaceship passes the Earth. A system of synchronised clocks in the Earth-Moon system is arranged along the x-axis, forming a frame of reference. This includes one clock on the Earth and one on the Moon. A similar system of synchronised clocks exists in the Spaceship frame of reference. As the ship passes the Earth, a clock on board the ship is compared against the clock on the Earth and both are seen to read a time of zero seconds. the same time (as seen from the Earth-Moon frame), a radio signal is sent from the Moon towards the Earth. The Moon clock also reads zero seconds at the moment the radio signal is transmitted. Some time later the radio signal arrives at the spaceship, having travelled at speed c. An observer S in the spaceship records the time as shown on the spaceship clock at the instant the radio signal arrives.

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