At t=0, an alien spaceship passes by the earth: let this be event A. At t=13 min (according to synchronized clocks on earth and Mars), the spaceship passes by Mars, which is 5 light-minutes from earth at the time: let this be event B. Radar tracking indicates that the spaceship moves at a constant velocity between earth and Mars. Just after the ship passes earth, people on earth launch a probe whose purpose is to catch up with and investigate the spaceship. This probe accelerates away from earth, moving slowly at first, but moving faster and faster as time passes, eventually catching up with and passing the alien ship just as it passes Mars. In all parts of this problem, you can ignore the effects of gravity and the relative motion of earth and Mars (which are small) and treat earth and Mars as if they were both at rest in the inertial reference frame of the solar system. Also assume that both the probe and the alien spacecraft carry clocks. 1. Draw a quantitatively accurate spacetime diagram of the situation, including labeled worldlines for the earth, Mars, the alien spacecraft, and the probe. Also label events A and B. 2. Whose clocks measure coordinate times between events A and B? Explain. 3. Whose clocks measure the proper times between these events? Explain.
At t=0, an alien spaceship passes by the earth: let this be event A. At t=13 min (according to synchronized clocks on earth and Mars), the spaceship passes by Mars, which is 5 light-minutes from earth at the time: let this be event B. Radar tracking indicates that the spaceship moves at a constant velocity between earth and Mars. Just after the ship passes earth, people on earth launch a probe whose purpose is to catch up with and investigate the spaceship. This probe accelerates away from earth, moving slowly at first, but moving faster and faster as time passes, eventually catching up with and passing the alien ship just as it passes Mars. In all parts of this problem, you can ignore the effects of gravity and the relative motion of earth and Mars (which are small) and treat earth and Mars as if they were both at rest in the inertial reference frame of the solar system. Also assume that both the probe and the alien spacecraft carry clocks.
1. Draw a quantitatively accurate spacetime diagram of the situation, including labeled worldlines for the earth, Mars, the alien spacecraft, and the probe. Also label events A and B.
2. Whose clocks measure coordinate times between events A and B? Explain.
3. Whose clocks measure the proper times between these events? Explain.
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4. Does any clock in this problem measure the spacetime interval between the events? If so, which one and why? If not, why not?
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