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An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 72.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.4 years as measured in a rest frame. Note that radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails.
(a) How long do the batteries on the space probe last as measured by mission control on Earth? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.)
(b) How far is the probe from Earth when its batteries fail as measured by mission control? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.)
(c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail?
(d) For what total time after launch is data received from the probe by mission control?
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