An interstellar space probe is launched from the Earth. After a brief period of acceleration it moves with a constant velocity, with a magnitude of 70.0% 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 15.0 yr as measured in a rest frame.
(a) How long do the batteries on the space probe last as measured by Mission Control on the Earth?
(b) How far is the probe from the Earth when its batteries fail, as measured by Mission Control?
(c) How far is the probe from the Earth when its batteries fail, as measured by its built-in trip odometer?
(d) For what total time interval after launch are data received from the probe by Mission Control? Note that radio waves travel at the speed of light and fill the space between the probe and the Earth at the time of battery failure.