An interstellar space probe is launched from earth. After a brief period of acceleration, it moves by a constant velocity, 70.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active incessantly. The batteries have a lifetime of 15.0 years as measured in a rest frame. a) How long do the batteries on the space probe last as measured by mission control on earth? b) How far is the probe from earth when its batteries fail as measured by mission control? c) How far is the probe from earth because measured with its built-in trip odometer when its batteries fail? d) For what total time after launch are data received from the probe by mission control? Note that radio waves travel at the speed of light and fill up the space between the probe and earth at the time the battery fails.