An interstellar space probe is launched from Earth. After a brief period of acceleration it moves by 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 15.9 years as measured in a rest frame.
1. How long do the batteries on the space probe last as measured by mission control on Earth?
2. How far is the probe from Earth when its batteries fail, as measured by mission control?
3. How far is the probe from Earth, as measured with its built-in trip odometer; when its batteries fail?
4. For what total time after launch is data received from the probe with mission control? Note that radio waves travel at the speed of light and fill the space among the probe and Earth at the time the battery fails.