An interstellar space probe is launched from Earth. After abriefperiod of acceleration it moves with a constantvelocity, 72.0%of the speed of light. Its nuclear-poweredbatteries supply theenergy to keep its data transmitter activecontinuously. Thebatteries have a lifetime of 15.9 years as measured in a restframe.
(a) How long do the batteries on the space probe last as measuredbymission control on Earth? yr (b) How far is the probe from Earth when its batteries fail,asmeasured by mission control? ly (c) How far is the probe from Earth, as measured by itsbuilt-intrip odometer; when its batteries fail? ly (d) For what total time after launch is data received from theprobeby mission control? Note that radio waves travel at the speedoflight and fill the space between the probe and Earth at the timethebattery fails. yr
