Imagine that in the year 2065, you are watching a live broadcast from the space
ID: 1291459 • Letter: I
Question
Imagine that in the year 2065, you are watching a live broadcast from the space station at the planet Neptune, which is 4 light-hours from the earth at the time. (assume that the TV signal from Neptune is sent to earth via a laser ligh communication system). At exactly 6:17 pm (as registered by the clock on your desk), you see a technician on the TV screen suddently exclaim, "Hey! we've detected an alien spacecraft passing by here." Let this be event A. Exactly 1 hour later, the alien spaceship is detected passing by earth: let this be event B. Assume that the earth and neptune stations can be considered parts of the inertial reference fram of the solar system, and assume that the spaceship travels at a constant velocity.
a) during the broadcast, you can see on your TV screen the face of a clock sitting on the technician's desk. What time should you see on this clock face at 6:17 pm your time if that clcock is synchronized with yours?
b) what is the coordinate time between events a and b in the solar system frame?
c) what is the speed of the alien spaceship, as measured in the solar system frame?
d) what kinds of time would the spaceship's clock measure between events a and b?
answers should be:
a) 2:17 pm
b) 5h
c) 4/5
d) all three kinds (coordiinate time, proper time, and spacetime interval)
explanations/work please
Explanation / Answer
a) as the broad casting is done from neptune,which takes 4 hour to reach to earth ,so we have to go beyond the 4 hr,hence the time is 6:17pm-4:00=2:17pm.
b) as given that the second event occurs near by earth after 1 hr,so this 1hr is the actual time,then after the time between the broadcast locations that is 4 hr is added to this actual time hence total time between the events is 5hr.
or in other words the second evevt brodcasted at 7:17 pm and the fisrt is broadcasted at 2:17 hence time difference is 5 hr.
c)as the total distance is 4light-hour and the time taken by the spaceship is 5hr.
so speed=4/5 light-hour per hour
d)all the kind of time measure by the space ship, as the time between the earth and neptune is measured by coordination time,proper time is measured during the observation observe from earth, and the space time during the speed calculation.