The new earth-Pluto SuperShuttle line boasts that it can take you between the tw

Question

The new earth-Pluto SuperShuttle line boasts that it can take you between the two planets (which are about 5.0 h apart in time) in 2.5 h (according to your watch)> Assume that acceleration and deceleration periods are very brief so that you spend essentially all the trip traveling at a constant velocity.

A) What time interval must the synchronized space station clocks register between the shuttle's departure from earth and its arrival at Pluto if the advertisement is true?

B) what is the shuttle's cruising speed?

Explanation / Answer

n 2.5 h (according to your watch)> Assume that acceleration and deceleration periods are very brief so that you spend essentially all the trip traveling at a constant velocity.
So: for the interval between leaving Earth and encountering Pluto:
In the spacecraft frame we have:
dtspacecraft = 2.5h
this is also the event distance ds (proper time measured by a watch at rest is the event distance)
ds = 2.5h
A) What time interval must the synchronized space station clocks register between the shuttle's departure from earth and its arrival at Pluto if the advertisement is true?
dtsolar system = 5h
B) what is the shuttle's cruising speed?
dtsolar system/dtspace craft = g = 5h/2h = 2.5
g = 1/sqrt(1-b2) = 2.5
b = sqrt(1 - 1/g2) = sqrt(1 - 1/2.52) = 0.917c

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