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Caught by surprise near a supernova, you race away from the explosion in your spaceship, hoping to outrun the high-speed material ejected toward you. Your Lorentz factor gamma relative to the inertial reference frame of the local stars is 22.4. To reach a safe distance, you figure you need to cover 9.00xx10^(16)m as measured in the reference frame of the local stars. How long will the flight take, as measured in that frame? |
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Answer» Solution :KEY IDEAS From Chapter 2, for constant speed, we know that speed `=("distance")/("time interval")"" `(36-19) Form Fig. 36-8, we see that because your Lorentz factor `gamma` relative to the stars is 22.4 (large), your relative speed v is almostc - so close that we can APPROXIMATE it as c. Then for speed `v~~c`, we must be careful that the distance and the time interval in Eq. 36-19 are measured in the same reference frame. Calculations: The given distance `(9.00xx10^(16)m)` for the LENGTH of your travel path is measured in the reference frame of the stars, and the requested time interval `DELTAT` is to be measured in that same frame. Thus, we can write (time interval relative to stars)`=("distance relative to stars")/(c )`. Then substituting the given distance, we find that (time interval relative to stars) `=(9.00xx10^(16)m)/(299 792 458m//s)` `=3.00xx10^(8)s=9.51y`. |
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