An alien spacecraft is flying overhead at a great distance a

An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for 0.190. The first officer on the spacecraft measures that the searchlight is on for 12.0 ms. What is the speed of the spacecraft relative to the earth expressed as a fraction of the speed of light ? and what is the proper time.

Solution

a) 0.190 * sqrt(1 - (v/c)^2) = 0.012

1- (0.012/0.190)^2 = (v/c)^2

v/c = sqrt(1- (0.012/0.190)^2) = v/c

I get 0.998

The speed of the craft is 0.998c

2)The Proper Time interval \"dT\" is defined as the interval measured in the rest frame of the light source. So .012 s is the Proper Time interval.