A space traveler takes off from Earth and moves at speed 0. 9900c toward the sta

Question

A space traveler takes off from Earth and moves at speed 0. 9900c

toward the star Vega, which is 26. 00 ly distance from Earth. How much

time (in years) will have elapsed by Earth clocks (a) when the traveler

reaches Vega and (b) when Earth observers receive word from the traveler

that she has arrived? (c) How much older will Earth observers calculate

the traveler to be (measured from her frame) when she reaches Vega than

she was when she started the trip? (Note: 1 ly is the distance that light

travels in 1 year.)

Explanation / Answer

(a) from the given the speed of the travelleris v = 0.9900 c = 0.99 ly / y if d is the distance travelled then we knowthat velocity = distance / time then the time will be ?t = d / v = (26.00 ly) / (0.99ly / y) = .......... y(b) the total time elapsed in the frame of earthis ?t + 26.0 y = .......y(c) we can see that the proper time interval ismeasured by a clock in the space ship so we get ?to = ?t / ? ? = 1 / ?(1 -

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