Question

18. A space traveler takes off from Earth and moves at speed 0.9800c toward the star Vega, which is 26.00 ly distant. How much time 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?

Answer #1

(a) speed of traveler = 0.98c

Distance of planet from earth = 26 light year

Time elapsed in earth frame = 26/0.98 = 26.5306 years

(B)after 26.5306 the traveler will reach Vega and will send the signel and this signal will travel with a speed of light c and will reach earth in 26 year

So total time taken by signal to reach earth = 26.5306 + 26

= 52.5306 years

(C)time elapsed in earth frame = 26.5306 years

Time elapsed in traveler frame = 26.5306(1 -
v^{2}/c^{2})^{0.5}

= 26.5306(1 -
(0.98c)^{2}/c^{2})^{0.5}

= 26.5306×0.198997 = 5.28 years

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