Suppose your friend mistakes a yardstick for a meter stick and measures the length of an intersection in your neighborhood. Is t
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Answer:
<em>a. 10 years</em>
<em>b. 6 years</em>
<em>c. 12 years behind</em>
<em></em>
Explanation:
speed of light c = 3x m/s
distance of sirius from earth = 8 lightyears = 8 x c x 60 x 60 x 24 x 365 = 252288000c meters
speed of spaceship = 0.8c
time taken to reach sirius = distance covered divided by speed
t = d/s = 252288000c/0.8c = 315360000 sec
<em>1 year = 60 x 60 x 24 x 365 sec = 31536000 sec</em>
315360000 sec = 315360000/31536000 = <em>10 yrs</em>
<em>the time as observed by Goslo will be shorter than the real time as measured within the ship due to relativistic effects. using the relativistic relation for time dilation we have</em>
t' = t
since v = 0.8c
v/c = 0.8
where t' is the relativistic time as observed by Goslo,
t is the time within the ship
t' = 10 x = <em>6 yrs</em>
<em></em>
If speedo turns around immediately after reaching sirius, his total distance will be 252288000c x 2 = 50457600c meter
time taken = 50457600c/0.8 = 630720000 sec = 20 yrs
time within the ship will be calculated from time dilation
t' = t
t' = 20 x = 378432000 sec = <em>12 years behind</em>