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Unit 7: Astrophysics Page 38
whatsoever! The observer in the But according to the twin in the
plane doesn’t experience slow rocketship, it takes only 7.5 years
motion or anything else strange to reach the star 10 years light
like that. In fact, the watch on her distant, using the equations for
wrist still ticks by as it always has. time dilation.
She does not notice anything
unusual in her reference frame. You really don’t need to know this,
but if you’re curious, here’s the
What time dilation really says is equation for figuring this out:
this: suppose there are a set of
identical twins on Earth. One twin
gets into a rocketship and travels t ' t= 1 v- 2
at 0.8c to a star 10 light years
from Earth.
t’ is the time for the observer
traveling at 0.8c.
v is the ratio of the traveling speed
over c, so for 0.8c/c this becomes
v = 0.8.
t = the time for the Earthbound
twin.
A light year is a measure of t '= 12 5 . years 1- ) 8 . 0 ( 2
distance, not time. It’s the distance
light travels in a year. Light year is
abbreviated by ‘ly’. So the speed of
So t’=7.5 years!
light is one light year per year.
Imagine the same star trip, but
The twin still on Earth sees the
now the ship turns around and
other reach the star in 12.5 years:
returns back to earth. According to
the Earthbound twin, the whole trip
Time = distance divided by speed:
takes 25 years. But according to
Time = 10 ly divided by 0.8 ly per the traveling twin, it took only 15
year to give 12.5 years. years. Now we have a set of
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