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Kunhee
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Homework Statement
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A spaceship is approaching Earth from the far side of the sun. The Earth and sun are 8 light minutes apart and the ship is traveling at .8c. Two events are indisputable. 1) the ship is at the sun 2) the ship is at the earth. Assume that the Earth and sun are at rest according to each other. The ship is detectable only after it passes the sun.
a) In the Earth's frame, how much time separates events 1 and 2?
b) In the Earth's frame, how much distance separates events 1 and 2?
c) How much time after first detecting the ship do humans on Earth have to prepare for its arrival?
d) In the ship's frame, how much time separates events 1 and 2?
e) In the ship's frame, how much distance separates events 1 and 2?
f) In the ship's frame, how far apart are Earth and sun?
The Attempt at a Solution
The Lorentz factor is 5/3 when we plug in .8c. I am having trouble setting up the problem.
What is the difference between a and c? Or e and f?
a) the time that separates the two events is simply t = d/v = 8c/.8c = 10 minutes
b) the distance that separates the two events is simply 8c = 8 light minutes.
c) Earth has 10 minutes to prepare for the ship's arrival.
d) t' = (5/3)(10) = 16.67 minutes
e) x' = (3/5)(8c) = 4.8 light minutes
f) Earth and Sun are 4.8 light minutes apart
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