- #1
whatisreality
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Homework Statement
I'm finding this very hard to get my head round! There's earth, and a star which is 6ly away, in the same reference frame. A starship sets out from the star, and another ship leaves Earth at the same time. Each one has ##v=0.6c##. What is the relative speed of the starship as seen by the Earth ship?
The starship explodes after it's a quarter of the way there. When do passengers on the Earth ship see the explosion? Their clock starts counting at departure.
Homework Equations
The Attempt at a Solution
For the first bit, from the velocity addition formula ##v'=0.88c##.
Second bit: Really struggling. According to a hint we were given , to solve this, I need to work out when in the Earth and star's frame the Earth ship it sees the explosion, and where it is at that moment.
If $v'=0.88c$, then ##\gamma = \frac{1}{1−0.88^2}##, and it sees 6ly as ##\frac{6ly}{\gamma}##. So in the Earth ship's frame the starship traveled 0.3384ly of 1.3536ly when it explodes. The speed of light is invariant, so the light from the explosion reaches the Earth ship 0.3384 years = ##1.07\times 10^7## seconds later.
So this was what I had done before I was given the hint, and the hint says to do something completely different, because my way is wrong. Why is it wrong? And how am I supposed to work out when the Earth ship sees the explosion in the Earth's frame? Thanks for any help!