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I am struggling on a problem involving 2 events seen in different reference frames and could do with advice or a starting point for this question:

A spaceship approaches a galaxy travelling with a speed of 0.1c relative to the galaxy. The crew on the spaceship observe two supernovae directly ahead in the galaxy. From the relative brightness, they determine that the supernovae are 10 light years apart, as measured in the spaceship restframe. The crew observed the supernovae at exactly the same time. a) Did the supernovae explode simultaneously in the spaceship rest frame? If not,which 1 exploded first, and what was the time delay between them in the spaceship rest frame? b) Astronomers on a planet in the rest frame of the supernovae at the midpoint between them also observe the supernovas. Did the supernovae explode simultaneously in their rest frame? If not, which one do they observe first?<

I assumed in the spaceships restframe there would just be a time difference of 10 years. However I am completely unsure if I am thinking about this question in the right way, and have little idea of how to tackle part b) as the planet being at a midpoint has thrown me off. Any advice, or a link to a similar already answered question would be much appreciated.

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  • $\begingroup$ Make sure to keep your sign conventions right in the calculation. $\endgroup$ – Viesr Dec 10 '15 at 6:27
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Your time difference answer is correct. They did explode at a time difference of 10 years in the spaceship frame. This question isn't a relativity question at all till now and what is given till now is just the data in a clever form to be able to do the part B of the question.

Now coming to part B,

Astronomers are in the middle in the rest frame of the supernovae, hence, for rest frame of the supernovae, Now, for them you've to find the coordinates between the events for the supernovae frame. For them the spaceship is moving at 0.1 c(assuming supernovae are at rest w.r.t. galaxy, this assumption is not from the question), the spatial difference between events for the spaceship is 10 light years for the space ship and time difference between the events is 10 years for the spaceship.

Now you can do the lorentz transformation, and if you find delta t between the two explosions to be non zero for the supernovae frame. It isn't simultaneous in the astronomer's frame. I think the time difference would come out to be something like ~11.8 years. The midpoint of the planet is w.r.t. the galaxy/supernovae frame according to the question.

Also, one can see that since light from first supernovae just manage to catch up with the second supernovae, hence these events are on the light like seperated w.r.t. the spaceship observer. Hence, they can't be simultaneous/time-like for any observer.

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