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.