Calculating Spacetime Interval: Alpha & Beta Supernovae

[2RIP]

Homework Statement
The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes.

An alien spacecraft passing through the galaxy finds that the distance between the two explosions is 120 ly. According to the aliens, what is the time between the explosions?

Relevant equations
c^2*t^2 - x^2 = c^2(t')^2 - (x')^2 The attempt at a solution
I tried using the spacetime interval equation but the distances are too small to see a difference and gives me a wrong answer. Then i did not include c^2 with the equation and i got the correct answer. Which is 67.1 years. I also tried to multiply x^2 and (x')^2 with c^2 and got the same answer. Is it under specific units, like light years, where we can neglect the c^2 or did I just used the wrong equation in the first place?

 

[Shooting Star]

Lightyear is the dist light travels in 1 year, so it's equal to c*1 year, and already the c is inside it, if you measure time in years. That's why you didn't have to multiply by c^2.

 

[ogb p]

As a scientist, it is important to consider the context and units when using equations to solve problems. In this case, since we are dealing with distances in light years, it is appropriate to neglect the c^2 term in the spacetime interval equation. This is because the speed of light, c, is already accounted for in the conversion from time to distance in light years. Therefore, your approach of neglecting the c^2 term in the equation was correct and led to the correct answer of 67.1 years. It is important to always check the units and context when using equations to ensure accurate solutions.