First Year Special Relativity Question

[NotAnAstrologer]

Homework Statement

Planets A and B are 10 light years apart in the reference frame of planet A. A deep-space probe is launched from A, and 5 years later (in reference frame A) a similar probe is launched from B. Does a reference frame exist in which these two events (a) are simultaneous and (b) occur at the same position. *Note*: Parts (a) and (b) are separate from each other so, you have to find one reference frame where they are simultaneous and then another where they occur at the same position. Δx = 10 Ly, T@Event 1 = 0 years, T@Event 2 = 5 years.

Homework Equations

In the textbook this is part of the time dilation section so... T_b = γT_a, Lorentz Transformations, s² = (cΔt)² - Δx² ?

The Attempt at a Solution

I tried to solve it using the space-time interval but, I think it might have something to do with the Lorentz Transformations and Time Dilation equations.

Thanks for your help.

 

[vela]

What exactly did you try? Show your work.

 

[NotAnAstrologer]

What exactly did you try? Show your work.

Erased it or threw it out because I thought it was wrong. I still have the diagram I drew though and I wrote down all the givens. Tbh, the more I think about it the more lost I get. No idea where to start without a velocity.

 

[vela]

Sounds like you need to do a bit more studying then before attempting this problem.

 

[phinds]

Sounds like you need to do a bit more studying then before attempting this problem.

+1 on that.

 

[NotAnAstrologer]

Actually I think I figured it out. T_a = T_b, using this knowledge I'm using one of the Lorentz transformation equations to isolate for V.