Relativity, time difference from two planets

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SUMMARY

The discussion focuses on the relativistic time difference between two stars, C and D, as observed from two planets, A and B, moving at a relative velocity of 0.7c. Planet A observes star D being born 10 years before star C, while planet B notes that star C is located 20 lightyears farther than star D. The calculated time difference in planet B's reference frame is Δt' = -5.6, indicating a misunderstanding of the relativistic equations, particularly the application of the Lorentz transformation.

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Homework Statement


Two planets A and B have relative velocities 0.7c.
They can observe the birth of two stars, C and D.
According to planet A, star D was born 10 years before star C was born.
According to planet B, star C was born 20 lightyears farther than star D.
What is the time difference between the birth of the stars in the reference frame of planet B.



The attempt at a solution
S: Planet A
S': Planet B

β=0.7 → γ=1.4

Δt'=γ(Δt-βΔx)
Δt'=-5.6

I assume this is incorrect.
I am really struggling with relativity, and my textbook only has a short section which doesn't explain too much. Any help will be appreciated.
 
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I assume this is incorrect.
Because the time period ended up negative?
Apart from that I cannot see what you did - you appear to have plugged some unspecified numbers into an equation.
 

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