Deriving formula ∆t=Lv/c^2 using special relativity

[DonutMaster]

Hello,

There is this formula ∆t=Lv/c^2 I can't remember how it's called, but it is used to determine time difference between two clocks (one is at rest and the other is moving speed of v). L is the distance between two clocks. How do you derive this formula using special relativity?

Example could be: Spaceship is moving towards Earth speed of v, distance between spaceship and Earth is L, find the time difference between clock on Earth and spaceship.

Thank you for your answers

 

[Mentz114]

Welcome. I've not seen that formula before. Where did you get it ? It is true that two observers in uniform relative motion will measure the others clock as slower in their coordinates. The formula is $t'=t/\sqrt{1-(v/c)^2}$.

 

[Nugatory]

It comes from "Introduction to Classical Mechanics With Problems and Solutions" by David Morin, Cambridge University Press. But L is not the distance from the Earth to the spaceship, it's the distance in the spaceship frame between two events that are spatially separated and simultaneous in the spaceship frame.