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

1. Jul 17, 2013

### 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.

2. Jul 17, 2013

### 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 $t'=t/\sqrt{1-(v/c)^2}$.

Last edited: Jul 17, 2013
3. Jul 17, 2013

### Staff: Mentor

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.

Last edited: Jul 17, 2013