# Calculating Time Dilation of a Rocket.

## Homework Statement

The problem was asking to find the time dilation of a rocket traveling upwards at 100,000 m/s with the reference point being earth for a duration of a day.

1/√(1-(β^2))
Δt = γΔt'

## The Attempt at a Solution

I've calculating gamma to be 1.000000055, but I'm a little confused on where to go next. Do I just multiple gamma by Δt'? However, that gives me an incorrect and unreasonable answer. The answer key says that the answer should be 9ns. Any help is appreciated thanks.

Simon Bridge
Homework Helper
Do I just multiple gamma by Δt'?
Pretty much - decide which observer and which clock.
However, that gives me an incorrect and unreasonable answer.
You probably picked the wrong clock or had the wrong number of nanoseconds in a day or somethinfg like that.
This is why we ask you to show your working - so we can figure out how to instruct you properly.
i.e. over the course of a day, one of the clocks will lose 9ns with respect to the other one. i.e. the question wants the difference between the elapsed times on each clock.

when 1day passes on the Earth, the Earth observer sees the rocket clock to have ticked off 1day+T nanoseconds. How do you find T?

I suspect that the supplied answer is incorrect. Nobody's perfect.

Simon Bridge