- #1
zardiac
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Homework Statement
You start at t=0 at rest on Earth and accelerate with uniform acceleration a away form earth.
Find a point in time [itex]t_0[/itex] such that when a beam emitted from Earth at [itex]t>t_0 [/itex]won't catch up.
Homework Equations
[itex]x(t)=c^2/a(\sqrt{1+\frac{a^2}{c^2}t^2}-1)[/itex]
The Attempt at a Solution
I think that light travel with velocity c. So if the beam is emitted at [itex]t=t_1[/itex] then at time t, the beam have traveled [itex] c(t-t_1) [/itex]. So I try to find the solution for [itex]x(t)=c(t-t_1)[/itex], and I end up with the following expression for [itex]t[/itex]:
[itex]t=\frac{a}{2c}\frac{t_1(2-a/c t_1)}{(a/c - a^2/c^2 t_1)}[/itex]
According to this the time would be negatic in the intervall [itex]t_1=c/a[/itex] and [itex]t_1=2c/a[/itex] So I think in this intevall the beam won't be able to catch up, but after [itex]t_1=2c/a[/itex] the time becomes positive again, which I don't know how to interpret.
Am I approaching this problem the wrong way?