# Homework Help: Find how long a beam of light emitted at a certain time takes to reach

1. Nov 9, 2013

### xdrgnh

1. The problem statement, all variables and given/known data
In the model of “Empty Universe” consider a galaxy X, which starts emitting light at time t = tH/1000 (14 My). If, at that time, the proper distance between “X” and our galaxy was 10 Mly at what time the first light from “X” is expected to arrive to our galaxy?

I posted this in the intro physics section because I suspect the math to do this is elementary. However the question is from my level 4000 Cosmology class.

2. Relevant equations

V=HD
Lp=Cth*ln(z+1)/z

Lp is proper length at time emitted and Cth is Hubble length.

3. The attempt at a solutionI'm pretty sure I just need to find how long it takes for the light beam to reach earth from galaxy X. To do that I just integrate the Hubbles law equation and get this exponential for D which is De^(Ht) then set it equal to x=ct where c is speed of light. However I'm being given equations for other things and I don;t know how they are relevant to this problem.