Find how long a beam of light emitted at a certain time takes to reach

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SUMMARY

The discussion focuses on calculating the time it takes for light emitted from galaxy X to reach Earth, given that the light is emitted at time t = tH/1000 (14 million years ago) and the initial proper distance is 10 million light-years. The relevant equations include Hubble's law (V=HD) and the proper length equation (Lp=Cth*ln(z+1)/z). The solution involves integrating Hubble's law to find the distance light travels over time and equating it to the speed of light to determine the arrival time of the light beam.

PREREQUISITES
  • Understanding of Hubble's Law and its application in cosmology.
  • Familiarity with the concept of proper distance in cosmological models.
  • Knowledge of integration techniques in calculus.
  • Basic understanding of the speed of light and its significance in astrophysics.
NEXT STEPS
  • Study the integration of Hubble's Law to derive distance over time.
  • Research the concept of proper distance and its implications in cosmology.
  • Learn about the Hubble length (Cth) and its role in cosmic expansion.
  • Explore the relationship between redshift (z) and distance in an expanding universe.
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in understanding the dynamics of light travel in cosmological contexts.

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Homework Statement

3. 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?



Homework Equations



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

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


The Attempt at a Solution



I'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.
 
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