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

In summary, the problem asks for the time it takes for light from galaxy X to reach our galaxy, given that galaxy X starts emitting at t = tH/1000 (14 My) and the proper distance between X and our galaxy is 10 Mly at that time. The relevant equations are V=HD and Lp=Cth*ln(z+1)/z, where Lp is proper length at time emitted and Cth is Hubble length. To solve the problem, the Hubble law equation can be integrated to get an exponential for D, which can then be set equal to x=ct, where c is the speed of light.
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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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1. What is the speed of light?

The speed of light is approximately 299,792,458 meters per second in a vacuum, which is the fastest known speed in the universe.

2. How do you calculate the time it takes for light to reach a certain distance?

You can calculate the time it takes for light to reach a certain distance by dividing the distance by the speed of light. The formula is t = d/c, where t is time, d is distance, and c is the speed of light.

3. Does light travel at the same speed in all mediums?

No, light travels at different speeds in different mediums. For example, light travels slower in water than in air. This is due to the different densities and properties of the medium.

4. Can light travel instantaneously?

No, light cannot travel instantaneously. It may seem that way to us because light travels so fast, but it still takes time for light to travel from one point to another.

5. Why is the speed of light considered a universal constant?

The speed of light is considered a universal constant because it is the same for all observers, regardless of their relative motion. This is a fundamental principle of Einstein's theory of relativity.

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