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As an arts student, I really find those cosmological questions hard to understand and hence come here to seek your kind help.

The Hubble constant $H_0$ is estimated to be about 65 km/s/Mpc, where 1 Mpc (megaparsec) is around 3.26 million light-years. At what distance would galaxies be moving away at exactly the speed of light? (I found that there is something called Hubble Radius, but is this the same as Hubble Radius?) If there were galaxies farther than the Hubble radius, how would they appear to us?

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Possible duplicate: physics.stackexchange.com/q/12049/2451 –  Qmechanic Apr 2 '13 at 13:36
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That's a very, very good question! Actually, the point you are addressing is the reason why physicists coined the term "observable universe". Those galaxies moving away from us with a speed bigger than the speed of light will never be visible (in the light they emit right now) to us and are outside the so-called "Hubble sphere". The distance you are looking for is $\frac{c}{H_0}$.

So as sad as it may sound, every second more and more galaxies and astronomical objects are leaving the observable universe, never to be seen again.

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The Hubble sphere is not a horizon - in fact there are galaxies receding faster than $c$ now that we will be able to see eventually. –  Chris White Jul 26 '13 at 19:15
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The Hubble sphere is the locus of points where the Hubble flow is equal to c. The Hubble sphere is not an event horizon.

All observed objects with a redshift greater than about 1.46 are outside the Hubble sphere. In other words, these objects are receding superluminally. Furthermore, these objects were outside of the Hubble sphere, and were receding superluminally at the time the light was emitted.

The diameter of the observable universe is greater than the diameter of the event horizon. We will never observe events that are currently happening outside of the event horizon, but we can still see events from galaxies that are currently outside of the event horizon via the light they emitted long ago.

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