# How does cosmological horizon depend on position?

Suppose I am at a certain point in the universe, and the cosmological horizon is a distance, $d$ $km$, away from me.

Suppose just beyond the cosmological horizon, say at $(d+1)km$, is the edge of a star called Star X. I cannot observe Star X because it is beyond the horizon. But let us suppose I have a friend who is positioned a distance of $(d - 1)\,\text{km}$ away from me, in the direction of Star X. So from my perspective, the set up will look like this:

Me --------------(($d-1)\,\text{km}$)-----------------Friend---($1\,\text{km}$)----Cos. Horizon---($1\,\text{km}$)---Star X

The numbers enclosed in the brackets represent the distance along that dotted line. That is, there is a distance of $1\,\text{km}$ between Friend and cosmological horizon from my perspective.

Will my friend be able to see star X? I assume his calculation of the cosmological horizon would also be distance $d$, so if he doesn't see star X, does this mean that from his perspective the distance of $1\,\text{km}$, has "expanded" to a distance of $d$ units?.

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Hi Chris. I have a thought that those parameters D+1, X, etc.. could be modified to TeX. –  Waffle's Crazy Peanut Jan 31 at 6:17