The Mishna, Eruvin 4:7, says that someone approaching his home before Shabas can designate a spot between his home and his current location as his Shabas location, and he gets a 2000-ama radius around that spot, so he can go home:

One who was coming on the road and it was getting dark for him, and he recognized a tree or fence and said "My spending Shabas is under it" — he said nothing [because the area under the tree or fence is too large to be designated as a location for these purposes]. "My spending Shabas is at the base of [that tree]" — he [may] walk from the place his feet are in until its base, [up to] 2000 amos, and from its base until his home, [up to another] 2000 amos. It turns out he walks, after it gets dark, 4000 amos.

Then 4:8 continues:

If he doesn't recognize [such a landmark], or is not an expert in halacha [to know that he can use the above rule], and he said [instead] "My spending Shabas is in my location", he has acquired his location for himself, 2000 amos in every direction.

Seemingly, then, this designation from afar must be at a tree or other landmark. "If he doesn't recognize" one, he can't do it. Why is that? Why can't he say "My spending Shabas is at the point 2000 amos in that direction" (pointing, or saying "east")? Why isn't that a good enough designation?

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    Maybe because an Eruv is an extreme leniency in Hilchos Shabbos, and so in order to avoid problems with walking out of the techum - an issur d'oraisa - Chazal wanted to make sure he knows exactly where his techum begins and ends? Not everyone had Rabbah Gamliel's telescope to measure 2000 amos (Eiruvin 43b), nor the ability to focus on exactly how many steps they've taken to measure when they reached 2000 amos from the techum (Yerushalmi Chagigah story about Acher). – DonielF Aug 6 '17 at 5:20
  • @DonielF isn't the deoraisa 12000 amos? (Or something like that) – Heshy Aug 6 '17 at 19:42
  • @Heshy Take another look at Shemos 16, when they venture too far out on Shabbos to collect the man that wasn't there. – DonielF Aug 6 '17 at 19:46
  • @DonielF what does that have to do with the shiur? – Heshy Aug 6 '17 at 19:55
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    @DonielF Rambam Shabbos 27:1. Deoraisa it's 12 mil which is 24000 amos. 2000 is miderabanan – Heshy Aug 6 '17 at 21:23

The Gemara (Eruvin 50b) seems to relate to your question and based on Rashi's explanation you have to designate an identifiable spot.

Even saying "around that stone" is sufficient.

However, just saying "at the 2,000 Ama spot on the horizon" is not considered a designation, since you cannot identify it, so you cannot designate it.

בד''א. דבמקום שאינו מסויים קני ליה מיהא ד''א לשביתה ואלפים מהן לכל רוח: במסיים ד''א. שקבע בד' בהן שהיה לו בהן סימן אילן או אבן ואמר באותן ד' תהא שביתתי:‏

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  • Yes, but… why? – msh210 Aug 6 '17 at 16:09
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    "since you cannot identify it" - since he's essentially "moving homes" for Shabbat to a new location. You can't relocate to "somewhere"; you have to have an exact address. – Danny Schoemann Aug 8 '17 at 12:48

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