Actual observable horizon for satellites on an orbit line map? On a casual star walk, (for comparison of identifying different objects) I witnessed some meteors, quite a few satellites gliding on their smooth and straight trajectories, and some airplanes with their much brighter (sometimes blinking) lights, lower altitude and the characteristic sense of moving towards and away from me. Suddenly one of the satellites seemed as if its motion had been a bit jittery, and its path started to curve inwards in an asymmetrical, gentle and large C-shape. The airplanes made noise, this one did not. Visually perfectly identical with all of the normal satellites. I had never seen anything like that before so I wondered if it could've been some debris colliding into things, but probably not. The best explanation I have for now is that it apparently might have been a satellite on a Tundra or Molniya orbit, as their ground tracks aren't the usual straight or sine wave shaped trajectories that we're used to. Most satellite tracking websites either didn't seem to have tracking options for those special types at all, or you could only see their locations for now, not a custom time. 

I'm in the capital city area of Finland, and when I saw the object, the time was 23:10 on the UTC+3 time zone, 12th of August 2016. Of what I found, the only strange looking ground track that comes even close would be Molniya 1-62, drawing a loop above Finland. What I can't find is a website that would allow me to rewind time to check where the satellite was at 23:10. But whether or not I should keep searching for that info.

I first have this question: If I look at the satellite tracks going across a map, how do I determine how far a satellite would be visible when viewed from the ground? If I looked at similar tracks for airplanes, it's much easier to understand that the ground area from which an airplane can be spotted doesn't span vast distances, but how this compares to a satellite is difficult to imagine as we don't perceive them in a three dimensional space, but spots gliding across the flat surface of a dome.
It is not that satellite. As it passes over Finland, it has an altitude of 27000km and a magnitude of about 12. You won't see it. All Molniya orbits are similar.

The website Satflare to shows the region in which satellites are visible (it uses a blue ring around the satellite) Your satellite was so high that it was visible from nearly the whole hemisphere.

I won't try to identify your object, except to say that an object as described is not in orbit.