I know somebody allready mentioned it but I wanted to use gifs
Are you kidding us?!! Equinox means half way point......
oh my god...
https://media.giphy.com/media/Ra1bmpxpsppNC/giphy.gif
Did anybody check systems 1182.2ly away from Jotunheim in direction of the Sarasvati?
https://im-01.gifer.com/3euB.gif
What else do we need until we start looking for the system where the player is beamed to at the end of a previous elite game?!
HIP 1182 = UY Sculptoris
HR 1182 exists as well, both are close to the bubble
PRAEA EUQ VA-F D11-11 is 1182.18ly from Jotunheim but there are a lot of others....
I genuinely don't know what most of your post means

As we've said at length:
1) We don't know if the Sarasvati was part of Equinox at all - we only know the logs were on it.
2) We don't know if the Sarasvati was part of Equinox in a significant way (i.e. a pivotal role, like a command ship, so it's position might be irrelevant)
3) We don't know if the Sarasvati has been moved at all over the past 150 years
4) We don't know if the Sarasvati is 150 years old, or if it's a new ship (the design is certainly very much like more modern megaships like the Zurara) that the logs and things were transferred to.
5) We don't know what "Equinox" refers to in this context.
6) We don't know why you'd call the project "Equinox" - for example British military projects have a randomly selected name, i.e. the names don't mean anything. The U.S. Military uses name that are often indicative of the actual project. So, "Equinox" might not really
mean anything.
7) Equinox does mean "half way point", but it also can be used in a couple of other ways (generally related to astronomy)
So sure, there
might be something in a system double the distance between Jotunheim and the Srasvati, it's definitely a good idea - but there's a lot else it could mean too.
a) The project might refer to "the darkest time", for example the Winter Equinox is the darkest point of the year (shortest day) - this might be a poetic way of describing the Thargoid War as being the "darkest point" of human history to date.
b) Equinox might refer to the general idea that the Equinox on Earth is the time when the Sun is almost directly above the Equator (which apparently isn't entirely correct). This might be a reference to a celestial location.
c) Equinox might be another reference to Julian, since there is a "Julian Equinox" in astronomy.
d) Equinox might be referencing the celestial coordinate system: " Thus when specifying celestial coordinates for an object, one has to specify at what time the vernal point and the celestial equator are taken. That reference time is called the equinox of date"
So, as I said, Equinox generally means the mid-point, but that doesn't mean is does mean that in this context, or that it means anything in any context. Sadly. There's no
obvious reason to call the project that -the ship isn't called Equinox, the project is, and there's no specific relation that we know of between the project and the ship other than the project logs were found on the ship.
*note* Yes, the most obvious explanation is that the Sarasvati was the home of Cassandra and the Equinox team, but the point is, we don't
know that.
What else do we need until we start looking for the system where the player is beamed to at the end of a previous elite game?!
You mean Miacke? There's been quite a few attempts to map the location of that system over to ED, since the galaxies aren't the same due to limited capabilities of computers back then compared to now it's a bit tricky. Some people (me included) think that it's probably the system in the Col70 sector that the probes point to, it's in the approximately correct direction and distance (though distances were different in FFE). Some people think it was the opposite way due to the map being reversed, so that would put it on the other side, out Formidine way.
Either way, best guess is that it's rimwards not corewards. Same as FFE. However, if you're relating this to the Equinox project it's worth remembering that Cassandra says quite clearly they don't know where the Thargoids went, and Miacke wasn't located until the crazy antics of that lone pilot in 3252 (and in ED we don't really know if that actually happened! We know the Thargoid ship that was built in orbit of Miacke existed in ED, but there's no telling where it came from.) Because of that it's unlikely they could position the Sarasvati "half way" between anything Thargoid related, since the only place they knew Thargoids were in the 3150's was the Pleiades.
It's also worth remembering that the first part of that story was to go to Polaris where INRA was guarding a Thargoid "transporter" that took you to Miacke, and Polaris is permit locked right now, so it's possible that that device might still be there - but I'm not sure if any of that is related to the Sarasvati, Equinox and Thunderchild, we just have so little to go on.
Definitely worth investing though.