Getting in is the easy part. Though getting out is virtually impossible. Last time I did so, I found the Sun does no damage and was unable to blow myself up. Eventually I had to DC, reconnect, Alt F4 at the time of connecting and trip the anticheat so it reset me at the last docked base. Pretty dodgy but It was the only way even with a smart guy I was talking to on Skype, figured was feasible. I don't know if they changed it since then. Bless my laggy connection, I feared I'd lose a CAU 8 Osiris in there. I guess slow connections are good for situations like that.
You can get in and exit from the outer sphere. However, to exit from the inner one, you need either ship with a jump drive with you, or a dockable object (so you can exit the same way you entered), since the invisible Nomad Gate is not normally dockable. There are none inside, though. The nomnom city doesn't have a docking option. You'd either have to make a POB there (trolololo))), or bring a ship with a docking bay, which will have to stay inside and sundive in order to return.
My ship automatically exploded one time I tried to relog, I should mention that.
Last time I checked I could get in to the outer sphere but couldn't get back out ("Dock denied"). I repeat, I am talking about the outer sphere here, the one with the floor-like giant structure.
Though its possible to enter the sphere, I've also been warned not to do again after I got in (with about 7 people at the time, see Explorers post)
Apparently last time I was in there, the person who I asked to help us get out stated that there was no way out and to boot it, the admins had to delete some files each time people went in there. I don't know if this is still the case but ya