"What was that spot in the sky?" - How to identify satellites First of all sorry for my immense ignorance in this matter and for all the stupid things I'll say here.
Yesterday, May 22nd 2017, I removed the telescope from its dusty box1 and decided to watch Jupiter. After about 2 minutes of observation I spotted something across the sky [X-files music in background], it was a little less bright as Jupiter's &quot;Galilean&quot; moons2.
Below you can see an accurate [Windows Paint] reconstruction of the fact I saw in my telescope. The red line indicates the direction of the thing (from right to left outside of the telescope).

Available data to help identify the object:
Time: May 22nd, 2017 @ 22:12 UTC
My position: {
    Lat: 41.720194062015096
    Long: 12.713427287843729
    Sea level: 540 m
    }
Direction: Probably South // The direction of Jupiter from that location at that time (didn't have a compass)
Telescope: {
    Focal length: 700 mm
    Diameter: 60 mm
    Lens: H 20 mm
    }

I only have data of the ISS and Iridium insights on an Android app3 so I am here to ask if there is some tool with which I can identify by myself as many satellites as possible across the sky.
Notes:

Winter is not nice with observers from here
Not visible at naked eye
I can almost certainly say that the &quot;thing&quot; was not the ISS or one of the Iridium satellites

P.s: I will post here what the object was (with reference if possible) as soon as I identify it for curious people like me.
This will be hard to track down. I'd suggest looking at something like SATVIEW Time Machine. I've entered the location and time you provided (I had to deviate by a few minutes to find something so maybe your time is not 100% accurate) and I can see there were a few satellites flying overhead. With enough work, you may be able to figure out which one was most likely the one you saw based on the Alt-Elev information detailed in the table.

There's plenty of other online satellite tracking websites out there, but keep in mind, most of them aren't going to have everything. And possibly, what you saw is in no database because it's a classified satellite in which case you probably won't find any record of it.