Maybe I am wrong but where did system want a picture? I was under the impression that the information is emough
The need to take a picture at the sync time is irrelevant as with the information asked by system, it can all be done with basic maths. It just needs to know what time the planet will be at at the sync time.
(Below is an example, not actual numbers)
For instance it is 1900local time, 0000 universal, in game time is 1500 with a 30 minute day. If next sync is at 1100 universal then that’s 22 days and 1500in game time at 6am my time.