Is there an option that allows me to search future skies exactly like the one we see today? How do I access it if it is available? I want to know when or if the sky will appear again as it appears on 09/24/2017?
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You can fast forward time and on the left menu it lets you go to a specific date
That is helpful, however I want the computer to do the work for me. I would like to identify certain constellations, planets, sun, and moon and have Stellarium tell me what dates and time those items will be in the same position in the future.
It's not possible. A better software for that task is some dedicated ephemeris calculator or astronomy calculation library (e.g. NOVAS, the ephem Python package, etc.)