There is a field in astrology called rectification, to find out your exact birth time.
"Astrology rectification is the branch of astrology that uses past events and various astrology techniques to determine the time of birth when it is unknown."...
astro.com (& any other astro-website) can't be so accurate.
Because not just every degree but even minutes & seconds are important for good astro-reading.
You have to find a astrology software, I recommend free Zet9 http://www.zaytsev.com/downloads.html
There you can adjust to show fixed...