How to determine Noon time?
Noon time here refers to solar noon. Solar noon is the moment when the sun transits the celestial meridian – roughly the time when it is highest above the horizon on that day. The celestial meridian is a great circle on the celestial sphere passing through the celestial poles and an observer's zenith. At northern hemisphere, the sun will be at south at noon.
Noon time is different with Duhr time. Refer to hadits xxx, Duhr prayer should be offered a few moment after the noon time as to let the sun moves a bit from its highest position in the day.
The formula is given in xxx. More elaboration on this topic is given in xxx and xxx.