Calculate the date and time given by the position of the sun (azimuth and altitude), as well as latitude and longitude

Question

In this regard, it is extremely useful question regarding the finding of the azimuth and height of the sun at a given date and coordinates. I want to find the opposite: times and dates when the sun will be in this position of the sky.

So I wonder if anyone can help with an existing formula or a modification related to it.

My current idea was to take two ranges with a difference of a couple degrees for both: one for azimuth (120-123 degrees) and altitude (18-21 degrees). Then write an algorithm to iterate through all days / times and check if certain ranges exist during that time. Looping through these days and using the attached algorithm does not mean that Big Big Small, nor will it be the best for performance.

Any help or advice appreciated, please.

Thanks.

Answer 1

There is useful material here (see links - in particular [12] - [15])

https://en.wikipedia.org/wiki/Position_of_the_Sun

One of the problems is that if you use this to define things like “on which days the sun will be right above the“ Heel ”in Stonehenge in Z-thousands of BC,” then there will be many sources of errors besides the precession and / or nutations (earthquakes change the period of the Earth's rotation, when the Sun is close to the horizon, you will receive some significant refraction). There is also http://www.stargazing.net/kepler/sun.html . However, since there are many days and days when the sun is in a certain position, the method of guessing the date and time window, and then Newton-style iteration, is iteratively probably the best. Perhaps if you could give more information about why you are trying to find the answer (ie, "When the shadow of an oak falls on a buried treasure ..."), could we be more useful?

Answer 2

After some thought, you can get this date:

if (ang>=0.0) date = (21.March) +ang*(21.June -21.March )/(23.4 degrees); else date = (21.September)-ang*(21.December-21.September)/(23.4 degrees); 

• the dates are pretty simple.
• ang - the current angle between the plane of the ecliptic and the plane of the equator of the Earth.
• must be measured during the day !!!

• if you measure the height of the sun (at your latitude) in astronomical drowsiness , then:

   ang = height - (90 degrees - your latitude) 

• to convert height measured anytime you need to apply vector math
• see calculating the angle between two planes
• see image for clarity

To calculate the time during the day, you will need to search

• standard time conversion (UTC) and stellar time
• It’s also a good idea to look for a sundial design that includes all calculations in geometric form.

Do not forget that this approach does not include precession, nutation ...

• if you consider this, then this task will become unsolvable due to the intersection of the path of the heavenly dome of the sun, which leads to several solutions for any given position of the sun.
• Fortunately, the precession is too slow, and we can skip it for several thousand years.
• and nutation has a small radius (only affects accuracy)