# The Equation of Time is the difference between our standard clock time and the time that would be based on the exact position of the Sun in the sky, for example, that measured by a sundial.
# The two are different because of two specific reasons:
1. The eccentricity of the Earth's orbit causes us to speed up and slow down in different parts of our annual orbit.
2. The Earth's axis is tilted to our orbit, and so the Sun's apparent motion along the (tilted) Ecliptic has a varying effect when viewed along the Equatorial plane.
After taking care of the conditions of the change in eccentricity of the Earth's orbit and its elliptical nature, the average number of days in a year turn out to be 365.2490448790509.
Using this number, we can calculate as follows:
The program flow was similar to your program with the number of weeks averaged to be = (average number of days in a year)/7. Also the accuracy of pi was taken to 100 digits.
The answer turned out to be equal to 32,758,501.32966996 as against your time_formula answer of 31,545,739.32
MY FORMULA FOR TIME---------
360/7=51.42857143/12.57146=4.0908988864/4=1.022724716*51=52.15896051*7=365.1127236*24=8,762.705366*60*60=31,545,739.32 SECONDS IN A YEAR TAKE AWY FROM THE NUMBER OF SECONDS IN A YEAR WITH ATOMIC SIDEREAL TIME
365.256363051 average days in a sidereal year*86,400 average seconds= 31,558149.76- 31,558,515.36=365.5957 seconds/60=6.093261667
minutes difference in a year..
Now Amie we reverse the formula to convert sidereal time into 360 days.
365.356363 52.17948042 1.023127067 *4=4.092508268 51.448804= 360.141628
Simple divide instead of multiply and multiply instead of divide and reverse the formula and subract .141628 days.
12,638.592 seconds difference from a perfect circle that is 360 days.!!
This is just tremendous Amie you can prove it by converting any size elipse into a circle come up with a formula that does that...
Our formula is 100% accurate as we can see by reversing it and converting and elipse into a circle.!!
Houston we have a problem.
When we convert 360.141628 with the formula we get 31,571,338.63
Take it form 31,558,149.76
And ou get 13,188.8724
Seconds difference from sideral time and sidereal time.
Maybe it is an error on the calculator.
Or maybe it is because it is not a perfect circle so the formula does not work forwards.
Or maybe it has to do with the precision of Pi which would be good as it means more digits or pi makes it more accurate.
But we know it is not a perfect circle so it cannt be converted perfectly into an elipse.
Maybe you can correct the formula so that it gives the right value for sidereal time.m
More problems when we use the clock formula value for time and reverse the signs from divison to multiplication.
We get 360.1458002
So it should give us 360 reversing signs on a calculator isn't terriby accurate try it on matlab
take the two figure away from one another and we get the very accurate -4.1722*10^-03 of a day.
Which is 6.007968 minutes.. How about that Aimie it is six minutes difference..........................141628-.1458002= 6.007968 minutes.
TIME GOES BOTH WAYS BACKWARD AND FORWARD.
If we reverse the formula to get 360 days then we reverse sidereal time to get 360.1389338.
The difference between a circle of 360 degrees and 360.1389338= 3.3344112 hours difference. 200.064672 minutes.
12,003.88032.
1.25012*10_04
7.50072*10-03 seconds in a year.