Dear JupiterAsc,
In the past when I have been asked a technical question about astronomical ephemeris calculation it usually means someone is developing their own astrological software program or app. I will reply to your question in that spirit.
For the calculation of planetary(and Solar) positions, the equation of time(difference between mean and true solar time) should not be needed; the position of the Sun and other Planets can be calculated exactly for any given instant in time.
What is needed is a calculation called Delta-T, which is similar in some ways to the equation of time, and what I originally thought you meant by your question before reading it again more carefully. I have spent some time writing this reply so I will post it anyway in the hope some might find it interesting.
Trying to make it as simple as I can : The earth rotates at a variable rate, that is, given an absolutely regular clock the time for 1 solar day is not the same in May 2014 as it was in January 1AD. Even though this difference might be very slight, it accumulates to a significant level over the course of hundreds of years. This presents a problem for the developers of astronomical ephemeris, as the position of a planet at a given point in time needs to be calculated with reference to an absolutely regular clock. This theoretical absolutely regular clock time is called “ephemeris time”. The difference between the local time on earth as defined by the earth's rotation, and this absolutely regular clock is called “Delta-T”. The calculation of Delta-T is necessary for all astrological software programs, and can amount to quite a substantial difference, especially for times in antiquity. The truth is that there is no really good and verified model of Delta-T, there are simply best guesses, usually based upon recorded astronomical phenomena in antiquity and the local time when they were observed. This means that, for example, it is not possible to know with certainty the minute of arc the sun was at the time of Julius Caesar's birth. Most professional level astrological software programs(including Prometheus) agree with each other as to this position because they all use the Swiss Ephemeris internally to do the astronomical calculations. This should not be taken as a sign that these values are in any way definitive.
The first program that we did at Capricorn Astrology Software was AstrologyExplorer3D version 1.0. In this program, we did not use the Swiss Ephemeris, but instead developed our own ephemeris based upon NASA's JPL Horizons, which we used as a baseline to verify our calculations. JPL Horizons did(at the time we created AstrologyExplorer3D ~ 2007 or so) differ from the Swiss Ephemeris calculations by quite a bit, especially for times in antiquity as both systems used different formulae to calculate the Delta-T. (Just to be clear we are not in any way endorsed or affiliated with JPL).
My advice for anyone wishing to create their own astrological software, regards calculations such as Delta-T, and the other myriad of calculations needed such as aberration, parallax, light-time correction and so on is :
1. Dont. Get and use the Swiss Ephemeris instead. The price for the professional licence will greatly pay for itself in the time you dont need to spend developing features for your ephemeris. Ultimately this was our main consideration in switching from a custom-written ephemeris to Swiss Ephemeris.
2. If you must develop your own ephemeris, get a copy of “The Explanatory Supplement to the Astronomical Almanac”
http://www.amazon.com/Explanatory-Supplement-Astronomical-Almanac-Urban/dp/1891389858. This book is not an easy read, be warned, but contains much of the theory and formulae needed to create an ephemeris, and we found it a valuable reference. Also, once you are finished with it, it may be profitably used as a gift for your least favourite friend.
3. The JPL horizons system
http://ssd.jpl.nasa.gov/horizons.cgi was invaluable to our development efforts as it allowed us to test each part of the calculations step-by-step from the initial positioning of the planets in ephemeris time as cartesian coordinates through to the final visual position of the planets. Make sure you use an equally good system to test your results against as you go, it will make life a whole lot easier.
4. Remember developing an ephemeris is a non-trivial task and using quality software development tools is a must. I dont want to stir up any controversy so I wont recommend any specific software, just make sure there are excellent debugging facilities and preferably edit-and-continue, which I certainly found very valuable on this task.
Peace be with you,
Gavin
welcome.