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Ken Ward's Astrology Pages
Astrology: Calculating Local Sidereal Time using the Midnight Ephemeris.
|We have found Mary's local sidereal time of birth using a
noon ephemeris and on this page we will calculate her local sidereal time again, using the
Her local mean time of birth has been calculated as:
From the midnight ephemeris, the sidereal time at midnight on the day of her birth is:
Mary's Local Sidereal Time of birth is the sidereal time at Greenwich at the instant that Mary was born.
Using the midnight ephemeris, we simply add the local time of Mary's birth to the sidereal time in the ephemeris for her day of birth and make some corrections to find her local sidereal time:
This comes to:
We subtract 24 hours to bring this time within the nornal range:
This is the uncorrected local sidereal time of birth. We need to correct this for the longitude and for birth time.
Because sidereal time is faster than regular time, we need to correct this figure by allowing 10 seconds for every hour of the local mean time. A sidereal day is 4 minutes short of a regular day, so we need to accelerate regular time to accord with sidereal time.
Because we added
The acceleration is 100 +2.5 seconds (or 103 seconds). We add this to our sidereal time so far:
1 hour 13 minutes 42 seconds + 1 minute 43 seconds (103 seconds) =
1 hour 15 minutes 25 seconds
We need a further correction for each 15 degree time zone. This is 10 seconds per zone. Five time zones make 50 seconds. Adding this correction we get the sidereal time for her place of birth as:
Our calculation of Mary's sidereal time with the noon ephemeris gave us this result:
Whereas our calculations with the Midnight Ephemeris gave this result:
The results are near enough.
However, why is there a difference?
There are two reasons for the differences:
It is possible there are very small errors in the ephemeris (unlikely, except for rounding errors!).
The purpose of this section is to explain why there are differences in the calculations using traditional values, such as 10 seconds per hour to allow for acceleration. You can safely skip this section if you aren't interested at the moment in these non-essential details.
The correction of 10 seconds for every hour is near enough, however, for greater accuracy, 1 second should be subtracted from the acceleration figure for every 6 hours.
For example, the sidereal time for the noon ephemeris for 7 May 1982 is:
To get the time for noon we add 12 hours:
Reduce to normal range by subtracting 24:
Add 2 minutes of traditional acceleration correction:
The noon ephemeris says 3 hours exactly. However, by subtracting our 1 second for every six hours, we get the correct figure:
Alternatively we can use the factor 1.002737909 to obtain the correction:
This figure gives us the correct sidereal time at noon:
If you look at the sidereal times in an ephemeris, you will notice that they differ each day by 3 minutes and 56 or 57 seconds, and not by 4 minutes. This means that approximately 1 second for every 6 hours needs to deducted when using the traditional 10 seconds per hour acceleration figure. This degree of accuracy is not needed in practice.
In our calculations using the midnight ephermis, we got the sidereal time as:
1 hour 16 minutes 15 seconds
Applying our rule for "10 hours 15 minutes 40 seconds" we get about 2 seconds, so the corrected sidereal time is:
1 hour 16 minutes 13 seconds
Which is the correct figure.
In this case, the midnight ephemeris required a larger value addition than the noon ephemeris required a smaller value subtraction, the special correction had to be applied to the work with the midnight ephemeris. On other occasions, when the birth is nearer midnight than noon, the calculations with the midnight ephemeris wouldn't require this method.
Errors due to taking the nearest second, etc, can produce small differences in the calculations. Had we taken 102.5 seconds above as 102 seconds, then rounding errors would have occurred.