Expert: Tom Whiting - 6/8/2009

Question
QUESTION: Is there a difference between midnight (12:00 am) and astronomical mid-night when the sun is at nader?  If so, how can the time of astronomical mid-night be calculated given the longitude, latitude and a particular date?

ANSWER: Hi Syed,
Yes, there is a big difference betweeen astronomical midnight
and standard time midnight of 12 am. and the same is true for
astronomical high noon 12 pm also....it applies to both.
First, us stupid humans add one hour (except for Hawaii, Arizona,
and parts of Indiana, who are all sane people)...called Daylight
savings time, although us astronomers prefer the term for DST
Daylight Stupid Time.
So that artificially adds one hour.  Then our standard time system
is based correctly on the 75, 90, 105, 120 etc. degree meridan of longitude, so you have to add 4 minutes of time if you are west of one of those standard meridians.  For instance, I'm at 80 degrees W Longitude which is 5 degrees west, or 20 minutes of time added
to the Eastern STandard time 75 degree longitude. So I add
1 hr 20 minutes, so astronomical high noon is at 1:20 pm EDT for
the 80 degree longitude, and thus astronomical midnight is at
1:20 am EDT for the 80 degree longitude. It's that simple.

{If you are east of a standard meridian, then you simply subtract
4 minutes of time per degree of longitude east of the standard}.

You didn't give your longitude, so I can't calculate it for your
location, but that's how you do it.
Latitude and date have nothing to do with it, except for that Daylight Saving Time...once that is not used in October thru February, then there is no need to add that one hour....just make the longitude time correction of 4 minutes of time for every one degree of longitude west of your standard meridian.  During those months, our astronomical noon is at 12:20 pm and astronomical midnight is at 12:20 am for 80 W. Longitude.

Oh, and nadir would not be the correct term....nadir is opposite the zenith by definition...astronomical noon and astronomical midnight are when the sun is the highest on YOUR meridian (a line directly overhead from due north to due south) and 'lowest' (midnight) is the opposite of that point, which is not the nadir.
Hope this helps,
Tom Whiting
Erie, PA  (at 80 degrees W.Longitude)

---------- FOLLOW-UP ----------

QUESTION: Tom, thanks for the explanation.  However, based upon my
very little knowledge gained from googling, I realize that
the 4 minute difference is an approximation.  We somehow
have to factor in something called the equation of time to
get a better result.  Based on the 4 minute difference, the
astronomical mid-night for Chicago will be (90-87.65)*4=9.4
or 12:51 am adding DST.  An online application gives the
answer as 12:59 Further more, their time changes with dates.    
I would appreciate your giving me a formula that is more
accurate than the 4 minute approximation.

Thank you
Syed

Answer
Hi Syed,
Yes, you are correct...I did not factor in the equation of solar time where the sun runs slow or fast due to our elliptical revolution around the sun. I didn't realize that you needed that information to that degree of accuracy. I just assumed that you wanted a pretty good approximation, not counting a fast sun or slow sun.
Well, I can't help with the formula (if there even is one) for a fast or slow sun across the sky. What I use is a Sky & Telescope chart or graph of same, and I see by that graph that during the month of June, the variation of solar time is less than 3 minutes.  Looks like the zero date is on or about June 10th. In July the sun runs slow up to about 6 minutes and by the end of August, they are even again (Solar time is zero change).  The most deviation occurs around November 1st where the sun is about 16 minutes fast, then even again around Christmas, then runs about 15 minutes slow around February.
Sorry, but that's the best I can do for you with regards to a "fast" or "slow" sun and the equation of time.  I never knew anyone who wanted that kind of accuracy for any one specific location for astronomical midnight...I see no purpose in that accuracy, even people looking for the gegenschein  (counterglow exactly opposite the sun)....needs that accuracy.
Clear skies,
Tom Whiting
Erie, PA