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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Eqn. of time**

**From:**Frank Reed CT

**Date:**2005 Jan 12, 18:46 EST

Bill, you wrote:

"Are the resulting times at Greenwich?"

Yes. You saw, I think, that the fourth step in my earlier post was to test
a case for 0h UT ("zero hours Universal Time" -- in other words, midnight
at Greenwich for the day just beginning). Actually, there is a small wrinkle to
worry about. The time variable in these calculations is actually dynamical time
("real" time) while UT wiggles around a bit because of the uneven rotation of
the Earth. The difference amounts to about a minute right now, and it will not
affect the outcome of the EqT calculation so you don't need to worry about
it in practice.

And:

And:

"To calculate 2006 it appears one could:

1. Continue the current spreadsheet, with 1 Jan, 2006 DT as 366

2. Use a new Sun mean longitude and anomaly for Jan 1 2006 (which may, or

may not be 280.7506 + 0.9856481*366 and 357.7244+0.9856003*366

respectively)."

1. Continue the current spreadsheet, with 1 Jan, 2006 DT as 366

2. Use a new Sun mean longitude and anomaly for Jan 1 2006 (which may, or

may not be 280.7506 + 0.9856481*366 and 357.7244+0.9856003*366

respectively)."

Yep. Either will work. But the second choice is perhaps pointless extra
work. The spreadsheet software can handle running sequences of serial dates very
easily. Try this (I'm assuming you're using Microsoft Excel, but every
spreadsheet has some similar technique): type the number 38353 in cell A1.
Now put the formula "=A1+1" in cell A2. Then fill down (Edit menu, Fill, Down)
from there for a thousand cells. You should end up with the formula "=A999+1" in
cell A1000 and similarly for every cell in between. Nothing fancy so far: you've
got a serial list of numbers. Next select all those cells (highlight them)
and go to the "Format" menu. Choose "Cells" and then in the dialog that appears
on the "Number" tab, select "Date". This tells the spreadsheet software to
display these serial numbers as dates. The first cell should now "apparently"
show "January 1, 2005" while it's still a number internally. Notice that
the month rollovers, year changes, even leap years occur automatically. Next, in
cell B1, enter the formula "=A1-38353" and fill down from there for a thousand
cells. But this time reformat all the cells in column B as "General" Numbers.
This is exactly that "DT" quantity that we need to calculate everything
else. Now you can go ahead and put the formulas for L, M, and EqT in
succeeding columns just as before. If you want to look at a different stretch of
time, just change the single number in cell A1. It's all automatic. There's lots
of other neat tricks you can do with date formatting and date functions in
spreadsheets. It's worth poking around in the Help for Excel to learn
more.

And you wrote:

And you wrote:

"I have been unable to determine by inspection what the Sun's mean
longitude

actually means or how it is calculated for say, Jan. 1, 2005. Can you shed

some light on that for me please?"

actually means or how it is calculated for say, Jan. 1, 2005. Can you shed

some light on that for me please?"

It's the Sun's mean ecliptic longitude. It's zero when the Sun is at the
vernal equinox and increases steadily at the rate of 360/365.25 degrees per day.
If you look at a star chart that shows the ecliptic with dates along it for the
Sun's position you can see that you have to go about 280 degrees around to get
from the "First Point of Aries" around to that spot in Sagittarius where the Sun
is found on the first of the year.

And:

And:

"3. Same questions for the Sun's mean anomaly."

The mean anomaly is an orbital parameter. It is similar to mean longitude
but measured from the Sun's perihelion instead of from the equinox. You probably
remember that perihelion occurs on Jan. 4 which is why the mean anomaly is just
shy of 360 degrees on Jan.1, 2005.

These two parameters, mean longitude and mean anomaly, are sufficient to
calculate EqT at this level of accuracy because the equation of time has two
basic causes. First, the Sun actually travels faster across the sky when we are
at perihelion. That means that the Sun "gets ahead" of its mean position during
some parts of the year and "falls behind" at other times. Second, because the
ecliptic is tilted, the mean Sun's steady motion is divided into portions which
are north-south and east-west. When the Sun is near the solstices (horizontal
parts of the ecliptic on a star map), its full motion is parallel to the
equator. But near the equinoxes only a fraction of the motion is parallel to the
equator. There are lots of interesting details and animations on this topic at a
web site which has been around almost since the w.w.w. got started. It is www.analemma.com.

-FER

42.0N 87.7W, or 41.4N 72.1W.

www.HistoricalAtlas.com/lunars