DAILY SUN TABLE

Most recent version at www.Pietro.org

 

Contents

Introduction
Data Input Instructions  

 Introduction

             
What is This? 
The DAILY SUN TABLE is an Excel 2000 spreadsheet that will determine daily solar phenomena
at a location for a whole month.  For each day the local time of the Sun's rise, transit, set and
time above the horizon is displayed in the Results Table.  Distributed as FREEWARE, this file can
be distributed freely as long as no modifications are made.  See the legal section for details.
   

  Fig #1: Input/Output Section Overview (V. 1.0.2 and up)

Daily Sun Table Screenshot

Results Table Uses          
This data is useful and educational.  Plan your trip to Alaska, Sweden or the tip of South America
based on the amount of sunlight at various times of the year.  Determine how many hours
between sunset and sunrise for astronomical observing at various locations (sorry, no
twilight calculations in this version). The backyard sundial should show high noon at the
transit time – if not there may be a problem with orientation. Also the difference between transit
time and 12:00 PM is the correction to add or subtract from your sundial that day to determine
civil time.            
             
How Was This Done?          
The calculations for this spreadsheet were taken from the "bible" of celestial calculations:
Astronomical Algorithms by Jean Meeus.  In testing, the accuracy of the results
were matched by tables in the Astronomical Almanac and the U.S. Naval Observatory
website.            
             
Other Data            
If you've ever tried to calculate rise, set and transit of a body using the "recipes" in the
Astronomical Algorithms, you'll find that dozens of preliminary calculations must first be made. 
Many of these offer interesting results, for a celestial mechanist, in their own right.  Extending off to
the right of the Results Table are columns of these preliminary calculations.  Each column
contains an embedded Excel comment with a page or equation number from the
Astronomical Algorithms to explain what that column is calculating.  Constants used by equations
can be found above many columns.  Armed with the context and results of the calculation, an
interested person could extend the worksheet to achieve other results.  For each date in the
spreadsheet you will find calculated information for:  
             
  Julian Centuries from J2000      
  Sun's Mean Longitude        
  Moon's Mean Longitude        
  Sun's Anomaly, Equation of Center and Longitude  
  Moon's Longitude Ascending Node of Mean Orbit  
  Sun's Apparent Longitude        
  Obliquity and Nutations of the Ecliptic      
  Sun's Apparent Right Ascension and Declination  
  Sidereal Time at Greenwich (UK) Meridian @ 0 Hours UT  
  Horizon to Noon Angle        
  Sun's Interpolated Apparent Right Ascension at Transit and Local Hour Angle
  Sun's Interpolated Apparent Right Ascension/Declination at Rising and Local Hour Angle
  Sun's Interpolated Apparent Right Ascension/Declination at Setting and Local Hour Angle
             
View Reference Comments        
View single comments by placing cursor over cells flagged with the comment triangle in the upper-right 
corner.  Keep a comment in view by right-clicking the cell and choosing "Show Comment."  View all
comments at once by using "View/Comments" off the main menu.  Comments prefixed with "AA"
are references to:          
   Astronomical Algorithms,  Jean Meeus, Willmann-Bell, Inc., 1991 2nd Printing
             
Fig #2: Comments for Extended Data

Problems/Questions?
Installation of the Analysis ToolPak may be required. See Tools/Add-Ins… on the Excel menu. 
Post questions on the Message Board at www.Pietro.org or e-mail them to:
Astro-Lib@Pietro.org.

 Input Time and Location Data

Fig #3: Input Section Details
Select the "Input-Output" tab to input data after reading these directions. On that sheet
the nine dark-gray fields at the top are for input of time and location data.  Details for
these fields are listed below.  Click the blue-underlined hyperlinks for websites
that will help you determine what numbers to enter.    
             
LONGITUDE
Requires three fields for degree, minute and second from the prime meridian. In the 
Americas check the "West?" box. In Europe, Asia and Africa uncheck the box.
A decimal display of your input is shown to the right.
LATITUDE
Requires three fields for degree, minute and second from the Equator. Southern hemisphere 
users should uncheck the "North?" box. A decimal display of your input is shown to the right.
START DATE
This field is for date input in standard Excel format. The date entered here will be the first date
on the Results Table. Thirty-one days of data will be displayed in the Results Table. 
TIME ZONE: DIFFERENCE ADDED TO UT...
This consists of a number field and check box for your time zone. Enter the number of hours to 
add to Universal Time (what many call Greenwich Mean Time, Zulu Time, etc.) to get the time in your 
time zone. This value will be the number of time zones you are from Greenwich, England.
In the continental USA the four time zones run are follows: EST: 5; CST: 6; MST: 7 and PST: 8. 
During Daylight Savings Time (Summer Time) check the "Summer Time?" box to add 1-hour to the
local time zone. Note that some States and Indian Reservations opt-out of Daylight Savings Time.
LEAP SECONDS CORRECTION
Enter in this field the number of seconds that Universal Time (UT) differs from Dynamical Time (DT). 
DT is a uniform time based on physical theory and UT varies as the Earth's rate of rotation changes. 
This difference increases when a leap-second is added to the official master clock that determines
civil time throughout the world.  Recently there has been a leap second about every 18-months -- but
the need is based on physical observations.  There was no plan to implement a leap second in the first
half of the year 2000, so the default (DT-UT) value of 64-seconds will probably be good until at least
2001.  You can check for changes since these words were written by clicking the section heading
and downloading the list of historic and current leap seconds from the U.S. Naval Observatory
(USNO).  As of this writing the last correction was January 1, 1999.  
             
The full explanation for the leap-seconds is a bit tricky because it involves several time standards.  The
USNO listing shows the difference between International Atomic Time (TAI) and Coordinated
Universal Time (UTC).  (The initials don't match the names because the official designations are in
French.)  The reason these atomic time-scales differ is that leap seconds are added to UTC to keep
it within 0.9-seconds of UT as the Earth's rotation (generally) slows.  Therefore UTC = UT +/-
(0.0...0.9).  When a leap second is inserted into the UTC clock, it takes 61-seconds to complete
that minute.  Therefore the UTC atomic clock falls behind the TAI atomic clock.  This is why the
TAI-UTC listing shows a positive number and UTC = TAI - Leaps, where Leaps is the number of
leap seconds.  DT in turn is 32.184-seconds ahead of TAI: DT = TAI + 32.184.  This to give it
continuity with an older system called Ephemeris Time (ET).  So the difference DT-UTC = (TAI +
32.184) - (TAI - Leaps); which means: DT-UTC = 32.184 + Leaps.  That leads us to determine the
quantity we need for our calculation: DT-UT = 32.184 + Leaps +/- (0.0...0.9).  For our purposes you
can round this value to the nearest second.  Historic, current and predicted values of DT-UT are
published yearly in the USNO Astronomical Almanac (pages K8, K9) available at many libraries.
             
Click these links for more on the Astronomical Almanac and the companion Explanatory Supplement:
Astronomical Algorithms, Jean Meeus, Willmann-Bell, Inc., 1991 2nd Printing
Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann, University Science Books, 1992
             
             
Entire contents Copyright 1997-2002 by Pietro Carboni. All Rights Reserved.