Correcting times for other locations

Times listed in the central Maryland monthly almanacs are for West Longitude 77 degrees and North Latitude 39 degrees. The almanac times are useful for other nearby locations after correcting to the desired location.

The algorithms given here assume a flat earth. This quite adequate for the region of interest (central Maryland area). Extending the corrections too far from this area (at least in longitude) would break down due to object motion (especially the moon).

Rise and set times must be corrected for a difference in both longitude and latitude (twilight times could be corrected the same way as rise/set times, but it will make little difference in practice). Transit times are corrected only for a longitude difference.

What you need to know

You must know your latitude and longitude. If you do not know these coordinates they may be found from one of the following geographic servers:

University of Michigan Geographic Name Server
Opens a new window.
Enter desired location. Ex: frederick,md
Enter exit to exit.
Bucknell Geographic Name Server
Gives a mosaic form.
Enter request the same way as above.
Not as fast and requires an extra download.

Convert coordinates from degrees, minutes, and seconds to degrees.

You also need to know the event time and azimuth.

Computing the time correction

The time correction has two independent components: longitude correction and latitude correction.
Both corrections are signed, be careful to handle the sign correctly.
Both corrections are added to the reference time to get the desired time.

LAT = Observer North Latitude in degrees (like 39.414)
LNG = Observer West Longitude in degrees (like 77.411)
AZI = Event azimuth in degrees (like 98.039)
T   = Event time (like 04:11:58)

Longitude Correction (constant for a given location)
CLNG = (LNG-77)*4 minutes of time

Latitude Correction
CLAT = 5.15*(LAT-39)*tan(AZI-90) minutes of time

This correction does not apply to transit times. Note that 5.15*(LAT-39) is a constant for a given latitude (5.15 = 4/cos(39 deg)).

Check that the latitude correction has the following signs:
   Azi   0- 90: -
   Azi  90-180: +
   Azi 180-270: -
   Azi 270-360: +

An example

The almanac lists the following rise and set times for December 22, 1994 at the reference location of 77 west, 39 north:

Event   Date          Time      Azi (deg)  Alt (deg)     SD (')
 . . .
SRS  1994-Dec-22   07:23:41     119.995     -0.271      16.29
MST  1994-Dec-22   10:05:10     281.994     -0.255      15.30
SST  1994-Dec-22   16:49:33     240.007     -0.271      16.29
MRS  1994-Dec-22   21:32:53      80.485     -0.256      15.37

To find the times at Frederick, MD for that day do the following:

Find the latitude and longitude of Frederick, MD from the Geographic Name Server:

Trying...
Connected to martini.eecs.umich.edu.
Escape character is '^]'.
# Geographic Name Server, Copyright 1992 Regents of the University of Michigan.
# Version 8/19/92.  Use "help" or "?" for assistance, "info" for hints.
.
frederick,md
0 Frederick
1 24021 Frederick
2 MD Maryland
3 US United States
R county seat
A 301
F 45 Populated place
L 39 24 51 N  77 24 39 W
P 28086
E 290
Z 21701 21709

So LAT = 39.414
   LNG = 77.411

The longitude correction is the same for all events.
For this location:
   CLNG = (LNG-77)*4 = (77.411-77)*4 = 1.64 minutes of time.

The latitude correction for ths latitude becomes:
   CLAT = 5.15*(LAT-39)*tan(AZI-90)
        = 5.15*(39.414-39)*tan(AZI-90)
        = 2.132*tan(AZI-90)

For sunrise:
   AZI = 119.995
   CLAT = 2.132*tan(119.995-90) = 1.23 minutes of time.
   CLNG + CLAT = 1.64 + 1.23 = 2.87 = 00:02:52
For sunset:
   AZI = 240.007
   CLAT = 2.132*tan(240.007-90) = -1.23 minutes of time.
   CLNG + CLAT = 1.64 - 1.23 = 0.41 = 00:00:25
For moonrise:
   AZI = 80.485
   CLAT = 2.132*tan(80.485-90) = -0.357 minutes of time.
   CLNG + CLAT = 1.64 - 0.357 = 1.28 = 00:01:17
For moonset:
   AZI = 281.994
   CLAT = 2.132*tan(281.994-90) = 0.453 minutes of time.
   CLNG + CLAT = 1.64 + 0.453 = 2.09 = 00:02:06

        Reference   Corrected   Computed
Event     Time        Time        Time for Frederick, MD
 SRS    07:23:41    07:26:33    07:26:34
 SST    16:49:33    16:49:58    16:49:57
 MRS    21:32:53    21:34:10    21:34:13
 MST    10:05:10    10:07:16    10:07:19

The corrected times for the sun differ from those computed for Frederick by 1 second. The corrected times for the moon differ from the computed by 3 seconds, just about what is expected due to the moon's faster eastward motion through the sky (about 50 minutes later rising time per day is about 2 seconds later rising time per minute. So for this example the expected motion effects are 2 and 4 seconds, again bringing the differences to 1 second).

How far can you push this correction?

I did the same example times for two cases: 5 degrees due south, and 5 degrees due west.

For the 5 degrees due south case the errors were 6 and 5 seconds for the sun times and 13 and 6 seconds for the moon times.

For the 5 degrees due west case the errors were 0 seconds for the sun times and 51 and 27 seconds for the moon times.

These are still likely within the uncertainties due to other effects.