Directions for Reading Lunar Ephemeris with JPL Horizons

The JPL HORIZONS system provides data on the apparent positions, lighting, and orientations of solar system bodies as observed from any location at any date/time. Results are based on the definitive JPL numerical integrations of planetary positions. Through the web interface, the user is able to specify the viewing geometry, and select the parameters of interest.  The results are then returned as a table listing the values of the selected parameters at any desired interval over any desired time span.  The operation is much simpler than it may at first appear.

The following directions explain, as an example, how to determine the position, lighting conditions and phase/librations of the Moon from Padua on the night of 30 November 1609.

1. Go to the HORIZONS Web-Interface at:

  http://ssd.jpl.nasa.gov/horizons.cgi

You will see a screen with a section of “Current Settings” with six options that can be changed.  Under that is a button that says “Generate Ephemeris”

2. Under “Ephemeris Type”: leave the setting at its default (OBSERVER).

3. Under “Target Body”, click “change”.  
a.	In the box that says “Lookup the specified body:” enter Moon and click Search.
b.	From the options offered, select Moon [Luna]

4. Under “Observer Location”, click “change”.  
a.	In the box that says “Lookup Named Location:” enter Padua and click Search.
b.	From the options offered, select Padua [Code 533] (or whatever location is desired).  The purist can enter the exact coordinates of Galileo’s house (if known) in “Specify Observer Coordinates” (but that would be overkill by a large margin).

5. Under “Time Span”, click “change”.  
1.	In the box that says “Start Time” enter 1609-11-30 12:00 (times are in UT)
2.	In the box that says “End Time” enter 1609-12-01 12:00
3.	Set the box that says “Step Size” to  1 minute (or whatever is desired)

6. Under “Table Settings”, click “change”. 
 
a.	Under “Select observer quantities from table below:”
a.	First click the button near the top that says “none” (this will clear all the check boxes).
b.	Check the following boxes:
i.	“4. Apparent AZ & EL” (this gives the position of the Moon’s center in the local sky)
ii.	“10. Illuminated fraction” (this gives the observed phase)
iii.	“14. Obs sub-lng & sub-lat” (this gives the librations)
iv.	“15. Sun sub-long & sub-lat” (this defines the lighting conditions – terminator position relative to surface features)
c.	Other parameters may be of interest (for example the N pole orientation).  Whatever is selected, there will be a brief explanation of each in the output.
b.	In “Optional observer-table settings:”
a.	Under Angle Format select decimal degrees.
b.	Under skip daylight check as desired (there is always a flag in the output telling if the Sun is up)
c.	Under CSV format, check as desired.  A CSV output file can be opened as a spreadsheet with EXCEL.  Otherwise a plain text format (fixed column widths) is easier to read.
d.	Set other selections as desired.  For example, there is an RTS mode available which will suppress all output expect a single line at each Rise, Transit and Set of the target object.

7. Under “Display/Output”, click “change”.   Select whatever format is desired.  I prefer plain text or download/save .

8. Having done the above, the display should look like this:

Current Settings
Ephemeris Type [change] : 	OBSERVER	
Target Body [change] : 	Moon [Luna] [301]	
Observer Location [change] : 	Padua [533] ( 11°52'17.4''E, 45°24'00.7''N, 43.7 m )	
Time Span [change] : 	Start=1609-11-30 12:00, Stop=1609-12-01 12:00, Step=1 m	
Table Settings [change] : 	QUANTITIES=4,10,14,15; angle format=DEG	
Display/Output [change] : 	download/save (plain text file)	

9.  Click the Generate Ephemeris button.  In the present case you will be asked to select a destination for the output, otherwise it will display directly on the screen.

10. A portion of the resulting output looks like this:

***************************************************************************************
 Date__(UT)__HR:MN     Azi_(a-appr)_Elev   Illu% Obsrv-lon Obsrv-lat Solar-lon Solar-lat
***************************************************************************************
1609-Nov-30 15:30 *m  197.5797  19.9605  14.844 353.82719   1.43347 128.57094   1.04032
1609-Nov-30 15:31 *m  197.8132  19.9094  14.847 353.82402   1.43360 128.56248   1.04030
1609-Nov-30 15:32 Cm  198.0465  19.8577  14.850 353.82086   1.43374 128.55402   1.04029
1609-Nov-30 15:33 Cm  198.2795  19.8053  14.854 353.81770   1.43386 128.54556   1.04027
...
1609-Nov-30 18:50  m  238.0800  -0.8129  15.595 353.33754   1.41274 126.87911   1.03717
1609-Nov-30 18:51  s  238.2525  -0.9562  15.600 353.33603   1.41254 126.87065   1.03715
1609-Nov-30 18:52     238.4249  -1.0999  15.604 353.33454   1.41234 126.86219   1.03714

As explained at the end of the output table, the “*” in the third column of the first three entries means the upper limb of the Sun is above the horizon at those times (hence it is “daylight”).  Thus we see the Sun setting from this location at 15:32 UT (changing to “C” = Civil twilight).  The refracted center of the Moon is at an altitude of 19.8577° and the (theoretical) phase is 14.850% illuminated.  

The sub-observer point is at 353.82086°(lon)/1.43374°(lat).  This is conventionally expressed as saying the librations are -6.17914°(lon)/ +1.43374°(lat). That is, greater than normal amounts of the west (Grimaldi) and north (Plato) hemispheres are visible.  Specifically the center of the apparent disk is located at 6.17914°W/+1.43374°N in the selenographic system, which is about midway between the craters Schröter and Mösting E. Ptolemaeus would be to the east of center on the observed lunar disk (to the right in the modern north-up view).

The sun (at 15:32 UT) is over a point at 128.55402° (lon -- measured to the east from central meridian) and 1.04029°N (lat).  The Sun’s longitude determines the terminator position near the equator, and the Sun’s latitude determines the twist of the terminator (CW or CCW and by how much).  The Sun’s longitude is conventionally expressed as the “colongitude” which is simply 90° - longitude of sub-solar point.  In this case the colongitude is 90-128.55402 = -38.55402°, but since colongitudes are usually expressed as positive numbers, one adds 360° to obtain the positive equivalent: 321.44598°.  

The final three lines shown above represent the setting of the Moon.  The “s” symbol in the third column means that the Moon’s refracted upper limb disappears below the horizon at 18:51 UT.  The Sun’s selenographic longitude (which determines the terminator position) has moved by  128.55402-126.87065 = 1.68337° compared to where it was at 15:32 UT (local sunset). 

Conclusion: on 30 Nov 1609, from Padua, Italy, from sunset to moonset, the Moon could be observed for about 3h 20m (from ~15:32 UT to ~18:51 UT), during which time the Sun’s colongitude advanced from 321.446 to 323.129°, with the Sun’s latitude at about 1.04°.

Notes: 

1.	Although JPL HORIZONS gives the sub-observer and sub-solar points to many decimal points, when checked for a geocentric observer these values tend to differ from those listed in the Astronomical Almanac -- supposedly based on the JPL ephemeris -- at the level of 0.01-0.02°.  I don’t know the reason for the discrepancies.
2.	The lighting at any specific point on the Moon’s surface (Sun’s local elevation and azimuth) can be determined by comparing the coordinates of that point with the coordinates of the sub-solar point using the usual rules of spherical trigonometry.  In particular the Sun’s distance from the local zenith is the angle measured along the great circle between the two points.

-- Jim Mosher (May 19, 2008)