saturnLs

saturnLs converts between Saturn solar longitude, Ls, and date. It iterpolates ephemeris output by JPL HORIZONS to convert between Ls and date with an error less than the day-to-day change in Ls. Functions are provided to convert among Ls, Gregorian calendar date, UNIX timestamp, and Julian date.

I intend to update this to calculate solar longitude of the Saturn barycenter rather than the planet itself, since this is not affected by the orbits of the moons (see "Additional details" section here), but for now that remains a project for future me.

Command line usage

The command line interface (CLI) attempts to distinguish between an Earth date or Ls and then converts to the other. If no argument is supplied, it returns the current Ls.

$ python saturnLs.py -h
usage: saturnLs.py [-h] [-S SATURN_YEAR] [-j] [-s] [-x] [date_or_Ls [date_or_Ls ...]]

positional arguments:
  date_or_Ls                       earth date or Ls

optional arguments:
  -h, --help                       show this help message and exit
  -S SATURN_YEAR, --saturn-year    SATURN_YEAR provide SY argument
  -j, --julian                     use Julian date
  -s, --simple                     simple output
  -x, --extended                   extended date range (1890 to 2160)

Examples

Converting Earth date to Ls:

$ python saturnLs.py
 Ls(now) = SY 3, 133.42°
$ python saturnLs.py 2013-01-2
 Ls(2013-01-2) = SY 3, 40.7329°
$ python saturnLs.py -s 2013-01-2
 3 40.7329
$ python saturnLs.py -x 1960-01-2
 Ls(1960-01-2) = SY 1, 106.439°
$ python saturnLs.py -x 1897-3 1955/4/18 'September 5, 1977' now
 Ls(1897-3) = SY -1, 62.8762°
 Ls(1955/4/18) = SY 1, 54.2137°
 Ls(September 5, 1977) = SY 1, 327.966°
 Ls(now) = SY 3, 133.417°

Converting Ls to Earth date:

$ python saturnLs.py 324
 Date(SY 3, 324°) = 2036-04-07 15:12:44.677901268
$ python saturnLs.py -j 324
 Date(SY 3, 324°) = 2464791.161006
$ python saturnLs.py -S 2 324.23
 Date(SY 2, 324.23°) = 2006-10-30 10:48:27.212989330
$ python saturnLs.py -sS 2 324.23
 2006-10-30 10:48:27.212989330
$ python saturnLs.py -sxS 0 324.23
 1947-12-11 04:35:18.865188956
$ python saturnLs.py -j -sxS 0 324.23
 2432530.691191
$ python saturnLs.py -xS 0 324.23 83.45 61.2
 Date(SY 0, 324.23°) = 1947-12-11 04:35:18.865188956
 Date(SY 0, 83.45°) = 1928-06-14 11:03:26.997027636
 Date(SY 0, 61.2°) = 1926-06-15 23:53:17.381674290

disclaimer

This grew out of my attempts to understand Saturn's orbit, specifically as it pertains to seasonal weather on Titan, but it is not being actively developed. I am posting this project in the hope that someone else may find it useful. Although I would like to develop this further to be more user-friendly and generalizable, that may never occur.

Feel free to contact me if you are interested in contributing or if you have an idea for improvements.

definitions

Temporary list of definitions from saturnLs.py:

• Ls: Solar longitude, apparent longitude of the sun seen from Saturn as defined in JPL Horizons.
• SY: Saturn year number where SY 1 is the Saturn year starting September 21, 1950.
• Ls2: Solar longitude since the beginning of SY 1 starting September 21, 1950.
• SCET: SpaceCraft Event Time (from Cassini), time in seconds since January 1, 1970 (UNIX epoch).
• JD (or JDUT): Julian Date, UT.
• datetime: Python datetime object (including numpy.datetime64, pandas.Timestamp, and astropy.time.Time).
• datestr (or datestring): Date and/or time as a string.

usage

Although there are plans to write a command-line tool using saturnLs, it is currently just a python library. Several functions are currently available for converting between Ls and dates, though there are plans to improve the API, possibly based on the astropy Time or the pandas Timestamp types.

examples

Convert a date string to Ls2:

> datestr = "2005-01-14 13:37:00"
> saturnLs.datestr_to_Ls2(datestr)
array(660.23240127)

Convert a date string to Ls (relative to the respective Saturn year):

> saturnLs.datestr_to_Ls(datestr)
300.23240126594817

Convert Ls2 to datetime:

> saturnLs.Ls2_to_datetime(660.232)
Timestamp('2005-01-14 13:20:23.619411230')

Convert between Ls2 and Saturn year and Ls:

> saturnLs.Ls2_to_SYLs(660.232)
(2.0, 300.23199999999997)
> saturnLs.SYLs_to_Ls2(SY=2, Ls=300.232)
> 660.232

details

Dates are in Universal Time (UT), defined in HORIZONS as follows:

This can mean one of two non-uniform time-scales based on the rotation of the Earth. For this program, prior to 1962, UT means UT1. After 1962, UT means UTC or "Coordinated Universal Time". Future UTC leap-seconds are not known yet, so the closest known leap-second correction is used over future time-spans.

dependencies

required

• python>=3.6
• numpy
• pandas

optional

• scipy Interpolations are done by scipy.interpolate.interp1d, and np.interp is used as a fallback.

ephemeris data

saturnLs can work with two different data sources: raw HORIZONS output, or the reduced output saved as a csv file. While the relevant data in both files is identical, the csv file is preferred, as it is significantly smaller and faster to load.

csv ephemeris

Several of the fields in the DataFrame can be calculated from date and Ls, so function load_csv_ephem is provided to do this when a csv file is loaded.

> df = saturnLs.load_csv_ephem("saturn-Ls-sparse.csv")
> df
           date       JDUT          SCET          Ls2          Ls   SY
0    1890-01-01  2411368.5 -2.524522e+09  -743.278567  336.721433 -2.0
1    1890-03-29  2411455.5 -2.517005e+09  -740.190532  339.809468 -2.0
...         ...        ...           ...          ...         ...  ...
1141 2159-05-28  2509765.5  5.976979e+09  2551.005581   31.005581  8.0
1142 2159-08-23  2509852.5  5.984496e+09  2553.809076   33.809076  8.0

[1143 rows x 6 columns]

By default, saturnLs loads the csv file whos path is specified by the variable ephem_csv. Included are two csv files that have been reduced from HORIZONS output. Solar longtidue, Gregorian calendar date, and Julian date are tabulated in the files saturn-Ls-sparse.csv and saturn-Ls.csv, at intervals of 87 days and 12 hours, respectively. An interval of 87 days was chosen to minimize the error in the interpolated Ls (when compared with the 12-hour HORIZONS output). Apparenntly due to oscillations caused by Titan, the interpolation error is very sensitive to the sampling interval.

loading HORIZONS ouput

saturnLs provides the function load_ephem to parse raw HORIZONS output (csv format) and load it into a pandas arrray. To load a new text file conaining HORIZONS output, run the following:

> import saturnLs
> df = saturnLs.load_ephem("saturn-Ls-1970_2040-sol.txt")
> df
                     date       JDUT          SCET          Ls2          Ls   SY
0     1970-01-01 00:00:00  2440587.5  0.000000e+00   224.558213  224.558213  1.0
4     1970-01-03 00:00:00  2440589.5  1.728000e+05   224.633295  224.633295  1.0
...                   ...        ...           ...          ...         ...  ...
51132 2039-12-29 12:00:00  2466152.0  2.208773e+09  1091.520676   11.520676  4.0
51136 2039-12-31 12:00:00  2466154.0  2.208946e+09  1091.587601   11.587601  4.0

[51134 rows x 6 columns]

The data loaded into df can then be saved using the function save_csv_ephem as follows:

> saturnLs.save_csv_ephem(df, fname="saturn-Ls.csv")

This saves a csv file with the date, JDUT, and Ls columns.

todo

• make CLI for Ls, date, JD
• improve loading performance
• find a better way of dealing with saturn years
• make more portable
• switch to "mean solar longitude" (planet system barycenter)
• generalize to other planets