TOC  | Last Section | Next Section | First Section

nutabl.

A table of nutation in longitude and obliquity

Overview

In addition to precession, the time-varying gravitational effects of the Sun and Moon on the non-spherical Earth drive nutation. Nutation is a small wobble of the Earth's rotational axis with an amplitude of about 9 arcsec and period of up to 18.6 years. Traditionally, nutation is represented by with variations in ecliptic longitude and obliquity (the angle between the ecliptic and the equator). Current models represent the nutation quantities with well-defined series. For efficiency, arc reads a previously generated nutation table for these values. Currently, the nutabl. file is generated yearly by MIT from the 1980 IAU nutation model (Seidelmann, P.K., "1980 IAU Theory of Nutation: The Final Report of the IAU Working Group on Nutation", Celestial Mechanics, Vol. 27, pp. 79-106, 1982, and Kaplan, G.H., "The IAU Resolutions of the Astronomical Constants, Time Scales, and teh Fundamental Reference Frame", United States Naval Observatory Circular No. 163, U.S. Naval Observatory, Washington, D.C., Dec. 10, 1981). This file is made available via anonymous FTP.

The nutabl. file has a two line header which describes the contents of the file followed by the table of values. The format of this file should be considered fixed. The first line of the header is purely descriptive and is ignored. The second describes the ephemeris and contains the following information:

  1. the format for reading/writing the table,
  2. the start time in PEP days,
  3. the stop time in PEP days,
  4. the maximum number of values on any line,
  5. the interval, in days, between entries in this table,
  6. and a scaling factor for the values in the table.
Note: internally, arc keeps the date in a variant of the Julian date called a PEP day to better distinguish it from a true Julian date. The PEP day equals
Julian date + 0.5
or
modified Julian date + 2400001.0.

In the current version of arc, only the start and stop time are read and used. The format for reading these values is: (35x, f7.0, 1x, f7.0). The other parameters are "hardwired" to:

  1. format = (1x, f5.0, 1x, 8(f7.0, 1x), 7x, i2),
  2. the start time is read from the header,
  3. the stop time is read from the header,
  4. values per line = 4, i.e. the four pair of nutation components,
  5. interval = 0.5 days (although positive numbers are used directly, negative numbers are interpreted as 2**interval days, therefore the header value corresponding to 0.5 days would be -1),
  6. and scaling factor = 1.0E-4.

Each line contains the PEP date - 2400000, and the components of the nutation values for that epoch. The first entry is at zero hours of the given start date; subsequent entries are every twelve hours thereafter.

Note: All nutation parameters are in units of 1.0E-4 arcsec. These values are no longer read using the format and scaling factor given in the header and entries must be consistent with this format.

Example 


Nutation ephemeris for Nov 96 - Feb 98    rwk 18 Dec 96
(1x,i5,8i8,8x,i2)                  2450361 2450920  4 -1          1.E-04
 50361   18089  -87411   18101  -87401   18075  -87363   17998  -87303
 50363   17864  -87225   17663  -87134   17392  -87035   17050  -86935
 50365   16635  -86839   16152  -86754   15604  -86686   15002  -86640
 50367   14355  -86622   13677  -86636   12983  -86685   12293  -86771
 50369   11624  -86894   10997  -87052   10429  -87243    9939  -87461
 50371    9540  -87700    9242  -87950    9052  -88204    8969  -88451
 50373    8990  -88681    9101  -88885    9287  -89056    9527  -89186
 50375    9795  -89272   10063  -89312   10304  -89307   10490  -89263
 50377   10597  -89185   10607  -89085   10505  -88972   10288  -88860
 50379    9956  -88762    9521  -88690    9000  -88653    8417  -88661
 50381    7799  -88717    7177  -88824    6580  -88980    6035  -89181
 50383    5566  -89418    5190  -89682    4914  -89962    4744  -90248
 50385    4673  -90528    4694  -90793    4791  -91035    4948  -91247
 50387    5146  -91425    5365  -91568    5587  -91674    5795  -91746
 50389    5974  -91786    6110  -91798    6193  -91787    6214  -91758
 50391    6168  -91716    6052  -91669    5865  -91621    5608  -91578
 50393    5285  -91547    4904  -91533    4473  -91542    4003  -91578
 50395    3509  -91646    3007  -91748    2514  -91886    2050  -92061


 TOC  | Last Section | Next Section | First Section

nutabl.html
January 14, 2000
Steve Hilla