J/A+A/471/1069 Lunar ephemeris long-term development (Kudryavtsev, 2007)
Long-term harmonic development of lunar ephemeris.
Kudryavtsev S.M.
<Astron. Astrophys. 471, 1069 (2007)>
=2007A&A...471.1069K 2007A&A...471.1069K
ADC_Keywords: Ephemerides ; Solar system
Keywords: celestial mechanics - methods: analytical - Moon
Abstract:
The aim of this study is to develop new analytical series representing
lunar coordinates to accuracy compatible with the accuracy of the
modern numerical ephemeris of the Moon.
Description:
The files contain numerical coefficients of the Poisson series representing
the geocentric ecliptic spherical coordinates of the Moon R, V and U where
R is the geocentric distance,
V is the spherical longitude,
U is the spherical latitude.
The series are obtained by spectral analysis of the long-term numerical
ephemeris of the Moon LE-405/406 (Standish 1998: JPL IOM 312.F-98-048).
There are two versions of the Poisson series for lunar coordinates R, V, U:
- the complete series, LEA-406a, include 42270 terms of minimal
amplitude equivalent to 1 cm and are valid over 1500-2500.
- the simplified series, LEA-406b, include 7952 terms of minimal
amplitude equivalent to 1 m and are valid over 3000BC-3000AD.
The formulation of the series is:
R = {SUM}[k=1,Records;i=0,2](Aki*ti*cos(Argki))
V = V0(t) + {SUM}[k=1,Records;i=0,2](Aki*ti*sin(Argki))
U = {SUM}[k=1,Records;i=0,2](Aki*ti*sin(Argki))
where
t is the time (TDB) in thousands of Julian years from J2000:
t=(JulianDate-2451545.0)/365250.0;
V0(t) is the mean longitude of the Moon referred to the moving ecliptic and
mean equinox of date as given by Simon et al. (1994A&A..282..663S)
[or use Eq.(37) of the paper];
Aki is the amplitude of the "k"th Poisson term of the order i;
Argki is the four-degree time polynomial argument defined as linear
combination of integer multipliers of 14 variables (Argj, j=1,14):
Delaunay variables l, l', F, D;
mean longitude of the ascending node of the Moon Ω;
mean longitudes of eight major planets λpl;
and the general precession in longitude pA.
So that Argki={SUM}[j=1,14](mkj*Argj+phiki),
where mkj are the integer multiplies and phiki are the phases.
The expressions for Argj are given by Simon et al. (1994A&A..282..663S)
[or use Eq.(38)-(51) of the paper].
The lunar coordinates R, V and U given by the series are referred to
the moving ecliptic and mean equinox of date. Transformation of the
coordinates to the reference frame of the numerical ephemeris
LE-405/406 (defined by the mean geoequator and equinox of epoch J2000)
should be performed with use of the precession quantities as given by
Simon et al. (1994A&A..282..663S) [or use Eq.(52)-(55) of the paper].
A Fortran 77 subroutine for calculation of lunar rectangular
coordinates on the base of the suggested Poisson series and two test
examples are also given.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table6.dat 147 7056 *Complete series for lunar coordinate R
table7.dat 147 10508 *Complete series for lunar coordinate V
table8.dat 147 7366 *Complete series for lunar coordinate U
table9.dat 147 1029 *Simplified series for lunar coordinate R
table10.dat 147 1753 *Simplified series for lunar coordinate V
table11.dat 147 1089 *Simplified series for lunar coordinate U
lea-406.for 108 606 *Fortran 77 subroutine for calculation of lunar
rectangular coordinates
lea-406a.for 107 57 *Test calculation of lunar rectangular
coordinates on the base of complete series
lea-406b.for 107 57 *Test calculation of lunar rectangular
coordinates on the base of simplified series
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Note on table6.dat: The time interval covers the Julian dates 2268932.5
(1500/1/1) to 2634166.5 (2500/1/1). The term minimum amplitude (for Poisson
terms - at the ends of the time interval) is 1cm. The total number of terms
is 10704. The maximum difference between R values given by the complete
Poisson series and numerical ephemeris LE-405/406 is 3.2m.
Note on table7.dat: The time interval covers the Julian dates 2268932.5
(1500/1/1) to 2634166.5 (2500/1/1). The term minimum amplitude (for Poisson
terms - at the ends of the time interval) is 0.0000055arcsec. The total number
of terms is 19116. The maximum difference between V values given by the
complete Poisson series and numerical ephemeris LE-405/406 is 0.0056arcsec.
Note on table8.dat: The time interval covers the Julian dates 2268932.5
(1500/1/1) to 2634166.5 (2500/1/1). The term minimum amplitude (for Poisson
terms - at the ends of the time interval) is 0.0000055arcsec. The total number
of terms is 12450. The maximum difference between U values given by the
complete Poisson series and numerical ephemeris LE-405/406 is 0.0018arcsec.
Note on table9.dat: The time interval covers the Julian dates 625673.5
(3000BC/1/1) to 2816787.5 (3000AD/1/1). The term minimum amplitude (for
Poisson terms - at the ends of the time interval) is 1m. The total number of
terms is 1996. The maximum difference between R values given by the
simplified Poisson series and numerical ephemeris LE-405/406 is 0.20km.
Note on table10.dat: The time interval covers the Julian dates 625673.5
(3000BC/1/1) to 2816787.5 (3000AD/1/1). The term minimum amplitude (for
Poisson terms - at the ends of the time interval) is 0.00055arcsec. The total
number of terms is 3770. The maximum difference between V values given by
the simplified Poisson series and numerical ephemeris LE-405/406 is
0.42arcsec.
Note on table11.dat: The time interval covers the Julian dates 625673.5
(3000BC/1/1) to 2816787.5 (3000AD/1/1). The term minimum amplitude (for
Poisson terms - at the ends of the time interval) is 0.00055arcsec. The total
number of terms is 2186. The maximum difference between U values given by
the simplified Poisson series and numerical ephemeris LE-405/406 is
0.33arcsec.
Note on lea-406.for: The subroutine calculates lunar rectangular coordinates on
the base of either complete series for lunar spherical coordinates
(table6.dat, table7.dat, table8.dat) or of simplified ones
(table9.dat, table10.dat, table11.dat).
The coordinates are geocentric and referenced to the Earth mean equator and
equinox of J2000 (the reference frame of numerical lunar ephemeris
LE-405/406).
The maximum difference between lunar positions calculated on the base of
LE-406 and of the complete series LEA-406a is 10 m over 1500-2500.
The maximum difference between lunar positions calculated on the base of
LE-406 and of the simplified series LEA-406b is 0.9 km over 3000BC-3000AD.
Note on lea-406a.for: This file gives an example of calling code for
calculation of lunar rectangular coordinates on the base of complete
LEA-406a series and the relevant test results.
Note on lea-406b.for: This file gives an example of calling code for
calculation of lunar rectangular coordinates on the base of simplified
LEA-406b series and the relevant test results.
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Byte-by-byte Description of files: table[69].dat
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Bytes Format Units Label Explanations
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2- 6 I5 --- Seq Sequental number of the term
9- 11 I3 --- mk1 Multiplier at the Arg.1, l (G1)
12- 14 I3 --- mk2 Multiplier at the Arg.2, l' (G1)
15- 17 I3 --- mk3 Multiplier at the Arg.3, F (G1)
18- 20 I3 --- mk4 Multiplier at the Arg.4, D (G1)
21- 23 I3 --- mk5 Multiplier at the Arg.5, Ω (G1)
25- 27 I3 --- mk6 Multiplier at the Arg.6 (Me) (G1)
28- 30 I3 --- mk7 Multiplier at the Arg.7 (Ve) (G1)
31- 33 I3 --- mk8 Multiplier at the Arg.8 (Ea) (G1)
34- 36 I3 --- mk9 Multiplier at the Arg.9 (Ma) (G1)
37- 39 I3 --- mk10 Multiplier at the Arg.10 (Ju) (G1)
40- 42 I3 --- mk11 Multiplier at the Arg.11 (Sa) (G1)
43- 45 I3 --- mk12 Multiplier at the Arg.12 (Ur) (G1)
46- 48 I3 --- mk13 Multiplier at the Arg.13 (Ne) (G1)
50- 52 I3 --- mk14 Multiplier at the Arg.14 (pa) (G1)
55- 68 F14.7 km Ak0 Amplitude of the Fourier term
71- 79 F9.6 m/yr Ak1 Amplitude of the 1st-order Poisson term
82- 90 F9.6 mm/yr2 Ak2 Amplitude of the 2nd-order Poisson term
93-109 F17.12 deg phik0 Phase of the Fourier term
112-128 F17.12 deg phik1 Phase of the 1st-order Poisson term
131-147 F17.12 deg phik2 Phase of the 2nd-order Poisson term
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Byte-by-byte Description of files: table[78].dat table1?.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
2- 6 I5 --- Seq Sequental number of the term
9- 11 I3 --- mk1 Multiplier at the Arg.1, l (G1)
12- 14 I3 --- mk2 Multiplier at the Arg.2, l' (G1)
15- 17 I3 --- mk3 Multiplier at the Arg.3, F (G1)
18- 20 I3 --- mk4 Multiplier at the Arg.4, D (G1)
21- 23 I3 --- mk5 Multiplier at the Arg.5, Ω (G1)
25- 27 I3 --- mk6 Multiplier at the Arg.6 (Me) (G1)
28- 30 I3 --- mk7 Multiplier at the Arg.7 (Ve) (G1)
31- 33 I3 --- mk8 Multiplier at the Arg.8 (Ea) (G1)
34- 36 I3 --- mk9 Multiplier at the Arg.9 (Ma) (G1)
37- 39 I3 --- mk10 Multiplier at the Arg.10 (Ju) (G1)
40- 42 I3 --- mk11 Multiplier at the Arg.11 (Sa) (G1)
43- 45 I3 --- mk12 Multiplier at the Arg.12 (Ur) (G1)
46- 48 I3 --- mk13 Multiplier at the Arg.13 (Ne) (G1)
50- 52 I3 --- mk14 Multiplier at the Arg.14 (pa) (G1)
55- 68 F14.7 arcsec Ak0 Amplitude of the Fourier term
71- 79 F9.6 mas/yr Ak1 Amplitude of the 1st-order Poisson term
82- 90 F9.6 uas/yr2 Ak2 Amplitude of the 2nd-order Poisson term
93-109 F17.12 deg phik0 Phase of the Fourier term
112-128 F17.12 deg phik1 Phase of the 1st-order Poisson term
131-147 F17.12 deg phik2 Phase of the 2nd-order Poisson term
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Global Notes:
Note (G1): the arguments are:
* Arg.1 is the Delaunay variable l. Use Eq. (41) of the paper.
* Arg.2 is the Delaunay variable l'. Use Eq. (40) of the paper.
* Arg.3 is the Delaunay variable F. Use Eq. (42) of the paper.
* Arg.4 is the Delaunay variable D. Use Eq. (39) of the paper.
* Arg.5 is the mean longitude of the ascending node of the Moon Ω.
Use Eq. (38) in the paper.
* Arg.6 is the mean longitude of Mercury λMe.
Use Eq. (43) of the paper.
* Arg.7 is the mean longitude of Venus λVe.
Use Eq. (44) of the paper.
* Arg.8 is the mean longitude of Earth λEa.
Use Eq. (45) of the paper.
* Arg.9 is the mean longitude of Mars λMa.
Use Eq. (46) of the paper.
* Arg.10 is the mean longitude of Jupiter λJu.
Use Eq. (47) of the paper.
* Arg.11 is the mean longitude of Saturn λSa.
Use Eq. (48) of the paper.
* Arg.12 is the mean longitude of Uranus λUr.
Use Eq. (49) of the paper.
* Arg.13 is the mean longitude of Neptune λNe.
Use Eq. (50) of the paper.
* Arg.14 is the general precession in longitude pA.
Use Eq. (51) of the paper.
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Acknowledgements:
Sergey Kudryavtsev, ksm(at)sai.msu.ru
(End) Sergey Kudryavtsev [SAI, Russia], Patricia Vannier [CDS] 04-Jun-2007