J/A+A/628/A84 Slowly diffusing planetary solutions freq. analysis (Fu+, 2019)
Frequency analysis and representation of slowly diffusing planetary solutions.
Fu Y.N., Laskar J.
<Astron. Astrophys. 628, A84 (2019)>
=2019A&A...628A..84F 2019A&A...628A..84F (SIMBAD/NED BibCode)
ADC_Keywords: Solar system ; Planets ; Ephemerides ; Models
Keywords: methods: numerical - celestial mechanics - ephemerides -
planets and satellites: dynamical evolution and stability - chaos
Abstract:
Over short time-intervals, planetary ephemerides have traditionally
been represented in analytical form as finite sums of periodic terms
or sums of Poisson terms that are periodic terms with polynomial
amplitudes. This representation is not well adapted for the evolution
of planetary orbits in the solar system over million of years which
present drifts in their main frequencies as a result of the chaotic
nature of their dynamics.
We aim to develop a numerical algorithm for slowly diffusing solutions
of a perturbed integrable Hamiltonian system that will apply for the
representation of chaotic planetary motions with varying frequencies.
By simple analytical considerations, we first argue that it is
possible to exactly recover a single varying frequency. Then, a
function basis involving time-dependent fundamental frequencies is
formulated in a semi-analytical way. Finally, starting from a
numerical solution, a recursive algorithm is used to numerically
decompose the solution into the significant elements of the function
basis.
Simple examples show that this algorithm can be used to give compact
representations of different types of slowly diffusing solutions. As a
test example, we show that this algorithm can be successfully applied
to obtain a very compact approximation of the La2004 solution of the
orbital motion of the Earth over 40Myr ([-35Myr,5Myr]). This example
was chosen because this solution is widely used in the reconstruction
of the past climates.
Description:
Plain-text tables providing all terms of R100 in the form of Eq. (31).
Together with the data presented in Table A.2 for computing f, these
two tables can be used to compute the eccentricity and inclination
variables from R100. The errors of R100 as solution representation are
shown in Fig.11. Based on the information in this figure, we expect
that our algorithm should be efficient in producing compact and
precise representations of long-term ephemerides of major solar system
bodies.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
tablea3.dat 102 100 100 coefficients of the decomposition of
z3 (Eq.31) (z3R100.dat)
tablea4.dat 102 100 100 coefficients of the decomposition of
ζ3 (Eq.31) (zeta3R100.dat)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: tablea3.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
2- 4 I3 --- No Index of the term
7- 8 I2 --- g1 Integer coefficients of g1 (Eq. 30)
10- 11 I2 --- g2 Integer coefficients of g2 (Eq. 30)
13- 14 I2 --- g3 Integer coefficients of g3 (Eq. 30)
16- 17 I2 --- g4 Integer coefficients of g4 (Eq. 30)
19- 20 I2 --- g5 Integer coefficients of g5 (Eq. 30)
22- 23 I2 --- g6 Integer coefficients of g6 (Eq. 30)
25- 26 I2 --- g7 Integer coefficients of g7 (Eq. 30)
28- 29 I2 --- g8 Integer coefficients of g8 (Eq. 30)
31- 32 I2 --- s1 Integer coefficients of s1 (Eq. 30)
34- 35 I2 --- s2 Integer coefficients of s2 (Eq. 30)
37- 38 I2 --- s3 Integer coefficients of s3 (Eq. 30)
40- 41 I2 --- s4 Integer coefficients of s4 (Eq. 30)
43- 44 I2 --- s5 Integer coefficients of s5 (Eq. 30)
46- 47 I2 --- s6 Integer coefficients of s6 (Eq. 30)
49- 50 I2 --- s7 Integer coefficients of s7 (Eq. 30)
52- 53 I2 --- s8 Integer coefficients of s8 (Eq. 30)
55- 56 I2 --- r1 Integer coefficients of r1 (Eq. 30)
58- 59 I2 --- r2 Integer coefficients of r2 (Eq. 30)
63- 82 D20.16 --- Absak Amplitude of ak(j) for z3
83-102 D20.16 deg Argakd Phase of ak(j) for z3
--------------------------------------------------------------------------------
Byte-by-byte Description of file: tablea4.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
2- 4 I3 --- No Index of the term
7- 8 I2 --- g1 Integer coefficients of g1 (Eq. 30)
10- 11 I2 --- g2 Integer coefficients of g2 (Eq. 30)
13- 14 I2 --- g3 Integer coefficients of g3 (Eq. 30)
16- 17 I2 --- g4 Integer coefficients of g4 (Eq. 30)
19- 20 I2 --- g5 Integer coefficients of g5 (Eq. 30)
22- 23 I2 --- g6 Integer coefficients of g6 (Eq. 30)
25- 26 I2 --- g7 Integer coefficients of g7 (Eq. 30)
28- 29 I2 --- g8 Integer coefficients of g8 (Eq. 30)
31- 32 I2 --- s1 Integer coefficients of s1 (Eq. 30)
34- 35 I2 --- s2 Integer coefficients of s2 (Eq. 30)
37- 38 I2 --- s3 Integer coefficients of s3 (Eq. 30)
40- 41 I2 --- s4 Integer coefficients of s4 (Eq. 30)
43- 44 I2 --- s5 Integer coefficients of s5 (Eq. 30)
46- 47 I2 --- s6 Integer coefficients of s6 (Eq. 30)
49- 50 I2 --- s7 Integer coefficients of s7 (Eq. 30)
52- 53 I2 --- s8 Integer coefficients of s8 (Eq. 30)
55- 56 I2 --- r1 Integer coefficients of r1 (Eq. 30)
58- 59 I2 --- r2 Integer coefficients of r2 (Eq. 30)
63- 82 D20.16 --- Absak Amplitude of bk(j) for ζ3
83-102 D20.16 deg Argakd Phase of bk(j) for for ζ3
--------------------------------------------------------------------------------
Acknowledgements:
Jacques Laskar, laskar(at)imcce.fr
(End) Patricia Vannier [CDS] 31-May-2019