J/A+A/324/366Theory of motion & ephemerides of Hyperion (Duriez+ 1997)

Theory of motion and ephemerides of Hyperion Duriez L., Vienne A. <Astron. Astrophys. 324, 366 (1997)> =1997A&A...324..366D (SIMBAD/NED BibCode)ADC_Keywords: Planets ; EphemeridesKeywords: Celestial mechanics - planets and satellites: Hyperion - ephemeridesDescription: In this paper, we present a new theory of motion for Hyperion, defined like in TASS1.6 for the other Saturn's satellites (Vienne & Duriez, 1995A&A...297..588V), by the osculating saturnicentric orbital elements referred to the equatorial plane of Saturn and to the node of this plane in the mean ecliptic for J2000.0. These elements are expressed as semi-numerical trigonometric series in which the argument of each term is given as an integer combination of 7 natural fundamental arguments (Table 3). These series (Tables 4 to 7) collect all the perturbations caused by Titan on the orbital elements of Hyperion, whose amplitudes are larger than 1km in the long-period terms and than 5km in the short-period ones. Taking also account of the perturbations from other satellites and Sun (Table 8), these series have been fitted to 8136 Earth-based observations of Hyperion in the interval [1874-1985]. The resulting series allows to produce new ephemerides for Hyperion, which have been compared to those previously given by Taylor (1992A&A...265..825T): Using the same set of observations and the same way to weight them, the root mean square (o-c) residual of the present theory is 0.156-arcseconds while the ephemerides of Taylor gives 0.203-arcseconds.File Summary:

FileName Lrecl Records Explanations

ReadMe 80 . This file table3 74 7 Fundamental arguments of the theory table4 70 105 Series for element p of Hyperion table5 70 214 Series for element q of Hyperion table6 70 179 Series for element z of Hyperion table7 70 52 Series for element zeta of Hyperion table8 92 46 Solar and short period perturbations of Hyperion tables.tex 102 1029 *Tables 3 to 8 in plain TeX format (1)

Note on tables.tex: in the same form exactly as the corresponding tables published in A&A

Byte-by-byte Description of file: table3

Bytes Format Units Label Explanations

1- 3 I3 --- Num Number of the argument 4- 8 A5 --- Arg Argument, see note (1) 9- 33 D25.15 rad/d Freq Frequency 34- 58 D25.15 rad Phas Phase 59- 74 F16.6 d Per ? Period

Note (1): psi: Synodic argument between Titan and Hyperion tau: argument of the libration pi7: longitude of the proper pericentre of Hyperion pi6: longitude of the proper pericentre of Titan Om7: longitude of the proper node of Hyperion Om6: longitude of the proper node of Titan Om0: longitude of the node of the invariable plane Each argument is (Freq * t + Phas) where: t = Julian Date - 2451545.0

Byte-by-byte Description of file: table4 table5 table6 table7

Bytes Format Units Label Explanations

1- 3 I3 --- Num Number of the term 4- 28 D25.15 rad Ampl Amplitude 29- 32 I4 --- N1 Argument (1) 33- 36 I4 --- N2 Argument (1) 37- 40 I4 --- N3 Argument (1) 41- 44 I4 --- N4 Argument (1) 45- 48 I4 --- N5 Argument (1) 49- 52 I4 --- N6 Argument (1) 53- 56 I4 --- N7 Argument (1) 57- 70 F14.2 d Per ? Period

Note (1): The argument of each term has to be computed as: N1*psi + N2*tau + N3*pi7 + N4*pi6 + N5*Om7 + N6*Om6 + N7*Om0 where psi, tau, pi7, pi6, Om7, Om6, Om0 are given in table3. This is the argument of a cosine in table4, of a sine in table5 and of a complex exponential in table6 and table7

Byte-by-byte Description of file: table8

Bytes Format Units Label Explanations

1- 3 A3 --- Ser Element of Hyperion (1) 4- 28 D25.15 rad Ampl Amplitude 29- 53 D25.15 rad/d Freq Frequency 54- 78 D25.15 rad Phas Phase 79- 92 F14.2 d Per ? Period

Note (1): p7 : perturbation of element p of Hyperion (series in cosine) q7 : perturbation of element q of Hyperion (series in sine) z7 : perturbation of element z of Hyperion (series in complex exponential) zt7: perturbation of zeta of Hyperion (series in complex exponential) The argument of each term is: (Freq * t + Phas), where: t = Julian Date - 2451545.0

Acknowledgements: L. Duriez(End)Patricia Bauer [CDS] 06-Mar-1997

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