2010A&A...522A..60L


Query : 2010A&A...522A..60L

2010A&A...522A..60L - Astronomy and Astrophysics, volume 522, A60-60 (2010/11-1)

Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations.

LASKAR J. and BOUE G.

Abstract (from CDS):

Since the original work of Hansen and Tisserand in the XIXth century, there have been many variations in the analytical expansion of the three-body disturbing function in series of the semi-major axis ratio. With the increasing number of planetary systems of large eccentricity, these expansions are even more interesting as they allow us to obtain for the secular systems finite expressions that are valid for all eccentricities and inclinations. We revisited the derivation of the disturbing function in Legendre polynomial, with a special focus on the secular system. We provide here expressions of the disturbing function for the planar and spatial case at any order with respect to the ratio of the semi-major axes. Moreover, for orders in the ratio of semi-major axis up to ten in the planar case and five in the spatial case, we provide explicit expansions of the secular system, and simple algorithms with minimal computation to extend this to higher order, as well as the algorithms for the computation of non secular terms.

Abstract Copyright:

Journal keyword(s): celestial mechanics - planets and satellites: dynamical evolution and stability - planetary systems - methods: analytical

Simbad objects: 11

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Number of rows : 11
N Identifier Otype ICRS (J2000)
RA
ICRS (J2000)
DEC
Mag U Mag B Mag V Mag R Mag I Sp type #ref
1850 - 2021
#notes
1 HD 12661 PM* 02 04 34.2883519451 +25 24 51.514208219   8.16   7.0   K0V 240 1
2 HD 69830 PM* 08 18 23.9469692487 -12 37 55.810202572   6.74 5.95     G8:V 481 1
3 HD 74156 PM* 08 42 25.1221445320 +04 34 41.146391815       7.2   G1V 209 2
4 HD 80606 PM* 09 22 37.5769478105 +50 36 13.434928660   9.78 9.00     G8V 293 2
5 HD 102272 * 11 46 23.5354467416 +14 07 26.353806918   9.71 8.71     K2 50 1
6 BD-07 4003 BY* 15 19 26.8271336166 -07 43 20.190958776 13.403 11.76 10.560 9.461 8.911 M3V 562 2
7 HD 168443 PM* 18 20 03.9331764016 -09 35 44.609316076   7.62 6.92     G6V 290 1
8 HD 169830 * 18 27 49.4852008378 -29 49 00.705771732   6.406 5.902 7.01   F7V 255 1
9 HD 183263 * 19 28 24.5715522357 +08 21 29.004325092   8.51 7.86     G2IV 107 1
10 HD 202206 PM* 21 14 57.7684954746 -20 47 21.162361638   8.79 8.07     G6V 203 1
11 HD 217107 ** 22 58 15.5411942071 -02 23 43.387117210   6.919 6.163     G8IV/V 344 1

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2021.09.23-03:46:59

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