Secular Evolution of Rings around Rotating Triaxial Gravitating Bodies
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lar Evolution of Rings around Rotating Triaxial Gravitating Bodies B. P. Kondratyeva, b, * and V. S. Kornoukhova a Faculty
b
of Physics, Lomonosov Moscow State University, Moscow, 119991 Russia Pulkovo Astronomical Observatory, Russian Academy of Sciences, St. Petersburg, 196140 Russia * e-mail: [email protected] Received April 7, 2020; revised May 14, 2020; accepted May 30, 2020
Abstract—The problem of the secular evolution of a thin ring around a rapidly rotating triaxial celestial body is formulated and solved. The technology for calculating secular perturbations is based on two formulas: the azimuthally averaged force field of the central body and the mutual energy Wmut of this body and a Gaussian ring. With Wmut instead of the usual perturbing function, a system of differential equations for the osculating elements of the ring is obtained. An equation is obtained that allows one to find the coefficients of the zonal harmonics of the azimuthally averaged potential of an inhomogeneous ellipsoid using a unified scheme. The method is applied to dwarf planet Haumea with refined masses of the rocky core and the ice shell and the coefficients C20 and C40 of the potential’s zonal harmonics. According to new data, the ring around Haumea has a slight obliquity and must precess. It was established that the period of the retrograde nodal precession of the Haumea’s ring (without regard to self-gravity) is TΩ = 12.9 ± 0.7 days and the period of the forward of the apside line precession is Tω ≈ 8.08 days . It is proven that the 3:1 orbital resonance for the particles of the Haumea’s ring is fulfilled only approximately and the averaging time of additional perturbations at a nonsharp resonance turned out to be an order of magnitude smaller than TΩ . This confirms the adequacy of the method. DOI: 10.1134/S1063772920100030
1. INTRODUCTION The rings around celestial bodies have attracted the attention of researchers for a long time. Of particular interest was the recent discovery of non-planetary rings around asteroid-centaur Chariklo [1–3] and dwarf planet Haumea [4]. These rings do not have shepherd satellites; therefore, their dynamics and evolution are influenced by the central body and must be carefully studied. Dwarf planet Haumea was discovered in 2005 [5] and revolves around the Sun with a period of 281.83 yr. Haumea is comparable in size to Pluto. Although it has a three times smaller mass, it has an elongated shape and rotates very quickly around its axis [6–8]:
T0 = 3.9155 ± 0.0001 h.
(1)
Haumea has two small satellites (Hi’iaka and Namaka) [5, 8, 9], which made it possible to determine its mass as
M = 4.006 ± 0.040 × 1024 g.
(2)
ered, and the following Haumea parameters were refined [4]:
a1 = (1161 ± 30) km, a2 = (852 ± 4) km, a3 = (513 ± 16) km,
(3)
R = 797.6 km, ρ = (1.885 ± 0.080) g/сm3. A more complete approach to studying the problem of rotating ellipsoidal bodies is given in [10]. To determine the Haumea’s space form, a method based on a system of eight equations was developed. This method con
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