Potential of a gaussian ring. A new approach

Kondratyev, B. P.

doi:10.1134/s0038094612040053

Cited by 20 publications

(8 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…where is the height of the test particle above the equatorial plane. The remaining coefficients and in potential (11) are equal to (12) The quantity in ( 12) is the volume-averaged radius of the body.…”

Section: Azimuthally Averagedmentioning

confidence: 99%

See 1 more Smart Citation

Secular Evolution of Rings around Rotating Triaxial Gravitating Bodies

Kondratyev

Корноухов

2020

Astron. Rep.

Self Cite

View full text Add to dashboard Cite

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 of this body and a Gaussian ring. With 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 and 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 days and the period of the forward of the apside line precession is . 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 . This confirms the adequacy of the method.

show abstract

Section: Azimuthally Averagedmentioning

confidence: 99%

“…The mass element of such a ring in an angular interval is (6) where is the angle of the true anomaly and is the eccentricity of the orbit. In the final analytical form, the Gaussian ring potential was found in [11] (see also [12]). In [13], the problem of the mutual energy of two coplanar gravitating Gaussian rings was solved.…”

Section: Introductionmentioning

confidence: 99%

Secular Evolution of Rings around Rotating Triaxial Gravitating Bodies

Kondratyev

Корноухов

2020

Astron. Rep.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Однако пространственный потенциал эллиптического кольца Гаусса долгое время оставался неизвестным и в общем аналитическом виде принципиально новым методом был получен в работе [4] (см. также [5]):…”

Section: Introductionunclassified

“…, a 1 , e 1 ) в точках второго (повернутого на угол β) внутреннего кольца Гаусса с параметрами (m 2 , a 2 , e 2 ). заданном потенциале ϕ из (24) от первого кольца Гаусса вклад во взаимную гравитационную энергию W mut двух колец от элемента массы второго кольца dm 2 будет равен dW mut = −ϕdm 2 , где[4] …”

unclassified

Взаимная Энергия Колец Гаусса

Кондратьев¹,

Корноухов²

2019

Журнал Технической Физики

View full text Add to dashboard Cite

A problem of mutual potential energy of two elliptical gravitating (or electrostatically charged) Gaussian rings is formulated and solved. The rings are coplanar, and their apsid lines generally have an angle of inclination to each other. The mutual energy of the rings is found in quadratic approximation with respect to ring eccentricities e _1 and e _2. At the first stage, the potential of the Gaussian ring is represented as a series in terms of eccentricity and determined at the points of another elliptical ring (note theoretical importance of such a result). Linear (with respect to quantities e _1 and e _2) terms are absent in the expression for the mutual energy of the rings, and the coefficients of the second-order terms ( $$e_{1}^{2}$$ and $$e_{2}^{2}$$ ) are equal to each other. Only one coefficient of mixed term ( e _1 e _2) is determined by the tilt angle of the apse lines. Such a result can be used to easily determine the moment of force between the rings that is needed for the study of small mutual oscillations of the Gaussian rings.

show abstract

“…In the general (nondegenerate) case, the spatial potential of the elliptical Gaussian ring was obtained by Kondratyev (2012).…”

Section: Introductionmentioning

confidence: 99%

Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

Kondratyev

2014

Sol Syst Res

Self Cite

View full text Add to dashboard Cite

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5 : 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravita tional forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simulta neous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6′′/yr and the period yr. These results are close to those obtained in the general theory (25.93′′/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β 1 ≈ 0.8403504° (Saturn) and β 2 ≈ 0.3409296° (Jupiter) around the point which is located at an angular dis tance of 1.647607° from the ecliptic pole.

show abstract

Potential of a gaussian ring. A new approach

Cited by 20 publications

References 1 publication

Secular Evolution of Rings around Rotating Triaxial Gravitating Bodies

Secular Evolution of Rings around Rotating Triaxial Gravitating Bodies

Взаимная Энергия Колец Гаусса

Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

Contact Info

Product

Resources

About