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The new formula for the angular velocity of rotating equilibrium figuresстатья
- Автор: Kondratyev B.P.
- Сборник: ABSTRACT BOOK The Fifteenth Moscow Solar System Symposium, October 21-25 2024
- Год издания: 2024
- Место издания: SPACE RESEARCH INSTITUTE (IKI) OF RUSSIAN ACADEMY OF SCIENCES. Moscow
- Первая страница: 272
- DOI: 10.21046/15MS3-2024
- Аннотация: The purpose of the report is to derive a new formula for the angular velocity of rotation of equilibrium figures of a gravitating fluid. An importantfeature of this formula is that the angular velocity is represented throughthe components of the internal and external parts of the gravitationalenergy of the body. Two variants of deriving the new formula are considered: i) for homogeneous equilibrium figures, and ii) for a wide class of inhomogeneous figures with a polytropic equation of state. The adequacyof the new formula is established and it is proven that for homogeneousbodies this formula gives the known expressions for the angular velocityfor classical Maclaurin spheroids and Jacobi ellipsoids. For the first time, itbecame necessary to express the constant integration of the equations ofmotion through the polytropic index and three global characteristics: mass,total gravitational energy, and rotational energy of the body. The advantage of this formula is that it can describe not only ellipsoidal equilibriumfigures, but also equilibrium figures of any other geometric shape, including toroidal. This expands the scope of application of the theory of equilibrium figures. The developed method is applied to a two-component modelof the dwarf planet Haumea.
- Добавил в систему: Кондратьев Борис Петрович