Protoplanetary three-body problem with variable masses and its solutions
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Keywords:
three-body problem, secular perturbations, protoplanets, variable masses, analogues of the Poincare second systemAbstract
Two protoplanetary three-body problem is considered in the case when the masses of all three bodies vary isotropically in different rates . It is assumed that the mass of the protoplanets much less than the mass of the proto-Sun . Laws of change masses of bodies are known. The bodies are assumed as material points. On the basis of motion equations in the Jacobi coordinates the problem is described in the analogues of the Poincare second system. The perturbation function is symbolically computed in the system of the analytical calculations Mathematica up to the second degree of small quantities inclusive. It is obtained the equations of secular perturbations and its solutions for the protoplanetary three-body problem with masses changing isotropically in different rates.References
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2. Prokopenya A.N., Minglibayev M.Zh., Mayemerova G.M. Symbolic calculations in studying the problem of three bodies with variable masses // Programming and Computer Software. – 2014. – Vol. 40, No. 2. – P. 79-85.
3. Minglibayev M.Zh., Mayemerova G.M. Investigation of the evolution equations of the three-body problem with variable masses // Applied Mathematical Sciences. – 2013. – Vol. 7, No. 89. – P. 4439-4454.
4. Minglibayev M.Zh., Mayemerova G.M. Investigation of the three-body-points problem with variable masses using the analytical calculation system “Mathematica”. Theory // Astronomical And Astrophysical Transactions. – 2013. – Vol. 28, No. 2. – P. 99-108.
5. Minglibayev M. Zh. Dynamics of gravitating bodies with variable masses and sizes. - Germany: LAP LAMBERT Acad. Publ., 2012. – 229 p.
6. Charlier C.L. Nebesnaya mehanika. – M.: Nauka, 1966. – 628 p.
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Mayemerova, G. M., Minglibayev, M. Z., & Prokopenya, A. N. (2015). Protoplanetary three-body problem with variable masses and its solutions. International Journal of Mathematics and Physics, 6(2), 36–40. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/146
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Informatics and Mathematical Modeling
