We study the dynamics of two-body problems with gravitational parameters μ = μ ( t ) decreasing with the time. In particular we focus our attention on the behavior of the orbital elements in the first two Gyldén–Mestchersky cases: in the first case (GM-I) ##IMG## [http://ej.iop.org/images/1538-3881/160/5/203/ajabb4e4ieqn1.gif] {$\mu {(t)={\mu }_{0}(1+\alpha t)}^{-1}$} , where μ 0 is the constant initial value of the parameter and α a small positive constant. In the second case (GM-II) ##IMG## [http://ej.iop.org/images/1538-3881/160/5/203/ajabb4e4ieqn2.gif] {$\mu {(t)={\mu }_{0}(1+2\alpha t)}^{-1/2}$} . In the GM-I problem, using a suitable transformation of the radius vector and the physical time, which reduces the original problem to a pure Kepler problem, we are able to obtain explicit analytical expressions of the orbital elements that hold true for all ##IMG## {$t\geqslant 0$...}

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关于质量逐渐减小的两体问题的轨道要素：吉尔登·梅切斯基斯基案例

我们研究了重力参数μ=μ（t）随时间减小的两体问题的动力学。特别是，我们将注意力集中在前两个Gyldén–Mestchersky情况下的轨道元素的行为：在第一种情况下（GM-I）## IMG ## [http://ej.iop.org/images/1538 -3881 / 160/5/203 / ajabb4e4ieqn1.gif] {$ \ mu {{t）= {\ mu} _ {0}（1+ \ alpha t）} ^ {-1} $}，其中μ0为参数的恒定初始值和α较小的正常数。在第二种情况下（GM-II）## IMG ## [http://ej.iop.org/images/1538-3881/160/5/203/ajabb4e4ieqn2.gif] {$ \ mu {（t）= {\ mu} _ {0}（1 + 2 \ alpha t）} ^ {-1/2} $}。在GM-I问题中，通过对半径向量和物理时间进行适当的转换，可以将原始问题简化为纯开普勒问题，