Problem 1.210

A cosmic body \(A\) moves to the Sun with velocity \(v_{0}\) (when far from the Sun) and aiming parameter \(l\) the arm of the vector \(\mathbf{v}_{0}\) relative to the centre of the Sun (Fig. 1.51\() .\) Find the minimum distance by which this body will get to the Sun.

Reveal Answer

\begin{aligned} &\text { 1.210. } r_{\min }=\left(\gamma m_{\mathrm{S}} / v_{0}^{2}\right)\left[\sqrt{1+\left(l v_{0}^{2} / \gamma m_{\mathrm{S}}\right)^{2}}-1\right], \text { where } m_{\mathrm{s}} \text { is the }\\ &\text { mass of the Sun. } \end{aligned}

Universal Gravitation