19.Спутники

$\tiny r(\varphi)\geq r(\varphi_{0}) => \frac{p}{1+ecos\varphi}\geq\frac{p}{1+ecos\varphi_{0}}\\ \varphi_{0}=0 =>cos^2\alpha*tg\alpha=0, \frac{V_{0}^2cos^2\alpha}{gR}-1=e; e\geq0 => cos^2\alpha\neq0 => tg\alpha=0 , \alpha=0\\ e=\frac{V_{0}^2}{gR}-1 => V_{0}^2\geq gR\\ a)\alpha=0 \\ b)\sqrt{gR}\leq V_{0}<\sqrt{2gR}; gR^2=g_{0}R_{0}^2, => g=...;\\ V_{k}<\sqrt{g_{0}R_{0}};\\ T=2\pi\sqrt{\frac{a^3}{\mu}}=\frac{2\pi}{R}*\sqrt{\frac{a^3}{g}} a=\frac{1}{2}(r_{p}+r_{a})=\frac{1}{2}(r(0)+r(\pi))=\frac{p}{1-e^2};$