16.Кеплера. Тяготение

$\tiny r=\frac{p}{1+ecos\varphi}, <=> u=\frac{1+ecos\varphi}{p};\\ e=\frac{c'}{a}, c'=\sqrt{a^2-b^2} F_{r}=-\frac{mc^2u^2}{p}(-ecos\varphi+1+ecos\varphi)=-\frac{c^2mu^2}{p}\\ \frac {c^2}{p}=\mu => F_{r}=-\mu\frac{m}{r^2}\\ 3 => c^2=\frac{4\pi^2a^2b^2}{T^2}=\frac{4\pi^2a^3p}{T} => \mu=\frac{c^2}{p}=4\pi^2\frac{a^3}{T^2}=const\\ F_{r1}=-\frac{\mu_{1}m_{2}}{r^2}, F_{r2}=-\frac{\mu_{2}m_{1}}{r^2}\\ \frac{\mu_{1}m_{2}}{r^2}=\frac{\mu_{2}m_{1}}{r^2} => \frac{\mu_{1}}{m1}=...=const;\\ \mu_{i}=fm_{i} F=f\frac{m_{1}m_{2}}{r^2}$