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How to derive the period of non-circular orbits?
By conservation of mechanical energy: $$ E(r_0)=-\frac{GMm}{r_0}+\frac{1}{2}\mu \left (\dot{r_0}^2+r_0^2 \omega_0^2 \right) $$ where R0 =Rmax. Because our body is located at the apoapsis the radial velocity is 0. Hence: $$ E(r_0)=-\frac{GMm}{r_0}+\frac{1}{2}\mu (r_0\omega_0)^2 $$ By the...- TheMisterOdd
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- Derivation Period
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- Forum: Advanced Physics Homework Help