Equation of the trajectory of a typical space object around any planet, in polar coordinates $(r, \theta)$ (i.e. a general conic section geometry), is given as follows. ( $h$ is angular momentum, $\mu$ is gravitational parameter, $e$ is eccentricity, $r$ is radial distance from the planet center, $\theta$, is angle between vectors $\vec{e}$ and $\vec{r}$.

(A) $r=\frac{\left(h^{2} / \mu\right)}{1-e \cos \theta}$

(B) $r=\frac{\left(h^{2} / \mu\right)}{e-\cos \theta}$

(C) $r=\frac{\left(h^{2} / \mu\right)}{1+e \cos \theta}$

(D) $r=\frac{\left(h^{2} / \mu\right)}{e+\cos \theta}$

Equation of the trajectory of a typical space object around any planet, in polar coordinates $(r, \theta)$ (i.e. a general conic section geometry), is given as follows. ( $h$ is angular momentum, $\mu$ is gravitational parameter, $e$ is eccentricity, $r$ is radial distance from the planet center, $\theta$, is angle between vectors $\vec{e}$ and $\vec{r}$.

(A) $r=\frac{\left(h^{2} / \mu\right)}{1-e \cos \theta}$

(B) $r=\frac{\left(h^{2} / \mu\right)}{e-\cos \theta}$

(C) $r=\frac{\left(h^{2} / \mu\right)}{1+e \cos \theta}$

(D) $r=\frac{\left(h^{2} / \mu\right)}{e+\cos \theta}$

1 Answer

127 votes

(C) $r=\frac{\left(h^{2} / \mu\right)}{1+e \cos \theta}$

127 votes

127