# What is the second $r$ in this equation for the Two Body Problem?

$$r=\frac{r^2\frac{\mathrm d\theta^2}{\mathrm dt}}{\frac{Gm_2^3}{\left(m_1+m_2\right)^2}\left(1+e\cos\theta\right)}$$

I have this equation for the radial distance of a planet from the barycenter. But I don't understand why there is an $$r$$ on both sides, the booklet from which this originates states that the $$r^2 \mathrm d\theta^2/\mathrm dt$$ is a constant, but what should it represent and how do I obtain this constant?

It is the angular momentum per unit mass, $$L$$
$$L = r^2\dot\theta = r^2 \frac{{\rm d}\theta}{{\rm d}t}$$
In a central potential (e.g., Kepler's potential) this is a conserved quantity. If at any point you know the position ($${\bf x}$$) and velocity ($${\bf v}$$) of the test mass then you can calculate it as
$${\bf L} = {\bf r}\times {\bf v}$$