Many one-dimensional Euler-Arnold equations can be recast in the form of a central-force problem Γtt(t,x)=−F(t,x)Γ(t,x), where Γ is a vector in R2 and F is a nonlocal function possibly depending on Γ and Γt. Angular momentum of this system is precisely the conserved momentum for the Euler-Arnold equation. In particular this picture works for the Camassa-Holm equation, the Hunter-Saxton equation, and the Okamoto-Sakajo-Wunsch family of equations. In the solar model, breakdown comes from a particle hitting the origin in finite time, which is only possible with zero angular momentum. Results due to McKean (for Camassa-Holm), Lenells (for Hunter-Saxton), and Bauer-Kolev-Preston/Washabaugh (for the Wunsch equation) show that breakdown of smooth solutions occurs exactly when momentum changes from positive to negative. I will discuss some conjectures and numerical evidence for the generalization of this picture to other equations such as the μ-Camassa-Holm equation or the DeGregorio equation.