Solution of the constant radial acceleration problem using Weierstrass elliptic and related functions    [PDF]

Dario Izzo, Francesco Biscani
We consider the constant radial acceleration problem. While the problem is known to be integrable and has received some recent attention in an orbital mechanics context, a closed form explicit solution, relating the state variables to an anomaly, has eluded all researchers so far. We show how such a solution exists and is elegantly expressed in terms of the Weierstrass elliptic and related functions $\wp$,$\zeta$ and $\sigma$. We show how previously known facts can be derived from the new explicit solution and discuss new insights such an approach reveal.
View original: http://arxiv.org/abs/1306.6448