# Is this paper correct?

1. Sep 14, 2006

### CarlB

It includes differential equations for Schwarzschild and Painleve coordinates:

Effects of general relativity in the motion of minor planets and comets
G. Sitarski,
Acta Astronomica (ISSN 0001-5237), vol. 33, no. 2, 1983, p. 295-304

The Schwarzschild differential equation is:

$$\ddot{\vec{r}} = -\frac{\vec{r}}{r^3} +\vec{r}\left( \frac{2}{r^4}-\frac{2\dot{vec{r}}\cdot\dot{\vec{r}}}{r^3} +\frac{3(\vec{r}\cdot\dot{\vec{r}}}{r^5}\right) +\dot{\vec{r}}\frac{2\vec{r}\cdot\dot{\vec{r}}}{r^3}.$$

For Painleve, the paper gives:

$$\ddot{\vec{r}} = -k^2\frac{\vec{r}}{r^3}\left(1 + 3\vec{r}\cdot\vec{r} - 6\dot{r}^2\right)$$

Of course I see now that they took a first order approximation of the true Schwarzschild metric. There should be factors of (r-2) in the denominators.[/edit]

Carl

Last edited: Sep 14, 2006