It includes differential equations for Schwarzschild and Painleve coordinates:(adsbygoogle = window.adsbygoogle || []).push({});

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

http://adsabs.harvard.edu/cgi-bin/n...ype=HTML&format=&high=446dbc38dc06742

The Schwarzschild differential equation is:

[tex]\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}.[/tex]

For Painleve, the paper gives:

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

[edit]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

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