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## Main Question or Discussion Point

For a 2 Body Equation:

[tex]x = - \frac{1}{2} \frac{GM}{r^2}cos(\theta) cos(\phi) t^2 +v_x t + x_0[/tex]

[tex]y= - \frac{1}{2} \frac{GM}{r^2} sin(\theta) cos(\phi) t^2 +v_y t + y_0[/tex]

[tex]z= - \frac{1}{2} \frac{GM}{r^2} sin(\phi) t^2 +v_z t + z_0[/tex]

[tex]r= sqrt(x^2 + y^2 + z^2)[/tex]

[tex]\theta = atan(\frac{y}{x})[/tex]

[tex]\phi = acos(\frac{z}{r})[/tex]

Given:[tex]v_x, v_y, v_z, x_0, y_0, z_0 and M.[/tex]

Now all I have to solve for t.

[tex]x = - \frac{1}{2} \frac{GM}{r^2}cos(\theta) cos(\phi) t^2 +v_x t + x_0[/tex]

[tex]y= - \frac{1}{2} \frac{GM}{r^2} sin(\theta) cos(\phi) t^2 +v_y t + y_0[/tex]

[tex]z= - \frac{1}{2} \frac{GM}{r^2} sin(\phi) t^2 +v_z t + z_0[/tex]

[tex]r= sqrt(x^2 + y^2 + z^2)[/tex]

[tex]\theta = atan(\frac{y}{x})[/tex]

[tex]\phi = acos(\frac{z}{r})[/tex]

Given:[tex]v_x, v_y, v_z, x_0, y_0, z_0 and M.[/tex]

Now all I have to solve for t.