Solve 2-Body Equation for t w/ Given Parameters

[Philosophaie]

For a 2 Body Equation:

$$x = - \frac{1}{2} \frac{GM}{r^2}cos(\theta) cos(\phi) t^2 +v_x t + x_0$$
$$y= - \frac{1}{2} \frac{GM}{r^2} sin(\theta) cos(\phi) t^2 +v_y t + y_0$$
$$z= - \frac{1}{2} \frac{GM}{r^2} sin(\phi) t^2 +v_z t + z_0$$


$$r= sqrt(x^2 + y^2 + z^2)$$
$$\theta = atan(\frac{y}{x})$$
$$\phi = acos(\frac{z}{r})$$

Given:$$v_x, v_y, v_z, x_0, y_0, z_0 and M.$$

Now all I have to solve for t.

 

[SteamKing]

I see a bunch of formulas. What do they represent?

 

[Philosophaie]

I am working in Cartesian Coordinates. I want to solve for x, y, z and t. I want to do this in Newtonian Physics.

For the fourth equation in the four equations and four unknowns I choose the geodesic:

$$(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2 + (\frac{dz}{dt})^2 = 0$$

Are the geodesic, the x equation, the y equation, and the z equation (above) correct?

 

[Simon Bridge]

I am working in Cartesian Coordinates. I want to solve for x, y, z and t. I want to do this in Newtonian Physics.

You want to solve for x,y,z, and t, for what?

Are the geodesic, the x equation, the y equation, and the z equation (above) correct?

It is not possible to tell since you won't tell us what these equations are supposed to represent. What system are you attempting to model?

I suspect that the equations are not correct.