Check my formulas

1. Aug 31, 2013

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.

2. Aug 31, 2013

SteamKing

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

3. Sep 1, 2013

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?

Last edited: Sep 1, 2013
4. Sep 22, 2013

Simon Bridge

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

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.