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Philosophaie
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I am working in classical mechanics. A planet is orbiting a star. The planet has a given velocity and a position vector from the star. How do I find the magnitude of the gravity in the x, y and z directions.
[tex]positionvector = (x_0, y_0, z_0)[/tex]
[tex]velocityvector = (v_x, v_y, v_z)[/tex]
[tex]x = \frac{1}{2}*g_x*t^2 + v_x*t + x_0[/tex]
[tex]y = \frac{1}{2}*g_y*t^2 + v_y*t + y_0[/tex]
[tex]z = \frac{1}{2}*g_z*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]
[tex]g = \sqrt{g_x^2 + g_y^2 + g_z^2} = -\frac{GM}{r^2}[/tex]
Any hints on how to find [tex](g_x, g_y, g_z)[/tex]
[tex]positionvector = (x_0, y_0, z_0)[/tex]
[tex]velocityvector = (v_x, v_y, v_z)[/tex]
[tex]x = \frac{1}{2}*g_x*t^2 + v_x*t + x_0[/tex]
[tex]y = \frac{1}{2}*g_y*t^2 + v_y*t + y_0[/tex]
[tex]z = \frac{1}{2}*g_z*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]
[tex]g = \sqrt{g_x^2 + g_y^2 + g_z^2} = -\frac{GM}{r^2}[/tex]
Any hints on how to find [tex](g_x, g_y, g_z)[/tex]
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