What is the Unit Normal Vector in Acceleration.[tex]\vec{u}_n[/tex] How would I go about calculating the normal. Wiki and Wolfram Alpha were very vague about calculating the normal of an orbit. I would like to know the normal to the orbit of a mass orbiting a much larger mass not counting any other gravitating masses in proximity.
Magnitude[tex]v = \sqrt{vx^2 + vy^2 + vz^2}[/tex]
Unit Tangent Vector[tex]\vec{u}_v =(\frac{vx}{v} ,\frac{vy}{v} ,\frac{vz}{v})[/tex]
Time derivative of velocity[tex]\frac{dv}{dt} =(\frac{(\frac{d(vx^2)}{dt} + \frac{d(vy^2)}{dt} + \frac{d(vz^2)}{dt})}{v})[/tex]
Acceleration[tex]\vec{a} = \frac{dv}{dt}*\vec{u}_v + \frac{v^2}{r}*\vec{u}_n[/tex]
How do you calculate[tex]\vec{u}_n[/tex]
Magnitude[tex]v = \sqrt{vx^2 + vy^2 + vz^2}[/tex]
Unit Tangent Vector[tex]\vec{u}_v =(\frac{vx}{v} ,\frac{vy}{v} ,\frac{vz}{v})[/tex]
Time derivative of velocity[tex]\frac{dv}{dt} =(\frac{(\frac{d(vx^2)}{dt} + \frac{d(vy^2)}{dt} + \frac{d(vz^2)}{dt})}{v})[/tex]
Acceleration[tex]\vec{a} = \frac{dv}{dt}*\vec{u}_v + \frac{v^2}{r}*\vec{u}_n[/tex]
How do you calculate[tex]\vec{u}_n[/tex]