# I Cartesian and polar quantities

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1. Sep 25, 2016

### cptolemy

Hi,

I have a little doubt. I have, refered to the Sun, the cartesian positions and velocities of an asteroid (in x, y and z coordinates - 6 values).

I can easely calculate the polar coordinates (longitude and latitude - along with distance).

My doubt is: how do I calculate the longitude and latitude speed in degrees/radians given the cartesian values? Is it the same way?

I'm sorry for this stupid doubt....

Kind regards,

CPtolemy

2. Sep 25, 2016

### Simon Bridge

Probably - long and lat are not polar coordinate representations, they are grid coordinates on the surface of a sphere.
You can convert $(x,y,z)$ to $(r,\theta,\phi)$ then you can convert $(v_x,v_y,v_z)$ to $(v_r, v_\theta, v_\phi)$ in the same way.
Position and velocity vectors convert between coordinate systems the same way.

You can check your understanding by finding $\vec v = \frac{\partial}{\partial t}(r,\theta,\phi)$