Cartesian and polar quantities

In summary, The conversation is about calculating the longitude and latitude speed in degrees or radians using cartesian values. The person with the doubt is wondering if the same method can be used to convert between the two coordinate systems for both position and velocity vectors. The response is that this is possible by converting between ##(x,y,z)## and ##(r,\theta,\phi)## and then applying the same conversion for velocity vectors. The understanding can be confirmed by finding the partial derivative of the position vector in terms of velocity vector components.
  • #1
cptolemy
48
1
Hi,

I have a little doubt. I have, referred 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
 
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  • #2
My doubt is: how do I calculate the longitude and latitude speed in degrees/radians given the cartesian values? Is it the same way?
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)##
 

1. What is the difference between Cartesian and polar coordinates?

Cartesian coordinates refer to the system of coordinates that uses two perpendicular axes, x and y, to locate a point in a plane. Polar coordinates, on the other hand, use a distance and an angle to locate a point in a plane.

2. How do you convert between Cartesian and polar coordinates?

To convert from Cartesian coordinates (x,y) to polar coordinates (r,θ), use the following equations:
r = √(x² + y²)
θ = tan⁻¹(y/x)

3. What are some real-life applications of Cartesian coordinates?

Cartesian coordinates are commonly used in navigation systems, graphing and mapping, computer graphics, and engineering calculations.

4. What are some real-life applications of polar coordinates?

Polar coordinates are often used in physics and engineering applications involving circular motion, such as in radar systems, satellite orbits, and planetary motion.

5. Can you use both Cartesian and polar coordinates in the same problem?

Yes, it is possible to use both Cartesian and polar coordinates in the same problem. In fact, some problems may be easier to solve using one coordinate system over the other. It is important to be familiar with both systems and know how to convert between them.

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