# Latitude Longitude -&gt; Polar Form -&gt; Cartesian Coordinates

1. Feb 28, 2008

### jwj11

[SOLVED] Latitude Longitude -&gt; Polar Form -&gt; Cartesian Coordinates

1. The problem statement, all variables and given/known data

I need to convert 46 Degrees North 80 Degrees west into Cartesian coordinates, based on the assumption that the earth is a sphere (althought it's not).

2. Relevant equations

http://en.wikipedia.org/wiki/Spherical_coordinate_system

3. The attempt at a solution

I've attempted to convert and I got ( -767.18, -4350.91, 4575 )
Not sure if this is correct. I'd like to know the North and West signs factor into the equation when plugging in. Can anyone help, or show me a step by step basis please??

2. Feb 28, 2008

### HallsofIvy

HOW have you set up your cartesian coordinate system? I assume the origin is at the center of the earth and the positive z-axis runs through the north pole. Is the positive x-axis pointing toward the Greenwich meridion (i.e. longitude= $\theta$= 0)? And be sure you handle $\phi$ correctly. In spherical coordinates $\phi$ is the "co-latitude": measured from the north pole rather than from the equator.

If so, then 80 degrees West longitude means that x will be positive (beyond 90 degrees W longitude would make x negative) but that y will be negative (any west longitude makes y negative). Since latitude is north, z will be positive but be sure to use $\phi$= 90- 46= 44 degrees.