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Latitude Longitude -> Polar Form -> Cartesian Coordinates

  1. Feb 28, 2008 #1
    [SOLVED] Latitude Longitude -> Polar Form -> 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


    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. jcsd
  3. Feb 28, 2008 #2


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    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= [itex]\theta[/itex]= 0)? And be sure you handle [itex]\phi[/itex] correctly. In spherical coordinates [itex]\phi[/itex] 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 [itex]\phi[/itex]= 90- 46= 44 degrees.
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