I am not sure how to convert my Cartesian xyz-coordinates into meters.
x = 0.666
y = 0.666
z = 0.327
a = 6,377,563.396 meters
b = 6,356,256.910 meters
If you are working with an ellipsoid with a=b>c, where
a=b=6,377,563.396 (towards the equator)
c=6,356,256.910 (towards the poles)
then
x=acos(u)cos(v)
y=acos(u)sin(v)
z=csin(u)
where -π/2≤ u ≤π/2
and -π≤ v ≤π
So from the known values of x,y and z, solve for u and v.
But I am not sure what you need in metres.
See:
http://en.wikipedia.org/wiki/Ellipsoid
To convert Cartesian xyz-coordinates into meters, you need to know the scale or unit of measurement that the coordinates are given in. Once you have this information, you can simply multiply each coordinate by the appropriate conversion factor.
In your case, you have provided two conversion factors:
a = 6,377,563.396 meters
b = 6,356,256.910 meters
Let's use these conversion factors to convert your Cartesian coordinates (x, y, z) into meters:
x = 0.666
y = 0.666
z = 0.327
To convert x into meters, you multiply it by the conversion factor a:
x (in meters) = x * a = 0.666 * 6,377,563.396 = 4,238,340.671136 meters
To convert y into meters, you multiply it by the conversion factor a:
y (in meters) = y * a = 0.666 * 6,377,563.396 = 4,238,340.671136 meters
To convert z into meters, you multiply it by the conversion factor b:
z (in meters) = z * b = 0.327 * 6,356,256.910 = 2,076,100.79137 meters
Therefore, the conversion of your Cartesian coordinates into meters is:
x = 4,238,340.671136 meters
y = 4,238,340.671136 meters
z = 2,076,100.79137 meters