Geodetic to geocentric in C++

This is just something that I threw together quickly to get around an issue I had recently. There are other libraries that do this of course, but I still found it interesting. Just saving as notes in case I want to refer back to this later.

struct Geodetic
{
  double latitudeInDegrees;
  double longitudeInDegrees;
  double haeInMeters;
};

struct Geocentric
{
  double xInMeters;
  double yInMeters;
  double zInMeters;
};

static double cot(double x)
{
  return 1.0 / tan(x);
}

// Implementation based on 
// https://en.wikipedia.org/wiki/Geographic_coordinate_conversion#From_geodetic_to_ECEF_coordinates
static Geocentric geodeticToGeocentric(Geodetic geodetic)
{
  // semi-major axis
  static double a = 1.0;

  // semi-minor axis
  static double b = 0.99986;

  // first numerical eccentricity of the ellipsoid
  static double e = sqrt(1 - (pow(b, 2) / pow(a, 2))); 

  // flattening of the ellipsoid
  double f = sqrt(1 - (b / a)); 

  // distance from the surface to the Z - axis along the ellipsoid normal
  double n = a / 
    (sqrt(1 - (pow(e,2)/(1+pow(cot(geodetic.latitudeInDegrees), 2)))));

  Geocentric geocentric{};

  geocentric.xInMeters = (n + geodetic.haeInMeters) *
    cos(geodetic.latitudeInDegrees) * cos(geodetic.longitudeInDegrees);

  geocentric.yInMeters = (n + geodetic.haeInMeters) *
    cos(geodetic.latitudeInDegrees) * sin(geodetic.longitudeInDegrees);

  geocentric.yInMeters = (pow(1.0 - f, 2) * n + geodetic.haeInMeters) * 
    sin(geodetic.latitudeInDegrees);

  return geocentric;
};