def pi: 3.14159265;
def radians: (. * pi) / 180;
def unradians: (. * 180) / pi;

def cartesian: (.latitude | radians) as $lat | (.longitude | radians) as $lon | {
  x: (($lat | cos) * ($lon | cos)),
  y: (($lat | cos) * ($lon | sin)),
  z: ($lat | sin)
};

def average: add / length;

map(cartesian)
| {
  x: map(.x) | average,
  y: map(.y) | average,
  z: map(.z) | average
}
| ((.x * .x + .y * .y) | sqrt) as $hypotenuse
| {
  longitude: atan2(.y; .x) | unradians,
  latitude: atan2(.z; $hypotenuse) | unradians
}