def METHOD_NAME(r, v):
    # Convert Cartesian rate and velocity vectors to angles and rates.
    x, y, z = r
    xdot, ydot, zdot = v
    length = length_of(r)
    lat = arcsin(z / (length + _AVOID_DIVIDE_BY_ZERO))
    lon = arctan2(y, x) % tau
    range_rate = dots(r, v) / length_of(r)
    x2 = x * x
    y2 = y * y
    x2_plus_y2 = x2 + y2 + _AVOID_DIVIDE_BY_ZERO
    lat_rate = (x2_plus_y2 * zdot - z * (x * xdot + y * ydot)) / (
        (x2_plus_y2 + z*z) * sqrt(x2_plus_y2))
    lon_rate = (x * ydot - xdot * y) / x2_plus_y2
    return length, lat, lon, range_rate, lat_rate, lon_rate