<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _geodetic_to_cartesian(cls, lat, lon, alt):
 """Conversion from latitude, longitude and altitude coordinates to cartesian with respect to an ellipsoid Args: lat (float):
 Latitude in radians lon (float):
 Longitude in radians alt (float):
 Altitude to sea level in meters Return: numpy.array: 3D element (in meters) """

        C = Earth.r / np.sqrt(1 - (Earth.e * np.sin(lat)) ** 2)
        S = Earth.r * (1 - Earth.e ** 2) / np.sqrt(1 - (Earth.e * np.sin(lat)) ** 2)
        r_d = (C + alt) * np.cos(lat)
        r_k = (S + alt) * np.sin(lat)

        norm = np.sqrt(r_d ** 2 + r_k ** 2)
        return norm * np.array([
            np.cos(lat) * np.cos(lon),
            np.cos(lat) * np.sin(lon),
            np.sin(lat)
        ])