def distance_to_point_on_equator(lng_rad, lat_rad, lng_rad_p1):
    """
    uses the simplified haversine formula for this special case (lat_p1 = 0)
    :param lng_rad: the longitude of the point in radians
    :param lat_rad: the latitude of the point
    :param lng_rad_p1: the latitude of the point1 on the equator (lat=0)
    :return: distance between the point and p1 (lng_rad_p1,0) in km
    this is only an approximation since the earth is not a real sphere
    """
    # 2* for the distance in rad and * 12742 (mean diameter of earth) for the distance in km
    return 12742 * asin(sqrt(((sin(lat_rad / 2)) ** 2 + cos(lat_rad) * (sin((lng_rad - lng_rad_p1) / 2)) ** 2)))