Suponiendo que obtenga $lat y $long como latitud/longitud de su punto de partida:
$sql = 'SELECT *, (6371 * acos(cos(radians(' . $lat . ')) * cos(radians(latitude)) * cos(radians(longitude) - radians(' . $lng . ')) + sin(radians(' . $lat . ')) * sin(radians(latitude)))) AS distance from table_name WHERE distance < 10';