How to get product details from product id in magento?

$model = Mage::getModel('catalog/product');
$_product = $model->load($productId);
echo $_product->getShortDescription();
echo $_product->getDescription();
echo $_product->getName();
echo $_product->getPrice();
echo $_product->getSpecialPrice();
echo $_product->getProductUrl();
echo $_product->getImageUrl();
echo $_product->getSmallImageUrl();
echo $_product->getThumbnailUrl();