Magento-How to Get Related Products by product Id

<?php
$model = Mage::getModel('catalog/product');
$product = $model->load($product_id);

// Get all related product ids of $product.
$allRelatedProductIds = $product->getRelatedProductIds();

foreach ($allRelatedProductIds as $id) {
            $relatedProduct = $model->load($id);

            // get Product's name
            echo $relatedProduct->getName();

            // get product's short description
            echo $relatedProduct->getShortDescription();

            // get Product's Long Description
            echo $relatedProduct->getDescription();

            // get Product's Regular Price
            echo $relatedProduct->getPrice();

            // get Product's Special price
            echo $relatedProduct->getSpecialPrice();

            // get Product's Url
            echo $relatedProduct->getProductUrl();

            // get Product's image Url
            echo $relatedProduct->getImageUrl();

        }
?>