You should check the weight as a first step to determine whether it's actually gold. A real coin would weigh 33.436 grams, or probably a couple tenths of a gram less to reflect metal lost due to wear. If the damage to your coin has removed additional metal the weight could be even lower. However, if it is some base-metal replica the weight would be much less, maybe only 20 grams or so.
By the way, the 1882 double eagle from the Philadelphia mint is a great rarity, worth tens of thousands of dollars even in worn condition. If your coin is genuine it is almost certainly the common San Francisco issue which would have a small S mintmark just below the eagle's tail. We can't tell from your picture but maybe you can examine it closely and decide if a mintmark is present. The Philadelphia coin has no mintmark.
Please let us know what you find out, and also post better images if possible.