Spherically symmetric means that it looks the same no matter which way you rotate it. You talked about a dense core, less dense middle-region planet, which is s

Spherically symmetric means that it looks the same no matter which way you rotate it. You talked about a dense core, less dense middle-region planet, which is spherically symmetric. If the planet had an ultra-dense region off to one side then it wouldn't be spherically symmetric and it would have gravity slightly stronger on one side than on the other... it's hard to imagine such a planet existing though.