Well pretty sure the depleted uranium instead of Tungsten would count as a weapon of mass destruction which the US is a signatory of the Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies (the basis for international space law), which expressly forbids the placement of those sorts of weapons in orbit, or on the moon, or other celestial bodies.
However since the treaty only limits nuclear, biological, and chemical. You could use tungsten or similar. The depleted uranium however I think might fall under the nuclear category. Though it could be argued either way.