The professors at your school might not be researching aerospace directly, but I'm willing to bet at least some of them are researching something in mechanical engineering that's related to aerospace.
There are countless components that go into aerospace design, and they hire nearly every engineering major. Anything such as fluid/heat flow, dynamics, mechanics/stress of materials, and others are important topics in aerospace design. If you explain how your research in one of these areas can be applied to improving aerospace systems, that makes it relevant. You might still have some disadvantages, but the engineering fields are becoming so interdisciplinary nowadays that there's a place for everybody.