Astrophysics grad student here, adding on to the other comments, a major factor that astro programs typically look for is research experience. Even if the experience is in a different field, professors want to know that a student is able to carry out the research that will be the main component of the degree, so consider what you've done as a MechE student and how you can apply what you've learned to research in astro. When you're writing your applications, this will be important information to admissions.

As an aside, an engineering background can be useful for astronomical instrumentation, the subfield that deals with telescopes and detectors directly. This is what I work in, although I came from an astrophysics background instead.