Pushing something into the sun requires removing most of it's orbital velocity not just a simple push. A small push in an orbit will create something on a very

Pushing something into the sun requires removing most of it's orbital velocity not just a simple push. A small push in an orbit will create something on a very similar orbit to you that absent a nearby body to induce a lot of drag will intersect with your orbit in 2 places (not at the same time you're there fortunately in pretty much every case).