The Stable Orbit of the Sun

I feel like the only reason we tend to think of orbits as stable is because they're pretty circular right but you can also go around the sun for a long time going around in like big ellipses. That whole arrangement can be stable you can be in a circular orbit forever around a star without ever falling in and the reason is at your speed and your radius vary say somebody comes along and pushes us towards the sun  so now we fall in a little bit towards the sun and gravity is getting stronger but we're now also going to speed up. If I put up some booster rockets on the earth it's not gonna maybe make the earth spiral and it's just going to change the