what is the evidence that supporting the idea that Neptune's orbit has gotten bigger?

Answer 1

I have not heard that we thought Neptune's orbit is getting larger. It is very difficult to accurately determine the orbit of a planet that is at the closest, over 2 billion miles away. We can get a fairly good estimate, but it is quite possible that Neptune has orbital wobbles, or even an elliptical orbit with varying aphelions and perihelions. For the orbit to become larger and eventually escape the Sun's gravity is highly unlikely, and would point to the presence of another star or superplanet in the region, which has NOT yet been discovered.

Answer 2

Computer modeling of planet formation suggests that Uranus and Neptune are now about twice as far from the Sun as they started. The models show there wasn't enough material that far out to form such large planets.

There was an article in the September 2007 Sky & Telescope describing how the solar system changed. It was fairly complex but basically there were a lot more asteroids back then and their combined gravitational influence pulled the large planets outward until Jupiter and Saturn got into a 2:1 resonance and destabilized everything. By the time the solar system was a billion years old, though, things had settled down to pretty much where they are now, and none of the planetary orbits have changed significantly since then.

Answer 3

The Jet Propulsion Laboratory (JPL) has calculated the orbits of the planets (including Neptune) for the period 3000 BC to 3000 AD. I would look at their data for evidence one way or another.

I would be very surprised if Neptune's orbit has changed size very much. I would also be surprised if it had not changed at all.