I reckon astronomers would find anything that entered our solar system and stayed in some solar orbit.

You'd be surprised how much stuff there is just in our neighborhood that we're unable to catch, yet. We mostly track dangerous stuff, the big enough - fast enough to destroy us, and we now have probably in the 6-7 figures objects tracked in the inner solar system. That's it. Elusive 9th planets and other major 'quests' are shots in the dark so far, mostly — read accounts on why they target some region of the sky, how narrow our observational capabilities are as we can only point to a very specific direction at a time with each telescope, etc.

So, some alien unmanned probe the likes of Voyager in large orbit around the Sun? Yeah, no chance in hell we'd detect that by random chance, we'd have to seriously upgrade our space infrastructure to even pretend 'monitoring' our close vicinity, let alone post-Jovian space. And we have virtually no knowledge of about half the distance between interstellar medium and the Sun, that's how limited we are to even modeling the closest star systems.

Edit: apparently double-post with aruggirello; I agree with him.

To underline this point: we shot a red tesla into space about 2 years ago [1]. We cannot detect it any more. We'd need a telescope with a mirror of 15km to see it. Due to uncertainties accumulating, even if we'd had a scope like that, we'd probably not be able to point it exactly enough.

Oh, and that thing is mostly between the orbits of Mars and earth - much smaller search space than "the entire solar system"

[1] https://www.whereisroadster.com/

You really mean anything at least comet/asteroid sized, passing within the inner Solar System with a speed and an albedo that would make it stand out against the background of stars (reaching at least say, apparent magnitude 8-10). Also, note that it should be found near the ecliptic plane, to improve the chances of detection.

Now, exchange that for a black-ish ship a few hundred meters sized, quietly coming from Vega to visit say, Saturn. Nobody would probably notice it coming and going, despite Saturn being one of the most popular targets of the entire sky.

You’re very mistaken. We still regularly find 300ft boulders in _Earth Orbit_. And routinely find city sized asteroid in asteroid belt and state sized minor planet in Kuiper belt. Suggesting that a ship can be found as long as it’s in Solar Orbit is an extremely misinformed opinion.

We have never found a 300 ft boulder in Earth Orbit.

Perhaps you mean in a solar orbit near the Earth?

True, but without radio transmissions, I bet we would spend decades arguing about whether it was actually an asteroid and a measurement anomaly. We can't really distinguish a rock from a Battlestar at those distances without physically flying over to look.

At this point we're relying almost exclusively on radio waves to detect any traces of intelligent life out there. So whether they're building moon stations in their neighborhood, or sending rockets here and there, we'd still look for their transmissions to identify their existence and to tell them apart from a random natural event.

And while intelligent life may exist on a planet for millions of years, their window of actually emitting something into the void in a manner we can detect with our tech today [0] will probably be a lot shorter than that.

This gives us a relatively tiny and limited visibility window into the history of life out there. Unless we manage to sync our window perfectly with theirs we'll never know they existed.

[0] https://www.xkcd.com/638/

Compounded by the fact that advanced space communications would likely rely mostly on laser beams[1], whose efficiency and general design fits much better with that environment and its infrastructure. Unless pointing directly at your instrument (good luck, what are the odds?) and missed by the intended receiver, the beam will never reach you anyway.

[1] Particularly if your operation is covert, discrete, observational, non-disruptive: you'd want to avoid signaling your presence in all directions, while wasting 99.99% of that energy away from your intended receiver. It's just military efficiency, a photon-VPN so to speak, that you'd need to "physically MitM" to hack.

Sorry to pile on, and I don't think you deserved the downvotes, but I'd like to point out there may be an undiscovered planet in the solar system.

https://en.m.wikipedia.org/wiki/Planet_Nine

There may also/instead be an undiscovered primordial black hole in the solar system.

https://www.sciencemag.org/news/2019/09/planet-nine-may-actu...