What will happen to this ship?

[Joey]

What will happen? This is a screenshot.

[Vanamonde]

It looks like it will end up in a highly elliptical orbit of the sun, looping until it happens to encounter Moho, Eve, or Kerbin, and then any number of trajectories could result.

[TelluriumCrystal]

As for the kerbals, they will all die from asphyxiation long before any of the above scenarios play out.

[Felsmak]

Hmm... Is this a trick question, by any chance?

[SmallChange]

Once your craft exits Kerbin's SOI, you will be in a Kerbol (solar) orbit. Your Kerbol orbit will be a little different than Kerbin's because you will be going at a different speed. Remember, Kerbin is orbiting Kerbol rather quickly. So, instead of just shooting off into space, you will be orbiting the sun.

[Joey]

It looks like it will end up in a highly elliptical orbit of the sun, looping until it happens to encounter Moho, Eve, or Kerbin, and then any number of trajectories could result.

So, it will eventually fall into another orbit?

[Tex_NL]

There is indeed a chance you enter another planets SoI but it could take a long, long time for it to happen. But it will never enter orbit around another planet. To achieve orbit you'd need to perform a braking burn at the correct moment to slow down.

[paleorob]

Unless you end or being aerocaptured by Eve...but even then it will be a decaying orbit with a periapsis inside the atmosphere.

[Qumefox]

You will just end up in a slightly elliptical solar orbit, similar to the kerbin's orbit.

[Vanamonde]

Kerbin is already moving around the sun at a fairly high rate of speed, so the speed you're seeing in your picture is a vector that will be added to Kerbin's velocity once you leave the planet's SOI. Since Kerbin's velocity is the greater, your ship's velocity will be a proportionally smaller deviation from Kerbin's motion. That means you will be pretty close to the plane of Kerbin's orbit, on an ellipse, the shape of which is hard to guess from the picture. (At a second look, I think I was wrong to say that this orbit would be "highly" elliptical, but it is going to be more elliptical than Kerbin's circular orbit.) But since the other planets are also more or less on the plane of Kerbin's orbit, it's likely that you will, sooner or later, pass close enough to one to be affected. This will, depending on the geometry, either slow you down and drop you to a lower solar orbit, or speed you up and through you to a higher solar orbit. There's a tiny chance of actually hitting a planet or moon at this time, but the odds are vastly against it. As Tex_NL points out, though, you should just pass through the encounter SOI and not enter orbit unless you brake. However, because there is a little bit of inaccuracy in KSP math, it actually is possible to end up in an orbit without a burn, but only if the geometry works out JUST right. But that's just a minor glitch in the game, and not a matter of orbital physics. But that might not be the end of the story. Depending on just how your ship gets thrown out a first encounter, it might end up having others. NASA sometimes intentionally sends probes on paths that cause them to pass and interact with several planets.

Edited May 17, 2013 by Vanamonde

[Rhomphaia]

Unless you end or being aerocaptured by Eve...but even then it will be a decaying orbit with a periapsis inside the atmosphere.

You could in theory then get a gravity assist from Gilly that raises your periapsis, leaving you in an Eve orbit at least until the next Gilly encounter. Odds against that are literally astronomical though.