Spawning asteroids automatically enter stable kerbin orbit

[Xd the great]

Trying out my first asteroid impact mission, and found a asteroid in kerbin orbit. Is it normal for such to happen?

[Zeiss Ikon]

It's not terribly uncommon for an asteroid to show up in as "orbiting Kerbin".  In most such cases, the rock will actually have an Ap outside Kerbin's SOI; rather than a stable orbit, it's on a very mildly hyperbolic trajectory, or might (even more rarely) be truly parabolic.  It is also possible for an asteroid to get temporarily captured due to a Mun (or, less frequently, Minmus) encounter.  These are temporary captures because the resulting orbit will always re-encounter the capturing body after some time, and generally either impact or get ejected again.

[Xd the great]

Well, what i mean is that both the apongee and periaphis is inside kerbin's SOI.

[Vanamonde]

Yes, this happens from time to time. 

[Tyko]

I've seen it as well, it's really rare though. Great find! In real life there are many Near Earth Objects, so it happens for real too.

[Zeiss Ikon]

12 hours ago, Xd the great said:

Well, what i mean is that both the apongee and periaphis is inside kerbin's SOI.

If the object has been captured due to gravity assist from the Mun (and everywhere I type "Mun" you can substitute "Minmus", though its much lower gravity means it's less likely to capture objects in the first place), it might well have apoapsis near or even a bit inside the Mun's orbit -- this would seem to be a stable orbit, but in fact, such an orbit will always reenter the Mun's SOI at some point (depending on the orbital period, this time frame might be "next orbit" or "rather a long time"); that next encounter will change the object's orbit.  If it doesn't impact the Mun, the Mun's gravity will either raise the apoapsis (with the likelihood of ejecting it from Kerbin's SOI) or lower it (but never so far it can't reenter the Mun's SOI -- I can't show you the math, but that's just the way it works).  In either case, the periapsis may also change; this means the object may be lost in four ways: impact with the Mun, impact with Minmus due to Munar assist, ejection from Kerbin's SOI due to Munar assist, or impact with Kerbin due to Munar assist (slowing/lowering the orbit).

Bottom line is, any such capture will be temporary.  Note that the Earth has such a captured asteroid orbiting beyond the Moon, but because Earth runs under Principia instead of patched conics, the body in question actually occupies an Earth-resonant Solar orbit, never getting far from Earth, but not really orbiting the Earth, either.  This body is estimated to have been in this kind of orbit for at least three hundred years, and is likely to remain so for some centuries to come -- but will eventually escape into an independent Solar orbit, like that from whence it came.

[Daniel Prates]

In my 1000+ hours of KSP, I have only seen this happen once. 

It is a thing to celebrate! Rendevouz-ing with an asteroid is not that hard, but slowing one down to keep in within Kerbin's SOI is very hard, specially for the bigger ones. And the only way you can really explore an asteroid, build stuff around it etc is when it is not leaving orbit within a few days!