Neptune’smoon Triton is thought to be a captured dwarf Planet. Why is this not more common, that large rounded objects get captured.
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Shortage of dwarf planets whose orbits intersect those of major planets.
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There are many, many more ways for the dwarf planet to impact the major planet or be slingshotted off in another direction entirely than there are ways for the dwarf planet to be captured into a stable orbit.
2a) “Roundedness” is a factor of the size of the object. If it has sufficient mass then all parts tend to fall in as close to the center as they can, hence the spherical shape of most everything Ceres-sized and larger.
Any slingshot that disrupts the tiny planet’s regular orbit just makes it more likely that it will eventually wander into another planet and go splat.
(Isn’t the moon supposed to be the result of this? A close encounter of the earth kind?)
This theory has been refined since, particularly to take into account the fact the Earth and the Moon have very similar isotopic compositions:
This isn’t a huge revision, it’s a modification, but it underscores one salient fact: The Earth and the Moon are very similar chemically, which is evidence in favor of the massive collision model of the Moon’s formation.
It’s really hard to capture things gravitationally, at least in the long term. If you can get into an orbit gravitationally, then you can get out of it gravitationally, too. About the best you can hope for is temporarily capturing a few things at once into unstable orbits, and then end up ejecting some of them in such a way as to leave the others stable.
I LOVE these highly scientific terms! 
We’ve gotten so used to “Big Bang,” we forget how silly it sounds!
It’s supposed to sound silly. Fred Hoyle (who disagreed with and rejected the theory) coined the term to BE silly.
The how come Triton was captured?
Well, he denied that. See Fred Hoyle - Wikipedia for the reference.
Because hard <> impossible, just relatively unlikely.
Neptune might have had a natural satellite or two that got ejected when Triton came into the picture. Or maybe Triton had some moons of its own (or was a moon of an even bigger dwarf planet).
Basically, if Triton had enough energy to be free from Neptune at some point, and it no longer does, something must have carried that energy away. In conventional human experience, there’s always wind resistance or friction or something so we don’t think too hard about why something loses energy, but among celestial bodies these aren’t large influences so we have to find out specifically where it all went.
Gravitational capture is impossible in a two-body system: either the satellite is on a hyperbolic/parabolic orbit, or it’s elliptical (and thus already in orbit).
So all captures must involve 3+ bodies, or some non-gravitational influence (outgassing, solar wind, etc.). But most of the time, the motion of satellites is well-approximated by a two-body calculation, so the capture doesn’t happen. Only in some unusual circumstances, such as a flyby of another satellite, can a capture possibly occur. And even then, as others have said, it’s rare–much more likely is that it will get flung off in some direction.
A better way to say that, most approached are from objects going way to fast.
Mostly either they hit or they just go on their way …
Some have skimmed earth’s surface (not just the atmosphere) AND THEN gone off somewhere else…left earth behind, with some of earth attached…
(same as how a bit of mars came to earth.)
The Earth does capture objects into temporary orbits. 2006 RH[sub]120[/sub] is the only known natural example, but it’s expected there are others. Another known one is artificial: J002E3 is thought to be the 3rd stage of Apollo 12 and it periodically enters and leaves Earth orbit.
In these cases, there is no third object that carries energy away. AIUI, what happens is that these objects go through either the L1 or L2 Lagrange points in a certain range of directions and at a slow enough speed that they start going around the Earth. The orbits are not a regular ellipse but rather loopy. Eventually they go back through the Lagrange point and escape to solar orbit. After a number of years, this process may repeat.
This kind of thing probably happens for other planets as well, but it’s unlikely to be how Triton was captured.
Until, Messrs Armstrong and others went and brought back sample, was’nt the prevalent theory that the Moon was a captured body as well?
Note that you don’t get Lagrangian points unless a third object is involved, so that is presumably where the excess energy disappears to.
That’s a point, but the third object in that case would be the Sun. (The Lagrange points are those of the Sun-Earth system, not those of the Earth-Moon system. I just realized that some people may have gotten the wrong idea there.) I suppose the Sun could gain a soupçon of a smidgen of energy in its orbit around the Earth and then lose it when the object leaves Earth orbit. Or for all I know, the other way around. The amount of energy in the transition is really small.
In addition to lagrange points requiring a third object, the third object involved in the interaction does not need to carry the energy all the way away (i.e. be ejected). A small wannabe satellite could shed energy by giving it to the moon, whereupon the moon would enter a very-slightly-higher orbit, rather than being ejected.